{"title":"Mathematical foundations Books","description":"","products":[{"product_id":"classical-descriptive-set-theory-9780387943749","title":"Classical Descriptive Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDescriptive set theory has been one of the main areas of research in set theory for almost a century. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI Polish Spaces.- 1. Topological and Metric Spaces.- 1.A Topological Spaces.- 1.B Metric Spaces.- 2. Trees.- 2.A Basic Concepts.- 2.B Trees and Closed Sets.- 2.C Trees on Produtcs.- 2.D Leftmost Branches.- 2.E Well-founded Trees and Rank.- 2.F The Well-founded Part of a Tree.- 2.G The Kleene-Brouwer Ordering.- 3. Polish Spaces.- 3.A Definitions and Examples.- 3.B Extensions of Continuous Functions and Homeomorphisms.- 3.C Polish Subspaces of Polish Spaces.- 4. Compact Metrizable Spaces.- 4.A Basic Facts.- 4.B Examples.- 4.C A Universality Property of the Hilbert Cube.- 4.D Continuous Images of the Cantor Space.- 4.E The Space of Continuous Functions on a Compact Space.- 4.F The Hyperspace of Compact Sets.- 5. Locally Compact Spaces.- 6. Perfect Polish Spaces.- 6.A Embedding the Cantor Space in Perfect Polish Spaces.- 6.B The Cantor-Bendixson Theorem.- 6.C Cantor-Bendixson Derivatives and Ranks.- 7.Zero-dimensional Spaces.- 7.A Basic Facts.- 7.B A Topological Characterization of the Cantor Space.- 7.C A Topological Characterization of the Baire Space.- 7.D Zero-dimensional Spaces aa Subspaces of the Baire Space.- 7.F Polish Spaces as Continuous Images of the Baire Space.- 7.F Closed Subsets Homcomorphic to the Baire Space.- 8. Baire Category.- 8.A Meager Sets.- 8.B Baire Spaces.- 8.C Choquet Games and Spaces.- 8.D Strong Choquet Games and Spaces.- 8.E A Characterization of Polish Spaces.- 8.F Sets with the Baire Property.- 8.G Localization.- 8.H The Banach-Mazur Game.- 8.I Baire Measurable Functions.- 8.J Category Quantifiers.- 8.K The Kuratowski-Ulam Theorem.- 8.L Some Applications.- 8.M Separate and Joint Continuity.- 9. Polish Groups.- 9.A Metrizable and Polish Groups.- 9.B Examples of Polish Groups.- 9.C Basic Facts about Baire Groups and Their Actions.- 9.D Universal Polish Groups.- II Borel Sets.- 10. Measurable Spaces and Functions.- 10.A Sigma-Algebras and Their Generators.- 10.B Measurable Spaces and Functions.- 11. Borel Sets and Functions.- 11.A Borel Sets in Topological Spaces.- 11.B The Borel Hierarchy.- 11.C Borel Functions.- 12. Standard Borel Spaces.- 12.A Borel Sets and Functions in Separable Metrizable Spaces.- 12.B Standard Borel Spaces.- 12.C The Effros Borel Space.- 12.D An Application to Selectors.- 12.E Further Examples.- 12.F Standard Borel Groups.- 13. Borel Sets as Clopen Sets.- 13.A Turning Borel into Clopen Sets.- 13.B Other Representations of Borel Sets.- 13.C Turning Borel into Continuous Functions.- 14. Analytic Sets and the Separation Theorem.- 14.A Basic Facts about Analytic Sets.- 14.B The Lusin Separation Theorem.- 14.C Sousliri’s Theorem.- 15. Borel Injections and Isomorphisms.- 15.A Borel Injective Images of Borel Sets.- 15.B The Isomorphism Theorem.- 15.C Homomorphisms of Sigma-Algebras Induced by Point Maps.- 15.D Some Applications to Group Actions.- 16. Borel Sets and Baire Category.- 16.A Borel Definability of Category Notions.- 16.B The Vaught Transforms.- 16.C Connections with Model Theory.- 16.D Connections with Cohen’s Forcing Method.- 17. Borel Sets and Measures.- 17.A General Facts on Measures.- 17.B Borel Measures.- 17.C Regularity and Tightness of Measures.- 17.D Lusin’s Theorem on Measurable Functions.- 17.E The Space of Probability Borel Measures.- 17.F The Isomorphism Theorem for Measures.- 18. Uniformization Theorems.- 18.A The Jankov, von Neumann Uniformization Theorem.- 18.B “Large Section” Uniformization Results.- 18.C “Small Section” Uniformization Results.- 18.D Selectors and Transversals.- 19. Partition Theorems.- 19.A Partitions with a Comeager or Non-meager Piece.- 19.B A Ramsey Theorem for Polish Spaces.- 19.C The Galvin-Prikry Theorem.- 19.D Ramsey Sets and the Ellentuck Topology.- 19.E An Application to Banach Space Theory.- 20. Borel Determinacy.- 20.A Infinite Games.- 20.B Determinacy of Closed Games.- 20.C Borel Determinacy.- 20.D Game Quantifiers.- 21. Games People Play.- 21.A The *-Games.- 21.B Unfolding.- 21.C The Banach-Mazur or **-Games.- 21.D The General Unfolded Banach-Mazur Games.- 21.E Wadge Games.- 21.F Separation Games and Hurewicz’s Theorem.- 21.G Turing Degrees.- 22. The Borel Hierarchy.- 22. A Universal Sets.- 22.B The Borel versus the Wadge Hierarchy.- 22.C Structural Properties.- 22.D Additional Results.- 22.E The Difference Hierarchy.- 23. Some Examples.- 23.A Combinatorial Examples.- 23.B Classes of Compact Sets.- 23.C Sequence Spaces.- 23.D Classes of Continuous Functions.- 23.E Uniformly Convergent Sequences.- 23.F Some Universal Sets.- 23.G Further Examples.- 24. The Baire Hierarchy.- 24.A The Baire Classes of Functions.- 24.B Functions of Baire Class 1.- III Analytic Sets.- 25. Representations of Analytic Sets.- 25.A Review.- 25.B Analytic Sets in the Baire Space.- 25.C The Souslin Operation.- 25.D Wellordered Unions and Intersections of Borel Sets.- 25. E Analytic Sets as Open Sets in Strong Choquet Spaces.- 26. Universal and Complete Sets.- 26.A Universal Analytic Sets.- 26.B Analytic Determinacy.- 26.C Complete Analytic Sets.- 26.D Classification up to Borel Isomorphism.- 27. Examples.- 27.A The Class of Ill-founded Trees.- 27.B Classes of Closed Sets.- 27.C Classes of Structures in Model Theory.- 27.D Isomorphism.- 27.E Some Universal Sets.- 27.F Miscellanea.- 28. Separation Theorems.- 28.A The Lusin Separation Theorem Revisited.- 28.B The Novilcov Separation Theorem.- 28.C Borel Sets with Open or Closed Sections.- 28.D Some Special Separation Theorems.- 28.E “Hurewicz-Type” Separation Theorems.- 29. Regularity Properties.- 29.A The Perfect Set Property.- 29.B Measure. Category, and Ramsey.- 29.C A Closure Property for the Souslin Operation.- 29.D The Class of C-Sets.- 29.E Analyticity of “Largeness” Conditions on Analytic Sets.- 30. Capacities.- 30.A The Basic Concept.- 30.B Examples.- 30.C The Choquet Capacitability Theorem.- 31. Analytic Well-founded Relations.- 31.A Bounds on Ranks of Analytic Well-founded Relations.- 31.B The Kunen-Martin Theorem.- IV Co-Analytic Sets.- 32. Review.- 32.A Basic Facts.- 32.B Representations of Co-Analytic Sets.- 32.C Regularity Properties.- 33. Examples.- 33.A Well-founded Trees and Wellorderings.- 33.B Classes of Closed Sets.- 33.C Sigma-ldoals of Compact Sets.- 33.D Differentiable Functions.- 33.E Everywhere Convergence.- 33.F Parametrizing Baire Class 1 Functions.- 33.G A Method for Proving Completeness.- 33.H Singular Functions.- 33.I Topological Examples.- 33.J Homeomorphisms of Compact Spaces.- 33.K Classes of Separable Banach Spaces.- 33.L Other Examples.- 34. Co-Analytic Ranks.- 34.A Ranks and Prewellorderings.- 34.B Ranked Classes.- 34.C Co-Analytic Ranks.- 34.D Derivatives.- 34.E Co-Analytic Ranks Associated with Borel Derivatives.- 34.F Examples.- 35. Rank Theory.- 35.A Basic Properties of Ranked Classes.- 35.B Parametrizing Bi-Analytic and Borel Sets.- 35.C Reflection Theorems.- 35.D Boundedness Properties of Ranks.- 35.E The Rank Method.- 35.F The Strategic Uniformization Theorem.- 35.G Co-Analytic Families of Closed Sets and Their Sigma-Ideals.- 35.H Borel Sots with F? and K? Sections.- 36. Scales and Uniformiiatiou.- 36.A Kappa-Souslin Sets.- 36.B Scales.- 36.C Sealed Classes and Urniformization.- 36.D The Novikov-Kondô Uniformization Theorem.- 36.E Regularity Properties of Uniformizing Functions.- 36.F Uniforniizing Co-Analytic Sets with Large Sections.- 36.G Examples of Co-Analytic Scales.- V Projective Sets.- 37. The Projective Hierarchy.- 37.A Basic Facts.- 37.B Examples.- 38. Projective Determinacy.- 38.A The Second Level of the Projective Hierarchy.- 38.B Projective Determinacy.- 38.C Regularity Properties.- 39. The Periodicity Theorems.- 39.A Periodicity in the Projective Hierarchy.- 39.B The First Periodicity Theorem.- 39.C The Second Periodicity Theorem.- 39.D The Third Periodicity Theorem.- 40. Epilogue.- 40.A Extensions of the Projective Hierarchy.- 40.B Effective Descriptive Set Theory.- 40.C Large Cardinals.- 40.D Connections to Other Areas of Mathematics.- Appendix A. Ordinals and Cardinals.- Appendix B. Well-founded Relations.- Appendix C. On Logical Notation.- Notes and Hints.- References.- Symbols and Abbreviations.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726900567,"sku":"9780387943749","price":43.19,"currency_code":"GBP","in_stock":true}]},{"product_id":"sheaves-in-geometry-and-logic-9780387977102","title":"Sheaves in Geometry and Logic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSheaves also appear in logic as carriers for models of set theory. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003e\"A beautifully written book, a long and well motivated book packed with well chosen clearly explained examples. … authors have a rare gift for conveying an insider’s view of the subject from the start. This book is written in the best Mac Lane style, very clear and very well organized. … it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field.\" (Wordtrade, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Prologue; Categorical Preliminaries; 1. Categories of Functors; 2. Sheaves of Sets; 3. Grothendieck Topologies and Sheaves; 4. First Properties of Elementary Topoi; 5. Basic Constructions of Topoi; 6. Topoi and Logic; 7. Geometric Morphisms; 8. Classifying Topoi; 9. Localic Topoi; 10. Geometric Logic and Classifying Topoi; Appendix: Sites for Topoi; Epilogue; Bibliography; Index of Notations; Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727916375,"sku":"9780387977102","price":61.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387977102.jpg?v=1720001409"},{"product_id":"level-up-maths-pupil-book-level-57-9780435537326","title":"Level Up Maths Pupil Book Level 57","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eTo ensure clear progression for every pupil, we have divided the course into four Pupil Books, supported by three Access Workbooks. Maths is put into contexts that make sense to pupils, showing them how it relates to other subjects and how useful it is in everyday life. With each concept presented in a clear, relevant and engaging way, pupils will be inspired to succeed!\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction\u003c\/p\u003e \u003cp\u003eUnit 1 Getting things in order - Number\/Algebra 1\u003c\/p\u003e \u003cp\u003eUnit 2 Get in line - Geometry and measures 1\u003c\/p\u003e \u003cp\u003eUnit 3 Definitely maybe - Statistics 1\u003c\/p\u003e \u003cp\u003eUnit 4 Look the part - Number 2\u003c\/p\u003e \u003cp\u003eUnit 5 Function frenzy - Algebra 2\u003c\/p\u003e \u003cp\u003eUnit 6 Measure up - Geometry and measures 2\u003c\/p\u003e \u003cp\u003eRevision 1\u003c\/p\u003e \u003cp\u003eUnit 7 Into the unknown - Algebra 3\u003c\/p\u003e \u003cp\u003eUnit 8 Clever calculations - Number 3\u003c\/p\u003e \u003cp\u003eUnit 9 Tons of transformations - Geometry and measures 3\u003c\/p\u003e \u003cp\u003eUnit 10 Under construction - Algebra 4\u003c\/p\u003e \u003cp\u003eUnit 11 Dealing with data - Statistics 2\u003c\/p\u003e \u003cp\u003eRevision 2\u003c\/p\u003e \u003cp\u003eUnit 12 Number know-how - Number 4\u003c\/p\u003e \u003cp\u003eUnit 13 The plot thickens - Algebra 5\u003c\/p\u003e \u003cp\u003eUnit 14 Putting things in proportion - Solving problems 1\u003c\/p\u003e \u003cp\u003eUnit 15 Back to the drawing board - Geometry and measures 4\u003c\/p\u003e \u003cp\u003eUnit 16 Statistically speaking - Statistics 3\u003c\/p\u003e \u003cp\u003eRevision 3\u003c\/p\u003e \u003cp\u003eIndex\u003c\/p\u003e","brand":"Pearson Education Limited","offers":[{"title":"Default Title","offer_id":48733776085335,"sku":"9780435537326","price":33.13,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780435537326.jpg?v=1720001633"},{"product_id":"introduction-to-proofs-and-proof-strategies-9781009096287","title":"Introduction to Proofs and Proof Strategies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eEmphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Every student in the sciences should be exposed to the basic language of modern mathematics, and standard courses such as calculus or linear algebra do not play this role. The ideal textbook for such a course should not attempt to be encyclopedic and should not assume special prerequisites. It should cover a carefully chosen selection of topics efficiently, engagingly, thoroughly, without being overbearing. Fuchs' text fits this description admirably. The level is right, the math is rock solid, the writing is very pleasant. The book talks to the reader, without ever sounding patronizing. A vast selection of problems, many including solutions, will be splendidly helpful both in a classroom setting and for self-study.' Paolo Aluffi, Florida State University\u003cbr\u003e'This well-written text strikes a good balance between conciseness and clarity. Students are led from looking more deeply into familiar topics, such as the quadratic formula, to an understanding of the nature, structure, and methods of proof. The examples and problems are a strong point. I look forward to teaching from it.' Eric Gottlieb, Rhodes College\u003cbr\u003e'Fuchs' text is an excellent addition to the 'transitions to proof' literature. I will use it when I next teach such a course. Except for the excellent 'Additional Topics' sections, the content is standard, but the spiraling presentation and helpful narrative around proofs are what truly elevate this text. Fuchs has made every attempt to connect the structure and rigor of mathematics with the intuition of the student. For example, the notion of function arises in three different chapters, with two increasingly rigorous 'provisional definitions,' before a complete definition is given within a wider discussion of relations. I anticipate this approach resonating with students. Fuchs' Chapter 3, which introduces logic and proof strategies, is the most usable presentation of the material I have seen or used. The practice of mathematics and mathematical thinking is communicated well, while opportunities for confusion and obfuscation via a blizzard of symbols are minimized.' Ryan Grady, Montana State University\u003cbr\u003e'This book is a must-have resource for an undergraduate mathematics student or interested reader to learn the fundamental topics in how to prove things. The text is thorough and of top quality, yet it is conversational and easy to absorb. Maybe the most important quality, it offers advice about how to approach problems, making it perfect for an introduction to proofs class.' Andrew McEachern, York University, Canada\u003cbr\u003e'This is a great choice of textbook for any course introducing undergraduates to mathematical proofs. What makes this book stand out are the early chapters, as well as the 'Additional Topics,' both with accompanying exercises. The book begins by gently introducing proof-based thinking by posing well-motivated prompts and exercises concerning familiar arithmetic of real numbers and the integers. It then introduces fields as a playground to practice working with axioms and drawing (sometimes surprising) conclusions from them. The book proceeds with introducing formal logic, mathematical induction, set theory, and relations on sets. The book's design nicely enables framing classes around a choice sampling among the abundant exercises. The book's 'Additional Topics' can serve to engage those students with a brimming imagination and who are already familiar with basic notions of proofs.' David Ayala, Montana State University\u003cbr\u003e'Fuchs' Introduction to Proofs and Proof Strategies is an excellent textbook choice for an undergraduate proof-writing course. The author takes a friendly and conversational approach, giving many worked examples throughout each section. Furthermore, each section is replete with exercises for the reader, along with fully worked solutions at chapter's end. This is exactly the 'get your hands dirty' approach students and readers will benefit greatly from!' Frank Patane, Samford University\u003cbr\u003e'The book Introduction to Proofs and Proof Strategies by Shay Fuchs takes the problem-solving approach to the forefront by accompanying the reader in the construction and deconstruction of proofs through numerous examples and challenging exercises. The fundamental principles of mathematics are introduced in a creative and innovative way, making learning an enjoyable journey.' Roberto Bruni, Università di Pisa\u003cbr\u003e'This textbook is easy to read and designed to enhance students' problem-solving skills in their first year of university. The book really stands out due to the variety and quality of exercises at the end of each chapter. The latter chapters dive into more advanced topics for interested students.' Marina Tvalavadze, University of Toronto Mississauga\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents; Preface; Part I. Core Material; 1. Numbers, Quadratics and Inequalities; 2. Sets, Functions and the Field Axioms; 3. Informal Logic and Proof Strategies; 4. Mathematical Induction; 5. Bijections and Cardinality; 6. Integers and Divisibility; 7. Relations; Part II. Additional Topics; 8. Elementary Combinatorics; 9. Preview of Real Analysis – Limits and Continuity; 10. Complex Numbers; 11. Preview of Linear Algebra; Notes; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738003648855,"sku":"9781009096287","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009096287.jpg?v=1723811673"},{"product_id":"geometry-9781071602973","title":"Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cdiv\u003eThis text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format - the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class.\u003c\/div\u003e\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\u003cdiv\u003e\n\u003ci\u003eGeometry\u003c\/i\u003e takes a different approach to presenting basic geometry for high-school students and others new to the subject.  Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and move them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certai\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book is intended to engage the reader visually, tactilely, and kinesthetically. … It has a good set of material to enliven more traditional geometry instruction. … There are problems and exercises throughout. The exercises are accompanied by solutions.” (MAA Reviews, October 10, 2020)\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePoints and Lines: A Look at Projective Geometry.- Parallel Lines: A Look at Affine Geometry.- Area: A Look at Symplectic Geometry.- Circles: A Look at Euclidean Geometry.\u003c\/div\u003e","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48738192687447,"sku":"9781071602973","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781071602973.jpg?v=1723811807"},{"product_id":"logic-and-structure-9781447145578","title":"Logic and Structure","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDirk van Dalen''s popular textbook \u003ci\u003eLogic and Structure\u003c\/i\u003e, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel''s famous incompleteness theorem. \u003c\/p\u003e\u003cp\u003ePropositional and predicate logic are presented in an easy-to-read style using Gentzen''s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. \u003c\/p\u003e\u003cp\u003eIn view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. \u003c\/p\u003e\u003cp\u003eThe last chapter on Gödel''s first incompleteness theorem is self-contai\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eFrom the reviews of the fifth edition:\u003c\/p\u003e\u003cp\u003e“This is the fifth edition of van Dalen’s respected and enduring logic textbook, first published in 1980. ... Intended as a text for an undergraduate course in logic, this text contains considerably more material than can be covered in one semester. … this is quite a good book and is certainly a very serious contender as a text for an undergraduate course, and should be carefully looked at by anybody teaching such a course.” (Mark Hunacek, MAA Reviews, June, 2013)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction.- Propositional Logic.- Predicate Logic.- Completeness and Applications.- Second Order Logic.- Intuitionistic Logic.- Normalization.- Gödel's theorem.\u003c\/p\u003e","brand":"Springer London Ltd","offers":[{"title":"Default Title","offer_id":48739330785623,"sku":"9781447145578","price":56.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781447145578.jpg?v=1720051927"},{"product_id":"the-flawed-genius-of-william-playfair-9781487545031","title":"The Flawed Genius of William Playfair","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book shares the life story of William Playfair, the father of statistical graphics, who experienced extreme ups and downs in his various careers, including as a statistician, economist, and fraudster.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface: Playfair Is Introduced    1. Playfair Is Sent to Newgate Prison  2. Playfair Goes to Birmingham to Work for Boulton and Watt  3. Playfair Goes to London to Set Up His Own Business  4. Playfair Evolves into a Writer by Profession  5. Playfair Expresses His Early Political Views 6. Playfair Makes His Mark on Statistical Graphics  7. Playfair Goes to Paris  8. Playfair Tries to Take Advantage of the French Revolution  9. Playfair Escapes from France and Returns to England  10. Playfair Becomes an Avid Anti-Jacobin Propagandist  11. Playfair Gets Involved with Forged Assignats  12. Playfair Starts a Bank and Goes Bankrupt  13. Playfair Ekes Out a Living as a Bankrupt  14. Playfair Has a Good Year during 1805 with Hints of Ending Badly  15. Playfair Has Serious Legal and Other Problems  16. Playfair Dabbles Deeply into Family History and Political Biography  17. Playfair Continues Writing and Tries a Few More Scams to Get to Paris  18. Playfair Returns to Paris  19. Playfair Spends His Last Few Years in England in Poverty    Afterword: Playfair Avoids a Shakespearean Epitaph    Appendix: Assignat Forging by French Emigres in England    Notes  Index","brand":"University of Toronto Press","offers":[{"title":"Default Title","offer_id":48739692216663,"sku":"9781487545031","price":38.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781487545031.jpg?v=1723812256"},{"product_id":"short-cuts-maths-navigate-your-way-through-the-big-ideas-9781837731092","title":"Short Cuts: Maths: Navigate Your Way Through the Big Ideas","description":"\u003cp\u003eYour expert guide to mastering the numbers behind the mysteries of modern mathematics.\u003cbr\u003e\u003cbr\u003e What with the mysteries of infinity and imaginary numbers, the power of mathematical modelling, and the logic and structures hiding behind real-life situations and digital worlds, the modern landscape of mathematics is an extraordinary place to explore. But how are you expected to navigate this enigmatic and abstract world?\u003cbr\u003e\u003cbr\u003e\u003ci\u003eShort Cuts: Maths\u003c\/i\u003e provides the map you need to start exploring seriously big ideas. Puzzling questions prompt 'short cut' answers written by experts in their field, with each one the setting-off point for instructions to help you plot your path through the mathematical maze.\u003c\/p\u003e","brand":"Icon Books","offers":[{"title":"Default Title","offer_id":48741932269911,"sku":"9781837731091","price":13.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781837731091.jpg?v=1720059354"},{"product_id":"the-logical-writings-of-karl-popper-9783030949259","title":"The Logical Writings of Karl Popper","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis open access book is the first ever collection of Karl Popper's writings on deductive logic.\u003cbr\u003eKarl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science (\"falsificationism\") and his social and political philosophy (\"open society\") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.\u003cbr\u003eThis collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e Part I: Articles.- Chapter 1. Introduction to Popper’s Articles on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 2. Are Contradictions Embracing? (1943) (Karl R. Popper).- Chapter 3. Logic without Assumptions (1947) (Karl R. Popper).- Chapter 4. New Foundations for Logic (1947) (Karl R. Popper).- Chapter 5. Functional Logic without Axioms or Primitive Rules of Inference (1947)(Karl R. Popper).- Chapter 6. On the Theory of Deduction, Part I. Derivation and its Generalizations (1948) (Karl R. Popper).- Chapter 7. On the Theory of Deduction, Part II. The Definitions of Classical and Intuitionist Negation (1948) (Karl R. Popper).- Chapter 8. The Trivialization of Mathematical Logic (1949) (Karl R. Popper).- Chapter 9. A Note on Tarski’s Definition of Truth (1955) (Karl R. Popper).-Chapter 10. On a Proposed Solution of the Paradox of the Liar (1955) (Karl R. Popper).- Chapter 11. On Subjunctive Conditionals with Impossible Antecedents (1959) (Karl R. Popper).- Chapter 12. Lejewski’s Axiomatization of My Theory of Deducibility (1974) (Karl R. Popper).- Chapter 13. Reviews of Popper’s Articles on Logic (Wilhelm Ackermann et.al).- Part II: Manuscripts.- Chapter 14. Introduction to Popper’s Manuscripts on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 15. On Systems of Rules of Inference (Karl R. Popper and Paul Bernays).- Chapter 16. A General Theory of Inference (Karl R. Popper).- Chapter 17. On the Logic of Negation (Karl R. Popper).- Chapter 18. A Note on the Classical Conditional (Karl R. Popper).- Part III: Correspondence.- Chapter 19. Introduction to Popper’s Correspondence on Logic (David Binder, Thomas Piecha, and Peter Schroeder-Heister).- Chapter 20. Popper’s Correspondence with Paul Bernays (Karl R. Popper and Paul Bernays).- Chapter 21. Popper’s Correspondence with Luitzen Egbertus Jan Brouwer (Karl R. Popper and Luitzen E. J. Brouwer).- Chapter 22. Popper’s Correspondence with Rudolf Carnap (Karl R. Popper and Rudolf Carnap).- Chapter 23. Popper’s Correspondence with Alonzo Church (Karl R. Popper and Alonzo Church).- Chapter 24. Popper’s Correspondence with Kalman Joseph Cohen (Karl R. Popper and Kalman J. Cohen).- Chapter 25. Popper’s Correspondence with Henry George Forder (Karl R. Popper and Henry George Forder).- Chapter 26. Popper’s Correspondence with Harold Jeffreys (Karl R. Popper and Harold Jeffreys).- Chapter 27. Popper’s Correspondence with Stephen Cole Kleene (Karl R. Popper and Stephen C. Kleene).- Chapter 28. Popper’s Correspondence with William Calvert Kneale (Karl R. Popper and William C. Kneale).- Chapter 29. Popper’s Correspondence with Willard Van Orman Quine (Karl R. Popper and Willard V. O. Quine).- Chapter 30. Popper’s Correspondence with Heinrich Scholz (Karl R. Popper and Heinrich Scholz).- Chapter 31.  Popper’s Correspondence with Peter Schroeder-Heister (Karl R. Popper and Peter Schroeder-Heister).- Concordances.- Bibliography.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743059915095,"sku":"9783030949259","price":44.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"the-real-numbers-an-introduction-to-set-theory-and-analysis-9783319015767","title":"The Real Numbers: An Introduction to Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWhile most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself.\u003c\/p\u003e\u003cp\u003eBy focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to \"assume\" the real numbers. Its prerequisites are calculus and basic mathematics.\u003c\/p\u003e\u003cp\u003eMathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets,  countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is a book of both analysis and set theory, and the analysis begins at an elementary level with the necessary treatment of completeness of the reals. … the analysis makes it valuable to the serious student, say a senior or first-year graduate student. … Stillwell’s book can work well as a text for the course in foundations, with its good treatment of the cardinals and ordinals. … This enjoyable book makes the connection clear.” (James M. Cargal, The UMAP Journal, Vol. 38 (1), 2017)\u003c\/p\u003e\u003cp\u003e“This book is an interesting introduction to set theory and real analysis embedded in properties of the real numbers. … The 300-plus problems are frequently challenging and will interest both upper-level undergraduate students and readers with a strong mathematical background. … A list of approximately 100 references at the end of the book will help students to further explore the topic. … Summing Up: Recommended. Lower-division undergraduates.” (D. P. Turner, Choice, Vol. 51 (11), August, 2014)\u003c\/p\u003e\u003cp\u003e“This is an informal look at the nature of the real numbers … . There are extensive historical notes about the evolution of real analysis and our understanding of real numbers. … Stillwell has deliberately set out to provide a different sort of construction where you understand what the foundation is supporting and why it is important. I think this is very successful, and his book … is much more informative and enjoyable.” (Allen Stenger, MAA Reviews, February, 2014)\u003c\/p\u003e\u003cp\u003e“This book will be fully appreciated by either professional mathematicians or those students, who already have passed a course in analysis or set theory. … The book contains a quantity of motivation examples, worked examples and exercises, what makes it suitable also for self-study.” (Vladimír Janiš, zbMATH, 2014)\u003c\/p\u003e\u003cp\u003e“The book offers a rigorous foundation of the real number system. It is intended for senior undergraduates who have already studied calculus, but a wide range of readers will find something interesting, new, or instructive in it. … This is an extremely reader-friendly book. It is full of interesting examples, very clear explanations, historical background, applications. Each new idea comes after proper motivation.” (László Imre Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Fundamental Questions.- From Discrete to Continuous.- Infinite Sets.- Functions and Limits.- Open Sets and Continuity.- Ordinals.- The Axiom of Choice.- Borel Sets.- Measure Theory.- Reflections.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743091241303,"sku":"9783319015767","price":32.39,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319015767.jpg?v=1720064071"},{"product_id":"number-theory-an-introduction-via-the-density-of-primes-9783319438733","title":"Number Theory: An Introduction via the Density of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNow in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of \u003ci\u003ep\u003c\/i\u003e-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.\u003cbr\u003eKey topics and features include:\u003cul\u003e\n\u003cli\u003eA solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eConcise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals\u003c\/li\u003e\n\u003cli\u003eDiscussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eMany interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers\u003c\/li\u003e\n\u003c\/ul\u003eThe user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make \u003ci\u003eNumber Theory: An Introduction via the Density of Primes\u003c\/i\u003e ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. … Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e“The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. … a good text for an introductory course … .” (Allen Stenger, MAA Reviews, maa.org, November, 2016)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- The Fields Q_\u003ci\u003ep\u003c\/i\u003e of \u003ci\u003ep\u003c\/i\u003e-adic Numbers: Hensel's Lemma.- References.- Index.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743095566679,"sku":"9783319438733","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"homological-methods-representation-theory-and-cluster-algebras-9783319745848","title":"Homological Methods, Representation Theory, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.\u003c\/p\u003e\u003cp\u003eThe six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003eThe courses held were:\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eAdvanced homological algebra\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eIntroduction to the representation theory of algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eAuslander-Reiten theory for algebras of infinite representation type\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster algebras arising from surfaces\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster tilted algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eCluster characters\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eIntroduction to K-theory\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eBrauer graph algebras and applications to cluster algebras\u003cbr\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction to the Representation Theory of  Finite-Dimensional Algebras: The Functorial Approach (M. I. Platzeck).- Auslander–Reiten Theory for Finite-Dimensional Algebras  (P. Malicki).-  Cluster Algebras From Surfaces (R. Schiffler).- Cluster Characters (P.-G. Plamondon).- A Course on Cluster Tilted Algebras (I. Assem).- Brauer Graph Algebras (S. Schroll). ","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743104151895,"sku":"9783319745848","price":41.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319745848.jpg?v=1723812632"},{"product_id":"mathematical-techniques-for-competitive-examinations-9789393330109","title":"Mathematical Techniques for Competitive","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis is a problem-based book aimed at high-school students interested in mathematical topics related to the ISI and CMI entrance tests as well as Mathematics Olympiads. This book will help students in designing a well-planned pathway to tackle complicated problems from topics such as number theory, combinatorics, algebra, calculus, Euclidean and coordinate geometry, probability and statistics.","brand":"Universities Press","offers":[{"title":"Default Title","offer_id":48743256424791,"sku":"9789393330109","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"learning-trigonometry-by-problem-solving-9789811232848","title":"Learning Trigonometry By Problem Solving","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters.The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college.We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743278805335,"sku":"9789811232848","price":42.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811232848.jpg?v=1720064895"},{"product_id":"john-napier-9780691155708","title":"John Napier","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eJohn Napier (1550-1617) is celebrated today as the man who invented logarithms--an enormous intellectual achievement that would soon lead to the development of their mechanical equivalent in the slide rule: the two would serve humanity as the principal means of calculation until the mid-1970s. Yet, despite Napier's pioneering efforts, his life and\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"John Napier fills a gap concerning an important, and often ignored, chapter of mathematical history.\"--George Szpiro, Nature \"In this engaging book, we learn more about Napier the mathematician, the religious zealot, the person.\"--Devorah Bennu, The Guardian, Grrl Scientist \"Edinburgh born John Napier, the inventor of logarithms, is in danger of fading into the shadows of the scientific landscape. In the new book John Napier: Life, Logarithms, and Legacy, Julian Havil does a marvelous job of bringing Napier back into the spotlight.\"--Stephanie Blanda, American Mathematical Society blog \"I'm sure after reading this entertaining and enjoyable book, Napier will climb some rungs on your ladder of famous mathematicians.\"--A. Bultheel, European Mathematical Society \"Havil ... gives a rich history of Napier's involvement in the Protestant reformation, his introduction of logarithms, and his legacy.\"--Choice \"With this book, the author continues his impressive series of illuminating, accessible monographs on the history of mathematics.\"--Bart J. I. Van Kerkhove, Mathematical Review \"This book fills a clear gap in published work on Napier and is likely to be the standard point of departure for those interested in his life and work for some years to come.\"--Mark McCartney, London Mathematical Society Newsletter \"It is clearly a very interesting book.\"--Ernesto Nungesser, Irish Math Society Bulletin \"Havil's attention to detail is without equal in the opinion of this reviewer.\"--John A. Adam, Scotia\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments xv  Introduction 1  Chapter One Life and Lineage 8  Chapter Two Revelation and Recognition 35  Chapter Three A New Tool for Calculation 62  Chapter Four Constructing the Canon 96  Chapter Five Analogue and Digital Computers 131  Chapter Six Logistics: The Art of Computing Well 155  Chapter Seven Legacy 179  Epilogue 207  Appendix A Napier's Works 209  Appendix B The Scottish Science Hall of Fame 210  Appendix C Scotland and Conflict 211  Appendix D Scotland and Reformation 216  Appendix E A Stroll Down Memory Lane 220  Appendix F Methods of Multiplying 229  Appendix G Amending Napier's Kinematic Model 232  Appendix H Napier's Inequalities 233  Appendix I Hos Ego Versiculos Feci 236  Appendix J The Rule of Three 238  Appendix K Mercator's Map 250  Appendix L The Swiss Claimant 264  References 270  Index 275","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865527497047,"sku":"9780691155708","price":31.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691155708.jpg?v=1722274398"},{"product_id":"elements-of-mathematics-9780691178547","title":"Elements of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[Stillwell] writes clearly and engagingly... [Elements of Mathematics] can appeal to various constituencies at different levels of mathematical sophistication.\"--Mark Hunacek, MAA Reviews \"A great exploration of elementary mathematics, its limitations, how infinity complicates things, and how various branches of mathematics fit together.\"--Antonio Cangiano, Math-Blog \"Stillwell is ... One of the better current mathematical authors: he writes clearly and engagingly, and makes more of an effort than most to provide historical detail and a sense of how various mathematical ideas tie in with one another... The features we have learned to expect from Stillwell (including, but not limited to, excellent writing) are present in [Elements of Mathematics] as well.\"--MAA Reviews \"An accessible read... Stillwell breaks down the basics, providing both historical and practical perspectives from arithmetic to infinity.\"--Gemma Tarlach, Discover \"[A] sophisticated treatment of topics usually described as elementary.\"--John Allen Paulos \"[Elements of Mathematics] is quite a tour de force, organized by areas of mathematics--arithmetic, computation, algebra, geometry, calculus, and so on--and in each area Stillwell manages to distill down the big ideas and the connections with other areas. He is a master expositor, and the text manages to be engaging and accessible without watering down the mathematics. I definitely learned new things from the book!\"--Brent Yorgey, Math Less Traveled blog \"From a lifetime of teaching, Stillwell has distilled some nice examples from the entire gamut of elementary mathematics.\"--Mathematical Reviews Clippings \"[A] wonderful book... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.\"--Victor Katz, Bulletin of the American Mathematical Society \"Elements of Mathematicsis a fine ... overview of the field of mathematics... The writing is clear, succinct, organized, and the diagrams [and] illustrations excellent... While some of the discussion is introductory or elementary, it always leads to deeper, more challenging ideas... [T]his will make a fine basic addition to most mathematicians' bookshelves.\"--Math Tango \"Stillwell uses his broad and impressive command of mathematics to transport a reader through each topic and to a higher level of understanding and questioning.\"--Convergence \"[A] wonderful book ... I think that [Elements of Mathematics] will itself become a modern classic and a reference work for anyone trying to learn basic topics in any of the major fields of mathematics.\"--Victor Katz, Bulletin of the American Mathematical Society \"[Elements of Mathematics] is a book that everybody should read. You will be the better for it.\"--Reuben Hersh, American Mathematical Monthly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Preface, pg. xi*1. Elementary Topics, pg. 1*2. Arithmetic, pg. 35*3. Computation, pg. 73*4. Algebra, pg. 106*5. Geometry, pg. 148*6. Calculus, pg. 193*7. Combinatorics, pg. 243*8. Probability, pg. 279*9. Logic, pg. 298*10. Some Advanced Mathematics, pg. 336*Bibliography, pg. 395*Index, pg. 405","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865539260759,"sku":"9780691178547","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691178547.jpg?v=1722274459"},{"product_id":"electronic-string-art-9781032512730","title":"Electronic String Art","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eString art is a well-known and popular activity that uses string, a board, and nails to produce artistic images (although there are variations that use different modalities). This activity is beloved because simple counting rules are used to create beautiful images that can both adorn walls and excite young minds. The downside of this highly tactile activity is that it is quite time-consuming and rigid. By contrast, electronic string art offers much more flexibility to set up or change nail locations and counting rules, and the images created from those changes change instantaneously.\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\u003cstrong\u003eElectronic String Art: Rhythmic Mathematics \u003c\/strong\u003e\u003c\/i\u003einvites readers to use the author's digital resources available on the ESA website to play with the parameters inherent in string art models while offering concise, accessible explanations of the underlying mathematical principles regarding how the images were created and how they change. Readers will have the opportunity to crea\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePart I. Preliminary Issues. 1. Introduction and Overview. 2. How Polygons are Drawn. 3. String Art Basics. 4. Issues involving Commonality. 5. Cycles. 6. Alternative ways to Obtain an Image. 7. Levels of Subdivision Points. 8. Shape-Shifting Polygons. 9. An Overarching Question. 10. Functionally Modified String Art files. 11. A sampling of Image Archetypes. 12. n = P images. 13. 60-Second Images. 14. Challenge Questions for Part II. 15. Centered-Point Flowers. 16. Double Jump Models. 17. Four Color Clock Arithmetic. 18. Larger Jump Set Models. 19. Busting out of our Polygonal Constraint. 20. Challenge Questions for Part III. 21. Basic Properties of Numbers. 22. Angles in Polygons and Stars. 23. Modular Arithmetic. 24. Modular Multiplicative Inverses, MMI. 25. A Guide to the Web Model. 26. Suggestions for Mathematics Teachers. \u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":48866310652247,"sku":"9781032512730","price":37.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"mathematics-for-the-million-how-to-master-the-magic-of-numbers-9781911440581","title":"Mathematics for the Million: How to Master the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eOne of the most illuminating, useful and exciting books ever published in the mathematical field\u003c\/strong\u003e\u003c\/p\u003e  \u003cp\u003eTaking only a modicum of knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus.\u003c\/p\u003e  \u003cp\u003eHis illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty.\u003c\/p\u003e  \u003cp\u003eMathematics is the language of size, shape, and order – a language Hogben shows one can both master and enjoy.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e'It makes alive the contents of the elements of mathematics' \u003cstrong\u003eAlbert Einstein\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e'Deals with maths in a way that they never taught us at school' \u003cem\u003e\u003cstrong\u003eDaily Express\u003c\/strong\u003e\u003c\/em\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e'If only I had been brought up on this book, the sense and meaning of mathematics would have been made clear to me... The book combines utmost brilliance with extraordinarily good common sense' \u003cstrong\u003eA. L. Rowse\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e'A great book of first-class importance' \u003cstrong\u003eH. G. Wells\u003c\/strong\u003e\u003c\/p\u003e","brand":"Duckworth Books","offers":[{"title":"Default Title","offer_id":48868977738071,"sku":"9781911440581","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781911440581.jpg?v=1722290649"},{"product_id":"advances-in-mathematics-research-volume-22-9781536123715","title":"Advances in Mathematics Research: Volume 22","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAdvances in Mathematics Research presents original studies on the leading edge of mathematics. Each article has been carefully selected in an attempt to present substantial research results across a broad spectrum. Chapter One summarizes the phase\/current generalized measures of the entropy\/information content in complex quantum states of molecular systems. Chapter Two reviews the current knowledge regarding Mavridis'' area (MA), with emphasis on the role of applied mathematics in its discovery, and aims to explore its mathematical expression. In Chapter Three a model of fractional difference has been defined by the author as a fractional Newton binomial with respect to the finite difference operator as parameter, therefore they obtained an alternative to fractional derivative, and further, as a by-product, they came across the so-called modified Riemann-Liouville derivative which ascribes a special role to the initial value of the considered function. Chapter Four presents some popular uses of exponential distribution in the context of ordered random variables. Chapter Five gives a comprehensive introduction to the Ricci flow on manifolds of dimension two which can be done in a reasonable fashion when the Euler characteristic is negative or zero. Chapter Six investigates some geometric properties by using the concepts of the geometric function theory and studies the convexity and star-like for the new operator.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886069461335,"sku":"9781536123715","price":205.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536123715.jpg?v=1722538707"},{"product_id":"advances-in-mathematics-research-volume-23-9781536125122","title":"Advances in Mathematics Research: Volume 23","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn the opening chapter by Victor Martinez-Lukacs, two kinds of matrices related to chemical problems are examined and an outline of their main properties about their eigenvalues is exhibited in order to demonstrate that all the ODE solutions are either stable or asymptotically stable. In chapter two by Ivan Kyrchei, the Cramer rules for the weighted Moore-Penrose solutions of left and right systems of quaternion linear equations are obtained. Next, in chapter three, Tadeusz Antczak showcases numerous sets of saddle point criteria for a new class of nonconvex non-smooth discrete minimax fractional programming problems. Marcia de F. B. Binelo, Airam T. Z. R. Sausen, Paulo S. Sausen, and Manuel O. Binelo provide a summary of electric mathematical models used for the prediction of batteries charge and discharge behaviour in chapter four. In chapter five, general methodology for the precise modelling and performance assessment of launch vehicles dedicated to microsatellites is proposed by M. Pontani, M. Palloney, and P. Teofilattoz. In chapter six, Nodari Vakhania exemplifies ties and relationships among some optimisation problems such as scheduling and transportation issues. In chapter seven, a geometry without using points in established by N. L. Bushwick, bringing the book to a close.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886071722327,"sku":"9781536125122","price":205.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536125122.jpg?v=1722538716"},{"product_id":"advances-in-mathematics-research-volume-24-9781536127669","title":"Advances in Mathematics Research: Volume 24","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886074638679,"sku":"9781536127669","price":205.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781536127669.jpg?v=1722538727"},{"product_id":"wavelets-classification-theory-applications-9781621002529","title":"Wavelets: Classification, Theory \u0026 Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886968713559,"sku":"9781621002529","price":152.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781621002529.jpg?v=1722542413"},{"product_id":"discrete-structures-9781906574826","title":"Discrete Structures","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"New Academic Science Ltd","offers":[{"title":"Default Title","offer_id":49084603040087,"sku":"9781906574826","price":33.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781906574826.jpg?v=1725552732"},{"product_id":"integer-and-combinatorial-optimization-9780471359432","title":"Integer and Combinatorial Optimization","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDiscrete optimization models are used to tackle a wide variety of problems in many fields, including operations research, management science, engineering, and mathematics. Written by two internationally recognized integer programming experts, this book presents the mathematical foundations, theory, and algorithms of discrete optimization methods.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFOUNDATIONS.\u003cbr\u003e \u003cbr\u003e The Scope of Integer and Combinatorial Optimization.\u003cbr\u003e \u003cbr\u003e Linear Programming.\u003cbr\u003e \u003cbr\u003e Graphs and Networks.\u003cbr\u003e \u003cbr\u003e Polyhedral Theory.\u003cbr\u003e \u003cbr\u003e Computational Complexity.\u003cbr\u003e \u003cbr\u003e Polynomial-Time Algorithms for Linear Programming.\u003cbr\u003e \u003cbr\u003e Integer Lattices.\u003cbr\u003e \u003cbr\u003e GENERAL INTEGER PROGRAMMING.\u003cbr\u003e \u003cbr\u003e The Theory of Valid Inequalities.\u003cbr\u003e \u003cbr\u003e Strong Valid Inequalities and Facets for Structured Integer Programs.\u003cbr\u003e \u003cbr\u003e Duality and Relaxation.\u003cbr\u003e \u003cbr\u003e General Algorithms.\u003cbr\u003e \u003cbr\u003e Special-Purpose Algorithms.\u003cbr\u003e \u003cbr\u003e Applications of Special- Purpose Algorithms.\u003cbr\u003e \u003cbr\u003e COMBINATORIAL OPTIMIZATION.\u003cbr\u003e \u003cbr\u003e Integral Polyhedra.\u003cbr\u003e \u003cbr\u003e Matching.\u003cbr\u003e \u003cbr\u003e Matroid and Submodular Function Optimization.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Indexes.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402573291863,"sku":"9780471359432","price":141.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471359432.jpg?v=1730480805"},{"product_id":"journey-through-genius-9780471500308","title":"Journey Through Genius","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ePraise for William Dunham s Journey Through Genius The Great Theorems of Mathematics Dunham deftly guides the reader through the verbal and logical intricacies of major mathematical questions and proofs, conveying a splendid sense of how the greatest mathematicians from ancient to modern times presented their arguments.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface v\u003c\/p\u003e \u003cp\u003eAcknowledgements ix\u003c\/p\u003e \u003cp\u003eChapter 1 Hippocrates' Quadrature of the Lune (ca 440 BC) 1\u003c\/p\u003e \u003cp\u003eChapter 2 Euclid's Proof of the Pythagorean Theorem (ca 300 BC) 27\u003c\/p\u003e \u003cp\u003eChapter 3 Euclid and the Infinitude of Primes (ca 300 BC) 61\u003c\/p\u003e \u003cp\u003eChapter 4 Archimedes' Determination of Circular Area (ca 225 BC) 84\u003c\/p\u003e \u003cp\u003eChapter 5 Heron's Formula for Triangular Area (ca AD 75) 113\u003c\/p\u003e \u003cp\u003eChapter 6 Cardano and the Solution of the Cubic (1545) 133\u003c\/p\u003e \u003cp\u003eChapter 7 A Gem from Isaac Newton (Late 1660s) 155\u003c\/p\u003e \u003cp\u003eChapter 8 The Bernoullis and the Harmonic Series (1689) 184\u003c\/p\u003e \u003cp\u003eChapter 9 The Extraordinary Sums of Leonhard Euler (1734) 207\u003c\/p\u003e \u003cp\u003eChapter 10 A Sampler of Euler's Number Theory (1736) 223\u003c\/p\u003e \u003cp\u003eChapter 11 The Non-Denumerability of the Continuum (1874) 245\u003c\/p\u003e \u003cp\u003eChapter 12 Cantor and the Transfinite Realm (1891) 267\u003c\/p\u003e \u003cp\u003eAfterword 285\u003c\/p\u003e \u003cp\u003eChapter Notes 287\u003c\/p\u003e \u003cp\u003eReferences 291\u003c\/p\u003e \u003cp\u003eIndex 295\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402619920727,"sku":"9780471500308","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471500308.jpg?v=1730481001"},{"product_id":"graphs-9780471513568","title":"Graphs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasic Concepts.\u003cbr\u003e \u003cbr\u003e Trees, Cutsets, and Circuits.\u003cbr\u003e \u003cbr\u003e Eulerian and Hamiltonian Graphs.\u003cbr\u003e \u003cbr\u003e Graphs and Vector Spaces.\u003cbr\u003e \u003cbr\u003e Directed Graphs.\u003cbr\u003e \u003cbr\u003e Matrices of a Graph.\u003cbr\u003e \u003cbr\u003e Planarity and Duality.\u003cbr\u003e \u003cbr\u003e Connectivity and Matching.\u003cbr\u003e \u003cbr\u003e Covering and Coloring.\u003cbr\u003e \u003cbr\u003e Matroids.\u003cbr\u003e \u003cbr\u003e Graph Algorithms.\u003cbr\u003e \u003cbr\u003e Flows in Networks.\u003cbr\u003e \u003cbr\u003e Indexes.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402621591895,"sku":"9780471513568","price":206.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471513568.jpg?v=1730481005"},{"product_id":"applied-numerical-methods-for-engineers-9780471575238","title":"Applied Numerical Methods for Engineers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten for engineering students, this textbook on numerical methods stresses the typical methods that engineers use in daily practice. 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This book begins with the definitions and properties of algebraic fields. It then discusses the theory of divisibility from an axiomatic viewpoint, rather than by the use of ideals. It also gives an introduction to p-adic numbers and their uses, which are important in modern number theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCh. I Algebraic Fields 1 Ch. II Theory of Divisibility (Kronecker, Dedekind) 33 Ch. III Local Primadic Analysis (Kummer, Hensel) 71 Ch. IV Algebraic Number Fields 141  Amendments 223","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403706048855,"sku":"9780691059174","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691059174.jpg?v=1730484303"},{"product_id":"benjamin-franklins-numbers-9780691129563","title":"Benjamin Franklins Numbers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eRevealing the mathematical side of Benjamin Franklin, this book explains the mathematics behind Franklin's popular \"Poor Richard's Almanac\", which featured such things as population estimates and a host of mathematical digressions. It includes optional math problems that challenge readers to match wits with the Founding Father himself.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Pasles...speculates gleefully on the oft-denied mathematical genius of Benjamin Franklin...Drawing on Franklin's letters and journals as well as modern-day reconstructions of his library, Pasles touches on Franklin's fondness for magazines of mathematical diversions; publication of arithmetic problems in Poor Richard's Almanac; startlingly accurate projections of population growth and cost-benefit arguments against slavery.\"--Publisher's Weekly \"In Franklin's Numbers, a book mixing intellectual history and mathematical puzzles (with solutions appended), Paul Pasles brings out a less-celebrated sphere of Franklin's intellect. He makes the case for the founding father as a mathematician.\"--Jared Wunsch, Nature \"Pasles delivers surprising news to Sudoku lovers: Benjamin Franklin once shared their passion...Pasles illuminates Franklin's innovative use of mathematical logic in settling moral questions and in assessing population trends. Franklin's mathematical pursuits thus emerge as a complement to his much-lauded work in politics and science. An unexpected but welcome perspective on the genial genius of Philadelphia.\"--Bryce Christensen, Booklist \"There is hardly a discipline on which Franklin did not stamp his mark during the 18th century. But the role that mathematics played in his life has been overlooked, argues Paul Pasles. Franklin, for instance, was fascinated with magic squares, and this book provides plenty of background to help the reader admire his interest.\"--New Scientist \"[This is] a book that is an easy read for the innumerate but which also provides nourishment for those more skilled in the niceties of math...Also included are some contemporary puzzles that offer the reader the chance to contest skills with Franklin himself.\"--James Srodes, The Washington Times \"Making frequent use of Franklin's writings as well as mathematical brainteasers of the type that Franklin enjoyed, Benjamin Franklin's Numbers is an engaging and thoroughly unique biography of a singular figure in American history.\"--Ray Bert, Civil Engineering \"I thoroughly enjoyed reading this book. It is written in a pleasant, conversational style and the author's enthusiasm for his subject is infectious. The text is richly embroidered with colorful details, both mathematical and historical.\"--Eugene Boman, Convergence: A Magazine of the Mathematical Association of America \"Pasles has succeeded in writing a book dealing with mathematics that is accessible to readers at all levels, yet thoroughly referenced and scholarly enough to satisfy researchers. His endeavor was eased by the fact that the bulk of the material concerns Franklin's magic squares and circles, which only require that the reader have the ability to add. Unexpectedly, Pasles contributes much that is new; he corrects the errors of previous authors and presents new ideas through literary sleuthing and mathematical analysis.\"--C. Bauer, Choice \"Pasles makes a convincing case for Franklin as the last true Renaissance man in what is an entertaining and informative book that will even appeal to readers with only limited knowledge of mathematics.\"--Physics World \"With seven years of diligent study, by going through a vast amount of archive material, references including primary sources and books and research papers, the author has produced a carefully documented and fascinating account to substantiate the theme he makes, namely, that Franklin 'possessed a mathematical mind.'\"--Man Keung Siu, Mathematical Reviews \"[Paul C. Pasles] and the publisher should ... be commended for producing a highly aesthetically pleasing book, with a color centerpiece showing many of Franklin's beloved magic squares in their full glory.\"--Eli Maor, SIAM Review \"This book will appeal to readers with an interdisciplinary interest in both history and mathematics. Teachers who enjoy showing students the many ways in which they can draw on mathematics to construct logical, real-world arguments will find useful examples for the classroom. The book also includes a variety of number puzzles that can be used to challenge students.\"--Michelle Cirillo, Mathematics Teacher \"I found Benjamin Franklin's Numbers a delightful book. I enjoyed studying and playing with the magic squares and patterns, and I was fascinated by the biographical tidbits about Franklin. This book is very well written, and I highly recommend it to anyone with an interest in mathematics or in Benjamin Franklin.\"--James V. 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This title includes helpful hints for when students are unsure of how to get started on a given problem.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"An excellent contribution to the list of elementary number theory textbooks. Number theory, it is true, has as rich a history as any branch of mathematics, and Watkins has done terrific work in integrating the stories of the people behind this subject with the traditional topics of elementary number theory. There is more than enough material here for a one-semester course, and while this is standard for textbooks at this level, the added historical and biographical material--which cover mathematical developments and people well into the 20th century--are well worth the increased weight of the text.\"--Mark Bollman, MAA Reviews","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403801076055,"sku":"9780691159409","price":71.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691159409.jpg?v=1730484585"},{"product_id":"count-like-an-egyptian-9780691160122","title":"Count Like an Egyptian","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe mathematics of ancient Egypt was fundamentally different from our math today. Contrary to what people might think, it wasn't a primitive forerunner of modern mathematics. This title provides an introduction to the intuitive and often-surprising art of ancient Egyptian math.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Count Like an Egyptian would make an excellent addition to math classrooms at many different levels. Reimer includes problems in the text and solutions in the back of the book, so the reader can practice techniques and get a feel for exactly how the system works as they go through the book. The mathematics is basic enough to be helpful for children learning fractions or multiplication for the first time, but it's also different enough from the methods most of us know that adults will get a lot out of it as well.\"--Evelyn Lamb, Scientific American \"History lovers will gain much more than just insight into the Egyptian mind-set. The author interleaves mathematical exposition with short essays on Egyptian history, culture, geography, mythology--all, like the rest of the book, beautifully illustrated... For a lively and inquiring mind the book has a good deal to offer. It is well written, lavishly illustrated, and just awfully interesting. The book is a pleasure to hold, to browse, and to read.\"--Alexander Bogomolny, Cut the Knot \"You get the feeling that David Reimer must be a pretty entertaining teacher. An associate professor of mathematics at the College of New Jersey, he has taken on the task of explaining ancient math systems by having you use them. And though it's not easy, he manages to lead you, step by step, through a hieroglyphic based calculation of how many 10-pesu loaves of bread you can make from seven hekat of grain.\"--Nancy Szokan, Washington Post \"An interesting combination of history, ancient literature and mythology, arithmetic puzzles and mathematics, and lavishly illustrated with numerous colour diagrams, this engaging book is unusual, thought-provoking and just plain fun to read.\"--Devorah Bennu, GrrlScientist, The Guardian \"Count Like an Egyptian is a beautifully illustrated and well-written book... Reimer's overriding goal is to demonstrate that Egyptian fraction arithmetic is fascinating, versatile, and well suited for whatever calls fractions into existence... By working through the material Reimer patiently and gently presents, the reader will have a more thorough understanding and appreciation of how Egyptian scribes made the calculations needed to administer an empire bent on building pyramids and granaries, surveying flooded riverside property, digging irrigation basins, and rationing or exchanging bread and beer supplies amongst its gangs of workers... This book should find a home in libraries used by middle school and high school mathematics teachers. It also provides a good resource for mathematics education professors and their students on the college level as they explore historical beginnings of mathematical ideas, make cultural comparisons, and develop interdisciplinary connections.\"--Calvin Jongsma, MAA Reviews \"An interesting combination of history, ancient literature and mythology, arithmetic puzzles and mathematics, and lavishly illustrated with numerous colour diagrams, this engaging book is unusual, thought-provoking and just plain fun to read.\"--GrrrlScientist \"This amusing popular introduction to an uncommon subject is a mental adventure that sheds new light on the thought processes of a lost civilization and will appeal both to those who enjoy mathematical puzzles and to Egyptophiles.\"--Edward K. Werner, Library Journal \"In general I really like this book and believe it is, if not necessarily a must for all Egyptophiles, then definitely one to put on the wish list as an interesting addition to your bookshelf... It is fun way of working through complicated and yet practical mathematics which makes the Rhind Papyrus come alive and gives an insight into the logical brain of ancient Egyptian scribes.\"--Charlotte Booth, charlottesegypt.com \"Reimer succeeds very well in transferring his enthusiasm tor the Egyptian system to the reader. The reactions from his students who were used tor a try-out are claimed to be positive. But even if you do not want to graduate as an Egyptian scribe, you may be charmed by the witty Egyptian system and you will be delighted by the colourful illustrations and Reimer's entertaining account of it all.\"--A. Bultheel, European Mathematical Society \"Count Like an Egyptian takes the reader step-by-step through the ancient Egyptian methods, which are surprisingly different from our own, and yet, in the capable hands of author David Reimer, surprisingly understandable. This lovely book has fun illustrations to demonstrate the various operations, basic geometry, and other tasks faced by the scribes... This book is a pleasure to read and makes Egyptian math a pleasure to learn.\"--Gretchen Wagner, San Francisco Book Review \"The book is intended to be used as a teaching tool and includes practice examples for the student. It would be difficult to imagine a work that more effectively covers this aspect of the ancient civilization.\"--JPP, Ancient Egypt \"David Reimer succeeds in keeping the mathematics in Count Like an Egyptian clever and light, raising this book into a rare category: a coffee table book that is serious and fun.\"--Robert Schaefer, New York Journal of Books \"This volume is ideal for anyone, and I truly mean anyone, young or old, mathematician, student or teacher, who wants to learn how the ancient Egyptians did mathematics... This book has all the Egyptian mathematics a general mathematician, teacher or student could ever want to learn. In particular it would be a perfect resource for a schoolteacher, elementary through lower division college. The material is presented in a direct and accessible manner.\"--Amy Shell-Gellasch, CSHPM Bulletin \"Overall this is a didactic and well written book, with many important illustrations, with some incursions in the mathematics of other ancient cultures.\"--European Mathematical Society \"With Reimer's guidance, motivating stories, and lighthearted remarks, readers can become facile with Egyptian algorithms and the insights they reveal... Valuable for all readers looking for a guided of an alternative to traditional school arithmetic and the torpor that algorithmic training causes.\"--Choice \"[T]his book is a worthwhile read for anyone interested in seeing exactly how ancient Egyptians dealt with mathematics. It will help put our present algorithms into perspective as simply one of many possible algorithms one could use to perform arithmetic operations.\"--Victor J. Katz, Mathematical Reviews Clippings \"[Reimer] ... set himself to understand and explain the ancient methods, and the result is an approachable, thorough and lavishly-produced book.\"--Owen Toller, Mathematical Gazette \"Count like an Egyptian is a beautifully glossy and colourful book; the presentation of hieroglyphs is particularly well done, and fully interated into the surrounding text... This book has given me a new perspective on day-to-day arithmetic.\"--Christopher Hollings, Mathematics Today \"This is a wonderful book, very well written, filled with illustrations on every page, witty, addressing anyone interested in grade school arithmetic.\"--Victor V. Pambuccian, Zentralblatt MATH \"Count Like an Egyptian is important for anyone interested in alternative algorithms... If you want to roll up your sleeves and learn some new mathematics, this is the book for you.\"--Michael Manganello, Mathematics Teacher \"An engaging and beautifully illustrated book that deals with the basics of ancient Egyptian mathematics, set in the wider context of other ancient mathematical systems.\"--Corinna Rossi, Aestimatio \"A great approach and a dedicated effort. One hopes the book will reflect that persistence and it does... This is a book that comes recommended, for anyone who wants to know where our current basis of mathematics comes from through to those with an interest in maths and history.\"--Gordon Clarke, Gazette of the Australian Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  Introduction ix  Computation Tables xi  1 Numbers 1  2 Fractions 13  3 Operations 22  4 Simplification 55  5 Techniques and Strategies 80  6 Miscellany 121  7 Base-Based Mathematics 144  8 Judgment Day 182  Practice Solutions 209  Index 235","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403802354007,"sku":"9780691160122","price":25.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691160122.jpg?v=1730484589"},{"product_id":"summing-it-up-from-one-plus-one-to-modern-number-theory-9780691170190","title":"Summing It Up  From One Plus One to Modern Number","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Offers a clear and beautiful progression from addition to modern number theory.\"--Math-Blog \"The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book.\"--Adhemar Bultheel, European Mathematical Society \"Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing.\"--Choice \"[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor.\"--Dominic Lanphier, American Mathematical Monthly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. xi*ACKNOWLEDGMENTS, pg. xv*INTRODUCTION: WHAT THIS BOOK IS ABOUT, pg. 1*CHAPTER 1. PROEM, pg. 11*CHAPTER 2. SUMS OF TWO SQUARES, pg. 22*CHAPTER 3. SUMS OF THREE AND FOUR SQUARES, pg. 32*CHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM, pg. 37*CHAPTER 5. SIMPLE SUMS, pg. 42*CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA, pg. 50*CHAPTER 7. INFINITE SERIES, pg. 73*CHAPTER 8. CAST OF CHARACTERS, pg. 96*CHAPTER 9. ZETA AND BERNOULLI, pg. 103*CHAPTER 10. COUNT THE WAYS, pg. 110*CHAPTER 11. THE UPPER HALF-PLANE, pg. 127*CHAPTER 12. MODULAR FORMS, pg. 147*CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE?, pg. 160*CHAPTER 14. CONGRUENCE GROUPS, pg. 179*CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED, pg. 186*CHAPTER 16. MORE THEORY OF MODULAR FORMS, pg. 201*CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS, pg. 213*BIBLIOGRAPHY, pg. 225*INDEX, pg. 227","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403826635095,"sku":"9780691170190","price":19.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691170190.jpg?v=1730484657"},{"product_id":"summing-it-up-from-one-plus-one-to-modern-number-theory-9780691178516","title":"Summing It Up  From One Plus One to Modern Number","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Offers a clear and beautiful progression from addition to modern number theory.\"--Math-Blog \"The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book.\"--Adhemar Bultheel, European Mathematical Society \"Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing.\"--Choice \"[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor.\"--Dominic Lanphier, American Mathematical Monthly\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. xi*ACKNOWLEDGMENTS, pg. xv*INTRODUCTION: WHAT THIS BOOK IS ABOUT, pg. 1*CHAPTER 1. PROEM, pg. 11*CHAPTER 2. SUMS OF TWO SQUARES, pg. 22*CHAPTER 3. SUMS OF THREE AND FOUR SQUARES, pg. 32*CHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM, pg. 37*CHAPTER 5. SIMPLE SUMS, pg. 42*CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA, pg. 50*CHAPTER 7. INFINITE SERIES, pg. 73*CHAPTER 8. CAST OF CHARACTERS, pg. 96*CHAPTER 9. ZETA AND BERNOULLI, pg. 103*CHAPTER 10. COUNT THE WAYS, pg. 110*CHAPTER 11. THE UPPER HALF-PLANE, pg. 127*CHAPTER 12. MODULAR FORMS, pg. 147*CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE?, pg. 160*CHAPTER 14. CONGRUENCE GROUPS, pg. 179*CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED, pg. 186*CHAPTER 16. MORE THEORY OF MODULAR FORMS, pg. 201*CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS, pg. 213*BIBLIOGRAPHY, pg. 225*INDEX, pg. 227","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403852554583,"sku":"9780691178516","price":15.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691178516.jpg?v=1730484720"},{"product_id":"millions-billions-zillions-9780691182773","title":"Millions Billions Zillions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Having a healthy skepticism toward numbers and giving readers the tools to think about math more logically is the purpose of this easily read, slight book. Brian W. Kernighan adroitly distills complex issues. His tone is more that of a mellow friend breaking down a concept that flummoxes you rather than an Ivy League professor expounding on the elegance of numbers.\"\u003cb\u003e---Jacqueline Cutler, \u003ci\u003eNJ.com\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Numbers, graphs and statistics can often be misleading and misrepresented. In \u003ci\u003eMillions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers\u003c\/i\u003e, Kernighan provides the reader with an entertaining and useful guide to avoid becoming a victim of number abuse.\"\u003cb\u003e---Ben Rothke, \u003ci\u003eRSA Conference\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"I can wholeheartedly recommend reading this book, because of the infectious way the author describes his interaction with numbers.\"\u003cb\u003e---J. Herret, \u003ci\u003eInternational Mathematical News\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This is a must-read for anyone looking to cure their “number numbness”\"\u003cb\u003e---Tibi Puiu, \u003ci\u003eZME Science\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403863859543,"sku":"9780691182773","price":17.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691182773.jpg?v=1730484747"},{"product_id":"millions-billions-zillions-9780691209098","title":"Millions Billions Zillions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403899216215,"sku":"9780691209098","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691209098.jpg?v=1730484833"},{"product_id":"when-least-is-best-9780691218762","title":"When Least Is Best","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Nahin has written a beautifully clear, fascinating book on a topic which is truly vital to so many areas of science and I would recommend anyone who enjoys puzzle solving and having new tools to tackle old (or new) problems should read it.\"\u003cb\u003e---Jonathan Shock, \u003ci\u003eMathemafrica\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403909603671,"sku":"9780691218762","price":15.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691218762.jpg?v=1730484860"},{"product_id":"basic-math-prealgebra-allinone-for-dummies-chapter-quizzes-online-9781119867081","title":"Basic Math  PreAlgebra AllinOne For Dummies","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eIntroduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAbout This Book 1\u003c\/p\u003e \u003cp\u003eFoolish Assumptions 2\u003c\/p\u003e \u003cp\u003eIcons Used in This Book 2\u003c\/p\u003e \u003cp\u003eBeyond the Book 3\u003c\/p\u003e \u003cp\u003eWhere to Go from Here 3\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 1: Getting Started with Basic Math \u0026amp; Pre-algebra 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1: Playing the Numbers Game 7\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eInventing Numbers 8\u003c\/p\u003e \u003cp\u003eUnderstanding Number Sequences 8\u003c\/p\u003e \u003cp\u003eEvening the odds 8\u003c\/p\u003e \u003cp\u003eCounting by threes, fours, fives, and so on 9\u003c\/p\u003e \u003cp\u003eGetting square with square numbers 9\u003c\/p\u003e \u003cp\u003eComposing yourself with composite numbers 10\u003c\/p\u003e \u003cp\u003eStepping out of the box with prime numbers 11\u003c\/p\u003e \u003cp\u003eMultiplying quickly with exponents 12\u003c\/p\u003e \u003cp\u003eFour Important Sets of Numbers 13\u003c\/p\u003e \u003cp\u003eCounting on the counting numbers 13\u003c\/p\u003e \u003cp\u003eIntroducing integers 13\u003c\/p\u003e \u003cp\u003eStaying rational 14\u003c\/p\u003e \u003cp\u003eGetting real 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2: The Big Four Operations 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Big Four Operations 15\u003c\/p\u003e \u003cp\u003eAdding things up: Addition 16\u003c\/p\u003e \u003cp\u003eTake it away: Subtraction 16\u003c\/p\u003e \u003cp\u003eA sign of the times: Multiplication 17\u003c\/p\u003e \u003cp\u003eDoing math lickety-split: Division 18\u003c\/p\u003e \u003cp\u003eApplying the Big Four Operations to Larger Numbers 18\u003c\/p\u003e \u003cp\u003eCalculating stacked addition 18\u003c\/p\u003e \u003cp\u003ePerforming stacked subtraction 19\u003c\/p\u003e \u003cp\u003eCalculating with stacked multiplication 21\u003c\/p\u003e \u003cp\u003eUnderstanding long division 22\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3: Counting on Success: Numbers and Digits 27\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eKnowing Your Place Value 28\u003c\/p\u003e \u003cp\u003eCounting to ten and beyond 28\u003c\/p\u003e \u003cp\u003eTelling placeholders from leading zeros 29\u003c\/p\u003e \u003cp\u003eReading long numbers 30\u003c\/p\u003e \u003cp\u003eClose Enough for Rock ‘n’ Roll: Rounding and Estimating 30\u003c\/p\u003e \u003cp\u003eRounding numbers 30\u003c\/p\u003e \u003cp\u003eEstimating value to make problems easier 32\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 34\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 3 Quiz 35\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 3 Quiz 36\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4: Staying Positive with Negative Numbers 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Where Negative Numbers Come From 38\u003c\/p\u003e \u003cp\u003eSign-Switching: Understanding Negation and Absolute Value 39\u003c\/p\u003e \u003cp\u003eAddition and Subtraction with Negative Numbers 41\u003c\/p\u003e \u003cp\u003eStarting with a negative number 41\u003c\/p\u003e \u003cp\u003eAdding a negative number 41\u003c\/p\u003e \u003cp\u003eSubtracting a negative number 42\u003c\/p\u003e \u003cp\u003eKnowing Signs of the Times (and Division) for Negative Numbers 44\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 47\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 4 Quiz 51\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 4 Quiz 52\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5: Putting the Big Four Operations to Work 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSwitching Things Up with Inverse Operations and the Commutative Property 56\u003c\/p\u003e \u003cp\u003eGetting with the In-Group: Parentheses and the Associative Property 59\u003c\/p\u003e \u003cp\u003eDistribution to lighten the load 61\u003c\/p\u003e \u003cp\u003eUnderstanding Inequalities 63\u003c\/p\u003e \u003cp\u003eDoesn’t equal (≠) 63\u003c\/p\u003e \u003cp\u003eLess than (\u0026lt;) and greater than (\u0026gt;) 63\u003c\/p\u003e \u003cp\u003eLess than or equal to (≤) and greater than or equal to (≥) 64\u003c\/p\u003e \u003cp\u003eApproximately equals (≈) 64\u003c\/p\u003e \u003cp\u003eMoving Beyond the Big Four: Exponents and Square Roots 65\u003c\/p\u003e \u003cp\u003eUnderstanding exponents 66\u003c\/p\u003e \u003cp\u003eDiscovering your roots 67\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 69\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 5 Quiz 72\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 5 Quiz 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 3: Getting a Handle on Whole Numbers 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Three E’s of Math: Equations, Expressions, and Evaluation 78\u003c\/p\u003e \u003cp\u003eSeeking equality for all: Equations 78\u003c\/p\u003e \u003cp\u003eHey, it’s just an expression 78\u003c\/p\u003e \u003cp\u003eEvaluating the situation 79\u003c\/p\u003e \u003cp\u003ePutting the Three E’s together 79\u003c\/p\u003e \u003cp\u003eIntroducing Order of Operations (PEMDAS) 80\u003c\/p\u003e \u003cp\u003eExpressions with only addition and subtraction 81\u003c\/p\u003e \u003cp\u003eExpressions with only multiplication and division 81\u003c\/p\u003e \u003cp\u003eMixed-operator expressions 82\u003c\/p\u003e \u003cp\u003eHandling Powers Responsibly 83\u003c\/p\u003e \u003cp\u003ePrioritizing parentheses 84\u003c\/p\u003e \u003cp\u003ePulling apart parentheses and powers 85\u003c\/p\u003e \u003cp\u003eFiguring out nested parentheses 86\u003c\/p\u003e \u003cp\u003eBringing It All Together: The Order of Operations 87\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 89\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 6 Quiz 98\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 6 Quiz 99\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7: Turning Words into Numbers: Basic Math Word Problems 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDispelling Two Myths about Word Problems 104\u003c\/p\u003e \u003cp\u003eWord problems aren’t always hard 104\u003c\/p\u003e \u003cp\u003eWord problems are useful 104\u003c\/p\u003e \u003cp\u003eSolving Basic Word Problems 105\u003c\/p\u003e \u003cp\u003eTurning word problems into word equations 105\u003c\/p\u003e \u003cp\u003ePlugging in numbers for words 109\u003c\/p\u003e \u003cp\u003eSend in the clowns 109\u003c\/p\u003e \u003cp\u003eOur house in the middle of our street 110\u003c\/p\u003e \u003cp\u003eI hear the train a-comin’ 110\u003c\/p\u003e \u003cp\u003eSolving More-Complex Word Problems 113\u003c\/p\u003e \u003cp\u003eWhen numbers get serious 113\u003c\/p\u003e \u003cp\u003eToo much information 115\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 120\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 7 Quiz 124\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 7 Quiz 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8: Divisibility and Prime Numbers 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eKnowing the Divisibility Tricks 128\u003c\/p\u003e \u003cp\u003eCounting everyone in: Numbers you can divide everything by 128\u003c\/p\u003e \u003cp\u003eIn the end: Looking at the final digits 128\u003c\/p\u003e \u003cp\u003eCount it up: Checking divisibility by adding and subtracting digits 130\u003c\/p\u003e \u003cp\u003eLess is more: Checking divisibility by subtracting 134\u003c\/p\u003e \u003cp\u003eCross-checking: Using multiple tests 135\u003c\/p\u003e \u003cp\u003eIdentifying Prime and Composite Numbers 136\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 139\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 8 Quiz 142\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 8 Quiz 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9: Divided Attention: Factors and Multiples 145\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eKnowing Six Ways to Say the Same Thing 146\u003c\/p\u003e \u003cp\u003eUnderstanding Factors and Multiples 146\u003c\/p\u003e \u003cp\u003eFinding Fabulous Factors 148\u003c\/p\u003e \u003cp\u003eDeciding when one number is a factor of another 148\u003c\/p\u003e \u003cp\u003eUnderstanding factor pairs 148\u003c\/p\u003e \u003cp\u003eGenerating a Number’s Factors 149\u003c\/p\u003e \u003cp\u003eDecomposing a Number into Its Prime Factors 150\u003c\/p\u003e \u003cp\u003eFinding the Greatest Common Factor 151\u003c\/p\u003e \u003cp\u003eGenerating the Multiples of a Number 153\u003c\/p\u003e \u003cp\u003eFinding the Least Common Multiple 153\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 155\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 9 Quiz 158\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 9 Quiz 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 4: Fractions 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10: Understanding Fractions 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSlicing a Cake into Fractions 164\u003c\/p\u003e \u003cp\u003eKnowing the Fraction Facts of Life 165\u003c\/p\u003e \u003cp\u003eTelling the numerator from the denominator 165\u003c\/p\u003e \u003cp\u003eFlipping for reciprocals 166\u003c\/p\u003e \u003cp\u003eUsing ones and zeros 166\u003c\/p\u003e \u003cp\u003eMixing things up 167\u003c\/p\u003e \u003cp\u003eKnowing proper from improper 167\u003c\/p\u003e \u003cp\u003eIncreasing and Reducing Terms of Fractions 169\u003c\/p\u003e \u003cp\u003eIncreasing the terms of fractions 170\u003c\/p\u003e \u003cp\u003eReducing fractions to lowest terms (simplifying fractions) 171\u003c\/p\u003e \u003cp\u003eConverting between Improper Fractions and Mixed Numbers 174\u003c\/p\u003e \u003cp\u003eKnowing the parts of a mixed number 174\u003c\/p\u003e \u003cp\u003eConverting a mixed number to an improper fraction 175\u003c\/p\u003e \u003cp\u003eConverting an improper fraction to a mixed number 176\u003c\/p\u003e \u003cp\u003eComparing Fractions with Cross-Multiplication 178\u003c\/p\u003e \u003cp\u003eWorking with Ratios and Proportions 180\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 182\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 10 Quiz 188\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 10 Quiz 189\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11: Fractions and the Big Four Operations 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMultiplying and Dividing Fractions 192\u003c\/p\u003e \u003cp\u003eMultiplying numerators and denominators straight across 192\u003c\/p\u003e \u003cp\u003eDoing a flip to divide fractions 194\u003c\/p\u003e \u003cp\u003eAdding and Subtracting Fractions with the Same Denominator 196\u003c\/p\u003e \u003cp\u003eAdding and Subtracting Fractions with Different Denominators 198\u003c\/p\u003e \u003cp\u003eThe easy case: Increasing the terms of one fraction 198\u003c\/p\u003e \u003cp\u003eThe difficult case: Increasing the terms of both fractions 200\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 202\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 11 Quiz 208\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 11 Quiz 209\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12: Mixing Things Up with Mixed Numbers 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMultiplying and Dividing Mixed Numbers 214\u003c\/p\u003e \u003cp\u003eAdding Mixed Numbers 216\u003c\/p\u003e \u003cp\u003eAdding mixed numbers that have the same denominator 216\u003c\/p\u003e \u003cp\u003eAdding mixed numbers that have different denominators 217\u003c\/p\u003e \u003cp\u003eAdding mixed numbers with carrying 217\u003c\/p\u003e \u003cp\u003eSubtracting Mixed Numbers 220\u003c\/p\u003e \u003cp\u003eSubtracting mixed numbers that have the same denominator 220\u003c\/p\u003e \u003cp\u003eSubtracting mixed numbers that have different denominators 221\u003c\/p\u003e \u003cp\u003eSubtracting mixed numbers with borrowing 222\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 225\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 12 Quiz 233\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 12 Quiz 234\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 5: Decimals and Percents 241\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 13: Getting to the Point with Decimals 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Basic Decimal Stuff 244\u003c\/p\u003e \u003cp\u003eCounting dollars and decimals 244\u003c\/p\u003e \u003cp\u003eIdentifying the place value of decimals 246\u003c\/p\u003e \u003cp\u003eKnowing the decimal facts of life 247\u003c\/p\u003e \u003cp\u003ePerforming the Big Four Operations with Decimals 252\u003c\/p\u003e \u003cp\u003eAdding decimals 253\u003c\/p\u003e \u003cp\u003eSubtracting decimals 254\u003c\/p\u003e \u003cp\u003eMultiplying decimals 256\u003c\/p\u003e \u003cp\u003eDividing decimals 257\u003c\/p\u003e \u003cp\u003eConverting between Decimals and Fractions 262\u003c\/p\u003e \u003cp\u003eSimple Decimal-Fraction Conversions 262\u003c\/p\u003e \u003cp\u003eChanging decimals to fractions 264\u003c\/p\u003e \u003cp\u003eChanging fractions to decimals 267\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 271\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 13 Quiz 279\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 13 Quiz 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 14: Playing the Percentages 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMaking Sense of Percentages 285\u003c\/p\u003e \u003cp\u003eDealing with Percentages Greater than 100% 286\u003c\/p\u003e \u003cp\u003eConverting to and from Percentages, Decimals, and Fractions 287\u003c\/p\u003e \u003cp\u003eConverting Percentages to Decimals 287\u003c\/p\u003e \u003cp\u003eChanging Decimals to Percentages 288\u003c\/p\u003e \u003cp\u003eSwitching from Percentages to Fractions 288\u003c\/p\u003e \u003cp\u003eConverting Fractions to Percentages 289\u003c\/p\u003e \u003cp\u003eSolving Percentage Problems 290\u003c\/p\u003e \u003cp\u003eFiguring out simple percent problems 291\u003c\/p\u003e \u003cp\u003eTurning the problem around 292\u003c\/p\u003e \u003cp\u003eDeciphering more-difficult percent problems 293\u003c\/p\u003e \u003cp\u003ePutting All the Percent Problems Together 294\u003c\/p\u003e \u003cp\u003eIdentifying the three types of percent problems 294\u003c\/p\u003e \u003cp\u003eSolving Percent Problems with Equations 295\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 299\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 14 Quiz 303\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 14 Quiz 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 15: Word Problems with Fractions, Decimals, and Percentages 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAdding and Subtracting Parts of the Whole in Word Problems 308\u003c\/p\u003e \u003cp\u003eSharing a pizza: Fractions 308\u003c\/p\u003e \u003cp\u003eBuying by the pound: Decimals 309\u003c\/p\u003e \u003cp\u003eSplitting the vote: Percentages 309\u003c\/p\u003e \u003cp\u003eProblems about Multiplying Fractions 310\u003c\/p\u003e \u003cp\u003eRenegade grocery shopping: Buying less than they tell you to 310\u003c\/p\u003e \u003cp\u003eEasy as pie: Working out what’s left on your plate 311\u003c\/p\u003e \u003cp\u003eMultiplying Decimals and Percentages in Word Problems 313\u003c\/p\u003e \u003cp\u003eTo the end: Figuring out how much money is left 313\u003c\/p\u003e \u003cp\u003eFinding out how much you started with 314\u003c\/p\u003e \u003cp\u003eHandling Percent Increases and Decreases in Word Problems 316\u003c\/p\u003e \u003cp\u003eRaking in the dough: Finding salary increases 316\u003c\/p\u003e \u003cp\u003eEarning interest on top of interest 316\u003c\/p\u003e \u003cp\u003eGetting a deal: Calculating discounts 317\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 319\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 15 Quiz 322\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 15 Quiz 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 6: Reaching the Summit: Advanced Pre-algebra Topics 327\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 16: Powers and Roots 329\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMemorizing Powers and Roots 329\u003c\/p\u003e \u003cp\u003eRemembering square numbers and square roots 330\u003c\/p\u003e \u003cp\u003eKeeping track of cubic numbers and cube roots 330\u003c\/p\u003e \u003cp\u003eKnowing a few powers of 2 and their related roots 331\u003c\/p\u003e \u003cp\u003eChanging the Base 332\u003c\/p\u003e \u003cp\u003eNegating a number raised to an exponent 332\u003c\/p\u003e \u003cp\u003eFinding powers of negative numbers 332\u003c\/p\u003e \u003cp\u003eFinding powers of fractions 333\u003c\/p\u003e \u003cp\u003eMixing negative numbers and fractions with exponents 333\u003c\/p\u003e \u003cp\u003eExponents of 0 and Negative Numbers 334\u003c\/p\u003e \u003cp\u003eExponents of 0 334\u003c\/p\u003e \u003cp\u003eNegative exponents 335\u003c\/p\u003e \u003cp\u003eFractional Exponents 337\u003c\/p\u003e \u003cp\u003eExponents of 1 2 337\u003c\/p\u003e \u003cp\u003eExponents of 1 3 338\u003c\/p\u003e \u003cp\u003eExponents of 1 4 , 1 5 , 1 , and so forth 6 339\u003c\/p\u003e \u003cp\u003eOther fractional exponents 339\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 341\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 16 Quiz 343\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 16 Quiz 344\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFirst Things First: Using Powers of Ten as Exponents 348\u003c\/p\u003e \u003cp\u003eCounting zeros and writing exponents 348\u003c\/p\u003e \u003cp\u003eExponential Arithmetic: Multiplying and Dividing Powers of Ten 350\u003c\/p\u003e \u003cp\u003eWorking with Scientific Notation 352\u003c\/p\u003e \u003cp\u003eWriting in scientific notation 352\u003c\/p\u003e \u003cp\u003eUnderstanding order of magnitude 354\u003c\/p\u003e \u003cp\u003eMultiplying with scientific notation 355\u003c\/p\u003e \u003cp\u003eDividing with Scientific Notation 356\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 357\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 17 Quiz 360\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 17 Quiz 361\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 18: How Much Have You Got? Weights and Measures 363\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Units 364\u003c\/p\u003e \u003cp\u003eAdding and subtracting units 364\u003c\/p\u003e \u003cp\u003eMultiplying and dividing units 364\u003c\/p\u003e \u003cp\u003eExamining Differences between the English and Metric Systems 365\u003c\/p\u003e \u003cp\u003eLooking at the English system 365\u003c\/p\u003e \u003cp\u003eLooking at the metric system 369\u003c\/p\u003e \u003cp\u003eEstimating and Converting between the English and Metric Systems 372\u003c\/p\u003e \u003cp\u003eEstimating in the metric system 373\u003c\/p\u003e \u003cp\u003eConverting units of measurement 375\u003c\/p\u003e \u003cp\u003eConverting between English and Metric Units 377\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 381\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 18 Quiz 388\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 18 Quiz 389\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 19: Getting the Picture with Geometry 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGetting on the Plane: Points, Lines, Angles, and Shapes 394\u003c\/p\u003e \u003cp\u003eMaking some points 394\u003c\/p\u003e \u003cp\u003eKnowing your lines 394\u003c\/p\u003e \u003cp\u003eFiguring the angles 395\u003c\/p\u003e \u003cp\u003eShaping things up 396\u003c\/p\u003e \u003cp\u003eGetting in Shape: Polygon (and Non-Polygon) Basics 396\u003c\/p\u003e \u003cp\u003eClosed Encounters: Shaping Up Your Understanding of 2-D Shapes 397\u003c\/p\u003e \u003cp\u003ePolygons 397\u003c\/p\u003e \u003cp\u003eCircles 399\u003c\/p\u003e \u003cp\u003eSquaring Off with Quadrilaterals 400\u003c\/p\u003e \u003cp\u003eMaking a Triple Play with Triangles 403\u003c\/p\u003e \u003cp\u003eGetting Around with Circle Measurements 405\u003c\/p\u003e \u003cp\u003eTaking a Trip to Another Dimension: Solid Geometry 406\u003c\/p\u003e \u003cp\u003eThe many faces of polyhedrons 407\u003c\/p\u003e \u003cp\u003e3-D shapes with curves 408\u003c\/p\u003e \u003cp\u003eBuilding Solid Measurement Skills 409\u003c\/p\u003e \u003cp\u003eSolving Geometry Word Problems 413\u003c\/p\u003e \u003cp\u003eWorking from words and images 413\u003c\/p\u003e \u003cp\u003eBreaking out those sketching skills 415\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 418\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 19 Quiz 425\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 19 Quiz 427\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 20: Figuring Your Chances: Statistics and Probability 431\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGathering Data Mathematically: Basic Statistics 432\u003c\/p\u003e \u003cp\u003eUnderstanding differences between qualitative and quantitative data 432\u003c\/p\u003e \u003cp\u003eWorking with qualitative data 433\u003c\/p\u003e \u003cp\u003eWorking with quantitative data 436\u003c\/p\u003e \u003cp\u003eLooking at Likelihoods: Basic Probability 439\u003c\/p\u003e \u003cp\u003eFiguring the probability 440\u003c\/p\u003e \u003cp\u003eOh, the possibilities! Counting outcomes with multiple coins 441\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 444\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 20 Quiz 447\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 20 Quiz 449\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 21: Setting Things Up with Basic Set Theory 451\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Sets 451\u003c\/p\u003e \u003cp\u003eElementary, my dear: Considering what’s inside sets 452\u003c\/p\u003e \u003cp\u003eSets of numbers 454\u003c\/p\u003e \u003cp\u003ePerforming Operations on Sets 455\u003c\/p\u003e \u003cp\u003eUnion: Combined elements 455\u003c\/p\u003e \u003cp\u003eIntersection: Elements in common 456\u003c\/p\u003e \u003cp\u003eRelative complement: Subtraction (sorta) 457\u003c\/p\u003e \u003cp\u003eComplement: Feeling left out 457\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 459\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 21 Quiz 461\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 21 Quiz 462\u003c\/p\u003e \u003cp\u003e\u003cb\u003eUnit 7: the X-files: Introduction to Algebra 463\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 22: Working with Algebraic Expressions 465\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSeeing How X Marks the Spot 466\u003c\/p\u003e \u003cp\u003eExpressing Yourself with Algebraic Expressions 466\u003c\/p\u003e \u003cp\u003eEvaluating Algebraic Expressions 467\u003c\/p\u003e \u003cp\u003eKnowing the Terms 470\u003c\/p\u003e \u003cp\u003eMaking the commute: Rearranging your terms 471\u003c\/p\u003e \u003cp\u003eIdentifying the coefficient and variable 472\u003c\/p\u003e \u003cp\u003eAdding and Subtracting Like Terms 473\u003c\/p\u003e \u003cp\u003eIdentifying like terms 473\u003c\/p\u003e \u003cp\u003eAdding and subtracting terms 474\u003c\/p\u003e \u003cp\u003eMultiplying and Dividing Terms 475\u003c\/p\u003e \u003cp\u003eSimplifying Expressions by Combining Like Terms 479\u003c\/p\u003e \u003cp\u003eRemoving Parentheses from an Algebraic Expression 481\u003c\/p\u003e \u003cp\u003eDrop everything: Parentheses with a plus sign 481\u003c\/p\u003e \u003cp\u003eSign turnabout: Parentheses with a negative sign 481\u003c\/p\u003e \u003cp\u003eDistribution: Parentheses with no sign 482\u003c\/p\u003e \u003cp\u003eFOILing: Dealing with Two Sets of Parentheses 484\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 487\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 22 Quiz 495\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 22 Quiz 496\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 23: Solving Algebraic Equations 499\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eUnderstanding Algebraic Equations 500\u003c\/p\u003e \u003cp\u003eUsing X in Equations 500\u003c\/p\u003e \u003cp\u003eChoosing among four ways to solve algebraic equations 501\u003c\/p\u003e \u003cp\u003eThe Balancing Act: Solving for x 503\u003c\/p\u003e \u003cp\u003eStriking a balance 504\u003c\/p\u003e \u003cp\u003eUsing the Balance Scale to Isolate X 504\u003c\/p\u003e \u003cp\u003eRearranging Equations and Isolating x 506\u003c\/p\u003e \u003cp\u003eRearranging terms on one side of an equation 506\u003c\/p\u003e \u003cp\u003eMoving terms to the other side of the equals sign 507\u003c\/p\u003e \u003cp\u003eRemoving parentheses from equations 509\u003c\/p\u003e \u003cp\u003eCross-multiplying 512\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 515\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 23 Quiz 525\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 23 Quiz 526\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 24: Tackling Algebra Word Problems 531\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eSolving Algebra Word Problems in Five Steps 531\u003c\/p\u003e \u003cp\u003eDeclaring a variable 532\u003c\/p\u003e \u003cp\u003eSetting up the equation 533\u003c\/p\u003e \u003cp\u003eSolving the equation 533\u003c\/p\u003e \u003cp\u003eAnswering the question 534\u003c\/p\u003e \u003cp\u003eChecking your work 534\u003c\/p\u003e \u003cp\u003eChoosing Your Variable Wisely 536\u003c\/p\u003e \u003cp\u003eSolving More-Complex Algebraic Problems 539\u003c\/p\u003e \u003cp\u003eCharting four people 539\u003c\/p\u003e \u003cp\u003eCrossing the finish line with five people 540\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 545\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 24 Quiz 549\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 24 Quiz 550\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 25: Graphing Algebraic Equations 553\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGraphing on the xy-Plane 554\u003c\/p\u003e \u003cp\u003eUnderstanding the axes, the origin, and the quadrants 554\u003c\/p\u003e \u003cp\u003ePlotting coordinates on the xy-plane 554\u003c\/p\u003e \u003cp\u003eGraphing equations on the xy-plane 555\u003c\/p\u003e \u003cp\u003eUnderstanding Linear Equations 559\u003c\/p\u003e \u003cp\u003eKnowing the most basic linear equation 559\u003c\/p\u003e \u003cp\u003eChanging the slope (m) 560\u003c\/p\u003e \u003cp\u003eChanging the y-intercept (b) 561\u003c\/p\u003e \u003cp\u003eUnderstanding slope-intercept form 562\u003c\/p\u003e \u003cp\u003eMeasuring the Slope of a Line 564\u003c\/p\u003e \u003cp\u003eEstimating slope 564\u003c\/p\u003e \u003cp\u003eEyeballing slope on the xy-plane 566\u003c\/p\u003e \u003cp\u003eUsing the two-point slope formula 569\u003c\/p\u003e \u003cp\u003eGraphing Linear Equations Using the Slope and y-intercept 572\u003c\/p\u003e \u003cp\u003ePractice Questions Answers and Explanations 574\u003c\/p\u003e \u003cp\u003eWhaddya Know? Chapter 25 Quiz 577\u003c\/p\u003e \u003cp\u003eAnswers to Chapter 25 Quiz 581\u003c\/p\u003e \u003cp\u003eIndex 583\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407178047831,"sku":"9781119867081","price":24.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119867081.jpg?v=1730498445"},{"product_id":"crocheting-adventures-with-hyperbolic-planes-9781138301153","title":"Crocheting Adventures with Hyperbolic Planes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWinner, Euler Book Prize, awarded by the Mathematical Association of America. With over 200 full color photographs, this non-traditional, tactile introduction to non-Euclidean geometries also covers early development of geometry and connections between geometry, art, nature, and sciences. For the crafter or would-be crafter, there are detailed instructions for how to crochet various geometric models and how to use them in explorations. New to the 2nd Edition; Daina Taimina discusses her own adventures with the hyperbolic planes as well as the experiences of some of her readers. Includes recent applications of hyperbolic geometry such as medicine, architecture, fashion \u0026amp; quantum computing.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"This beautifully and profusely illustrated second edition of \"Crocheting Adventures with Hyperbolic Planes\" is a unique and extraordinary instructional manual and guide that is unreservedly recommended for personal, professional, community, and academic library\"\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e—James A. Cox, Editor-in-Chief, \u003cem\u003eMidwest Book Review\u003c\/em\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"This book shows just how fun deep mathematics can be and reveals the importance of thinking of mathematics with your hands, eyes and body — not just the brain. More importantly, it shows how good mathematics needs input from all sorts of people and cultures, in particular here the geometry essential to fibre arts.\"\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e—Professor Edmund Harris, University of Arkansas, co-author of \u003ci\u003ePatterns\/Visions of the Universe\u003c\/i\u003e with Alex Bellos\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"This is a lovely introduction to hyperbolic geometry and how to represent it in a tactile, playful way. The book takes you through a wonderful history of both the maths and the art, exploring how we have perceived the world around us over the centuries and how this applies today. You get to explore the concepts with your own hands and really see how it all works. As both a mathematician and a crocheter I’m itching to make my own hyperbolic planes and use them in all sorts of places!\"\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e—Samantha Durbin, The Royal Institution of Great Britain\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThis is the second edition of the book Crocheting Adventures with Hyperbolic Planes, which won the 2012 Euler Book Prize[. . . . ]This book presents an amazing hybrid approach to two seemingly different audiences: mathematicians and fiber artists.\u003c\/p\u003e\u003cp\u003eFor the mathematician, the book presents a tactile approach to the very theoretical concepts in hyperbolic geometry, providing clear directions on how to construct objects in hyperbolic geometry. This book is a great introduction to hyperbolic geometry for anyone wanting to know about the subject and would be a great asset to any undergraduate math student studying non-Euclidean geometries.\u003c\/p\u003e\u003cp\u003eFor the fiber artist interested in crochet, the book does a great job of explaining very advanced mathematics in an inviting and understanding way, encouraging artists to pursue more mathematics to incorporate into their creative works. It also provides insight into the creative process of developing mathematics, showing that mathematicians and artists both use very creative processes.\u003c\/p\u003e\u003cp\u003eThis book is extremely well-written and organized. [. . . .] The book also weaves together the history and development of non-Euclidean geometries and their connections to many different areas such as art, biology and nature, physics, computer science, music, chemistry, and architecture. Each chapter has a clear purpose, and the imagery really complements the writing. \u003c\/p\u003e\u003cp\u003eAt the end of the book, there is a section on how to make models. For the artist interested in crochet, the directions are a little bit more mathematical, but they are presented clearly. It will definitely be quite different than any pattern you have read before! For the mathematician who would like to have some tactile hyperbolic models, there are directions for making models out of paper as well. \u003c\/p\u003e\u003cp\u003eThis book is more than just a great introduction to hyperbolic geometry, it is a great book to showcase the work of mathematicians and the process of discovering mathematics. As mathematicians, we often only present our finished and most-polished versions of our work, and we don’t let many people see the process by which this polished mathematics was developed.This book gives the reader insight into that process and illuminates the creativity involved in the development of mathematics.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e—Rachelle Bouchat, \u003cem\u003eMAA Reviews \u003c\/em\u003eOctober 2019\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003ePraise for previous edition\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"2012 Euler Book Prize Winner ...elegant, novel approach... that is perfectly capable of standing on its mathematical feet as a clear, rigorous, and beautifully illustrated introduction to hyperbolic geometry. It is truly a book where art, craft, science, and mathematics come together in perfect harmony.\"\u003cbr\u003e\u003cstrong\u003e—MAA, December 2011\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"This book is richly illustrated with photographs and colored illustrations and it has been produced on high-quality paper. It would be a useful addition to the library of a school or university.\"\u003cbr\u003e\u003cstrong\u003e—\u003cem\u003eGazette-Australia\u003c\/em\u003e, May 2011\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"Daina's crochet models break through the austere, formal stereotype of mathematics and present a path to a whole-brain understanding of a beautiful cluster of simple and significant ideas. The book helps to change the way of thinking about mathematics - an art of human understanding!\"\u003cbr\u003e\u003cstrong\u003e—Corina Mohorianu, Zentralblatt MATH, September 2009\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"The models illustrated in this book are prime examples of art influencing mathematics. Daina provides the necessary instructions for even novices to crochet and create hyperbolic models of their own.\"\u003cbr\u003e\u003cstrong\u003e—Swami Swaminathan, Canadian Mathematical Society Notes, October 2009\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\"It lays out the fundamental knowledge for appreciation of tactile hyperbolic manifolds cautiously and accessibly. ... an enjoyable read for a general audience.\"\u003cbr\u003e\u003cstrong\u003e—David Jacob Wildstrom, \u003cem\u003eMathematical Reviews\u003c\/em\u003e, December 2009\u003c\/strong\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eForeword by William Thurston. Introduction. What Is the Hyperbolic Plane? Can We Crochet It?. What Can You Learn from Your Model?. Four Strands in the History of Geometry. Tidbits from the History of Crochet. What is Non-Euclidean Geometry?. Pseudosphere. Metamorphoses of the Hyperbolic Plane. Other Surfaces with Negative Curvature. Looking for Applications of Hyperbolic Geometry. Hyperbolic Crochet goes Viral. Appendix: How to Make Models.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":49407217598807,"sku":"9781138301153","price":45.59,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781138301153.jpg?v=1730498604"},{"product_id":"proofs-and-fundamentals-9781441971265","title":"Proofs and Fundamentals","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003ethis section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a ‘transition’ course.” (Margret Höft, zbMATH 1012.00013, 2021)\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“The contents of the book is organized in three parts … . this is a nice book, which also this reviewer has used with profit in his teaching of beginner students. It is written in a highly pedagogical style and based upon valuable didactical ideas.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 174, 2014)\u003c\/p\u003e\u003cp\u003e“Books in this category are meant to teach mathematical topics and techniques that will become valuable in more advanced courses. This book meets these criteria. … This book is well suited as a textbook for a transitional course between calculus and more theoretical courses. I also recommend it for academic libraries.” (Edgar R. Chavez, ACM Computing Reviews, February, 2012)\u003c\/p\u003e\u003cp\u003e“This is an improved edition of a good book that can serve in the undergraduate curriculum as a bridge between computationally oriented courses like calculus and more abstract courses like algebra.” (Teun Koetsier, Zentralblatt MATH, Vol. 1230, 2012)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the Second Edition Preface to the First Edition To the Student To the Instructor Part I. Proofs 1. Informal Logic 2. Strategies for Proofs Part II. Fundamentals 3. Sets 4. Functions 5. Relations 6. Finite and Infinite Sets Part III. Extras 7. Selected Topics 8. Explorations Appendix: Properties of Numbers Bibliography Index","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49408340623703,"sku":"9781441971265","price":43.19,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441971265.jpg?v=1730502509"},{"product_id":"exploring-geometry-9781498760805","title":"Exploring Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003e\u003cem\u003eExploring Geometry, Second Edition\u003c\/em\u003e\u003c\/strong\u003e promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFeatures:\u003c\/strong\u003e\u003c\/p\u003e\u003cli\u003eSecond edition of a successful textbook for the first undergraduate course\u003c\/li\u003e\u003cli\u003eEvery major concept is introduced in its historical context and connects the idea with real life\u003c\/li\u003e\u003cli\u003eFocuses on experimentation\u003c\/li\u003e\u003cli\u003eProjects help enhance student learning\u003c\/li\u003e\u003cli\u003eAll major software programs can be used; free software from author\u003c\/li\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eGeometry and the Axiomatic Method\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEarly Origins of Geometry\u003c\/p\u003e\u003cp\u003eThales and Pythagoras\u003c\/p\u003e\u003cp\u003eProject 1 - The Ratio Made of Gold\u003c\/p\u003e\u003cp\u003eThe Rise of the Axiomatic Method\u003c\/p\u003e\u003cp\u003eProperties of the Axiomatic Systems\u003c\/p\u003e\u003cp\u003eEuclid's Axiomatic Geometry\u003c\/p\u003e\u003cp\u003eProject 2 - A Concrete Axiomatic System\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eEuclidean Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAngles, Lines, and Parallels ANGLES, LINES, AND PARALLELS 51\u003c\/p\u003e\u003cp\u003eCongruent Triangles and Pasch's Axiom\u003c\/p\u003e\u003cp\u003eProject 3 - Special Points of a Triangle\u003c\/p\u003e\u003cp\u003eMeasurement and Area\u003c\/p\u003e\u003cp\u003eSimilar Triangles\u003c\/p\u003e\u003cp\u003eCircle Geometry\u003c\/p\u003e\u003cp\u003eProject 4 - Circle Inversion and Orthogonality\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAnalytic Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThe Cartesian Coordinate System\u003c\/p\u003e\u003cp\u003eVector Geometry\u003c\/p\u003e\u003cp\u003eProject 5 - Bezier Curves\u003c\/p\u003e\u003cp\u003eAngles in Coordinate Geometry\u003c\/p\u003e\u003cp\u003eThe Complex Plane\u003c\/p\u003e\u003cp\u003eBirkhoff's Axiomatic System\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eConstructions\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEuclidean Constructions\u003c\/p\u003e\u003cp\u003eProject 6 - Euclidean Eggs\u003c\/p\u003e\u003cp\u003eConstructibility\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eTransformational Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEuclidean Isometries\u003c\/p\u003e\u003cp\u003eReflections\u003c\/p\u003e\u003cp\u003eTranslations\u003c\/p\u003e\u003cp\u003eRotations\u003c\/p\u003e\u003cp\u003eProject 7 - Quilts and Transformations\u003c\/p\u003e\u003cp\u003eGlide Reflections\u003c\/p\u003e\u003cp\u003eStructure and Representation of Isometries\u003c\/p\u003e\u003cp\u003eProject 8 - Constructing Compositions\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eSymmetry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eFinite Plane Symmetry Groups\u003c\/p\u003e\u003cp\u003eFrieze Groups\u003c\/p\u003e\u003cp\u003eWallpaper Groups\u003c\/p\u003e\u003cp\u003eTilting the Plane\u003c\/p\u003e\u003cp\u003eProject 9 - Constructing Tesselations\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eHyperbollic Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eBackground and History\u003c\/p\u003e\u003cp\u003eModels of Hyperbolic Geometry\u003c\/p\u003e\u003cp\u003eBasic Results in Hyperbolic Geometry\u003c\/p\u003e\u003cp\u003eProject 10 - The Saccheri Quadrilateral\u003c\/p\u003e\u003cp\u003eLambert Quadrilaterals and Triangles\u003c\/p\u003e\u003cp\u003eArea in Hyperbolic Geometry\u003c\/p\u003e\u003cp\u003eProject 11 - Tilting the Hyperbolic Plane\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eElliptic Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eBackground and History\u003c\/p\u003e\u003cp\u003ePerpendiculars and Poles in Elliptic Geometry\u003c\/p\u003e\u003cp\u003eProject 12 - Models of Elliptic Geometry\u003c\/p\u003e\u003cp\u003eBasic Results in Elliptic Geometry\u003c\/p\u003e\u003cp\u003eTriangles and Area in Elliptic Geometry\u003c\/p\u003e\u003cp\u003eProject 13 - Elliptic Tiling\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eProjective Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eUniversal Themes\u003c\/p\u003e\u003cp\u003eProject 14 - Perspective and Projection\u003c\/p\u003e\u003cp\u003eFoundations of Projective Geometry\u003c\/p\u003e\u003cp\u003eTransformations and Pappus's Theorem\u003c\/p\u003e\u003cp\u003eModels of Projective Geometry\u003c\/p\u003e\u003cp\u003eProject 15 - Ratios and Harmonics\u003c\/p\u003e\u003cp\u003eHarmonic Sets\u003c\/p\u003e\u003cp\u003eConics and Coordinates\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFractal Geometry\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThe Search for a \"Natural\" Geometry\u003c\/p\u003e\u003cp\u003eSelf-Similarity\u003c\/p\u003e\u003cp\u003eSimilarity Dimension\u003c\/p\u003e\u003cp\u003eProject 16 - An Endlessly Beautiful Snowflake\u003c\/p\u003e\u003cp\u003eContraction Mappings\u003c\/p\u003e\u003cp\u003eFractal Dimension\u003c\/p\u003e\u003cp\u003eProject 17 - IFS Ferns\u003c\/p\u003e\u003cp\u003eAlgorithmic Geometry\u003c\/p\u003e\u003cp\u003eGrammars and Productions\u003c\/p\u003e\u003cp\u003eProject 18 - Words Into Plants\u003c\/p\u003e\u003cp\u003eAppendix A: A Primer on Proofs\u003c\/p\u003e\u003cp\u003eAppendix A □ A Primer on Proofs 497\u003c\/p\u003e\u003cp\u003eAppendix B □ Book I of Euclid’s \u003ci\u003eElements \u003c\/i\u003e\u003c\/p\u003e\u003cp\u003eAppendix C □ Birkhoff’s Axioms \u003c\/p\u003e\u003cp\u003eAppendix D □ Hilbert’s Axioms \u003c\/p\u003e\u003cp\u003eAppendix E □ Wallpaper Groups \u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409293615447,"sku":"9781498760805","price":99.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498760805.jpg?v=1730506313"},{"product_id":"common-core-math-workouts-grade-7-9781622234707","title":"Common Core Math Workouts, Grade 7","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Mark Twain Media","offers":[{"title":"Default Title","offer_id":49410712600919,"sku":"9781622234707","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"john-napier-logarithm-john-9781905267668","title":"John Napier: Logarithm John","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eWhen John Napier published his invention of logarithms in 1614 he was announcing one of the greatest advances in the history of mathematics, and log tables were used universally until the mid 1970s. With his Rabdologia, an ingenious calculating tool composed of numbered rods which came to be known as 'Napier's Bones', he enabled people in the marketplace to do multiplication sums without knowing any multiplication tables. Perhaps the most extraordinary thing about this most extrordinary man was that his great inventions were made without the stimulus of talking to other mathematicians in mainstream Europe. Working away in comparative isolation in a tower house in Scotland, Napier produced methods of calculation that literally changed lives all over the world. He is the father of the slide-rule and the grandfather of today's calculators. Despite his achievements, he remains curiously uncelebrated, and this absorbing story of his life aims to give John Napier his true status. This new edition has been redesigned in a new format and has a new cover.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eReview of first edition: 'What a wonderful little book; it is beautifully written and has wonderful photographs and illustrations ... Moreover it accomplishes its purpose, to give us a glimpse into the nature and times of John Napier.' History of Mathematics Newsletter\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAcknowledgements\u003c\/p\u003e  \u003cp\u003e1 An Astonishing World\u003c\/p\u003e  \u003cp\u003e2 A Privileged Beginning\u003c\/p\u003e  \u003cp\u003e3 A Very Young Student\u003c\/p\u003e  \u003cp\u003e4 Travel was not for the Faint hearted\u003c\/p\u003e  \u003cp\u003e5 The Student comes Home\u003c\/p\u003e  \u003cp\u003e6 A Country Laird or a Sorcerer?\u003c\/p\u003e  \u003cp\u003e7 Weapons against the Spaniards\u003c\/p\u003e  \u003cp\u003e8 Logarithms - The Quantum Leap\u003c\/p\u003e  \u003cp\u003e9 The World's First Pocket Calculator\u003c\/p\u003e  \u003cp\u003e10 Up amongst the Greats\u003c\/p\u003e  \u003cp\u003eSelected Bibliography\u003c\/p\u003e","brand":"NMSE - Publishing Ltd","offers":[{"title":"Default Title","offer_id":49414237651287,"sku":"9781905267668","price":6.78,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781905267668.jpg?v=1730522925"},{"product_id":"fuzzy-logic-recent-applications-and-developments-9783030664763","title":"Fuzzy Logic: Recent Applications and Developments","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eSince its inception, fuzzy logic has attracted an incredible amount of interest, and this interest continues to grow at an exponential rate. As such, scientists, researchers, educators and practitioners of fuzzy logic continue to expand on the applicability of what and how fuzzy can be utilised in the real-world. In this book, the authors present key application areas where fuzzy has had significant success. The chapters cover a plethora of application domains, proving credence to the versatility and robustness of a fuzzy approach.\u003c\/p\u003e  A better understanding of fuzzy will ultimately allow for a better appreciation of fuzzy. This book provides the reader with a varied range of examples to illustrate what fuzzy logic can be capable of and how it can be applied. The text will be ideal for individuals new to the notion of fuzzy, as well as for early career academics who wish to further expand on their knowledge of fuzzy applications. The book is also suitable as a supporting text for advanced undergraduate and graduate-level modules on fuzzy logic, soft computing, and applications of AI.\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eRecognising Handwritten Digits Using a Fuzzy Neural Network\u003cbr\u003e \u003ci\u003eJoshua Reynolds and Tianhua Chen\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Assessment of Student Academic Performances\u003cbr\u003e \u003ci\u003eShangen Yang and Tianhua Chen\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eA Hybrid Fuzzy Neural Network for Image Recognition\u003cbr\u003e \u003ci\u003eSamaresh Nayak and Tianhua Chen\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eA Fuzzy Diagnostic System for Heart Disease\u003cbr\u003e \u003ci\u003eSiyue Song, Tianhua Chen, and Grigoris Antoniou\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eAnalysing Medical Notes using Fuzzy Logic\u003cbr\u003e \u003ci\u003eSiyue Song, Tianhua Chen, and Grigoris Antoniou\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFostering Positive Personalisation through Fuzzy Clustering\u003cbr\u003e \u003ci\u003eRaymond Moodley\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Logic in Modern Information Retrieval\u003cbr\u003e \u003ci\u003eSteve Wade\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Applied to Sentiment Analysis\u003cbr\u003e \u003ci\u003eOrestes Appel\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Logic, a Logicians Perspective\u003cbr\u003e \u003ci\u003ePatrick Fogarty\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eApplications of Fuzzy Logic in an Automated Warehouse\u003cbr\u003e \u003ci\u003ePatrick Fogarty\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eCan Fuzzy Systems Assist with Project Planning?\u003cbr\u003e \u003ci\u003eDaniel Maia and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Logic in Autonomous Vehicles\u003cbr\u003e \u003ci\u003eDavid McDougall and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eAI Spawning Fuzzy Logic Fuzzy Inference System\u003cbr\u003e \u003ci\u003eReece Carey and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eThe Application of Fuzzy Logic on Intelligent Transportation Systems\u003cbr\u003e \u003ci\u003eNath Lloyd and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eFuzzy Logic Applied to Water Processes\u003cbr\u003e \u003ci\u003eWill Chapman and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eApplications of Fuzzy Logic in Autonomous Vehicles\u003cbr\u003e \u003ci\u003eSam Asquith and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003ePredicting Cyber Threats using Fuzzy Logic\u003cbr\u003e \u003ci\u003eJarrad Morden and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eImplementations of Fuzzy Logic in Camera Systems\u003cbr\u003e \u003ci\u003eSophie Hughes and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eApplication of a Fuzzy Logic Control System for Stock Market Prediction Based on Technical Indicators and Fundamental Analysis\u003cbr\u003e \u003ci\u003eHumza Nazir and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eThe Application of Fuzzy Logic in Determining Outcomes of Sporting Events\u003cbr\u003e \u003ci\u003eSpencer Deane and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e  \u003cp\u003eUsing Fuzzy Logic to Educate People on Phishing\u003cbr\u003e \u003ci\u003eHarry Taylor and Arjab Khuman\u003c\/i\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415628390743,"sku":"9783030664763","price":123.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030664763.jpg?v=1730527571"},{"product_id":"essential-mathematics-for-undergraduates-a-guided-approach-to-algebra-geometry-topology-and-analysis-9783030871765","title":"Essential Mathematics for Undergraduates: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the book’s structure.\u003c\/p\u003e\u003cp\u003ePart 1 introduces the mathematical language and its rules together with the basic building blocks. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3. Part 4 breaks down the traditional, outdated barriers between areas, exploring in particular the interplay between algebra and geometry. Two appendices form Part 5: the Greek etymology of frequent terms and a list of mathematicians mentioned in the book. Abundant examples and exercises are disseminated along the text to boost the learning process and allow for independent work.\u003c\/p\u003e\u003cp\u003eStudents will find invaluable material to shepherd them through the first years of an undergraduate course, or to complement previously learnt subject matters. Teachers may pick’n’mix the contents for planning lecture courses or supplementing their classes.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book being reviewed is a collection of what the author considers to be essential material for undergraduates … . it has to be said that many students will find that there is plenty to learn from this well-written book, which would also be a useful reference text had there been a properly compiled index.” (Peter Shiu, The Mathematical Gazette, Vol. 107 (570), November, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: Basic Objects and Formalisation - Round-up of Elementary Logic.- Naive Set Theory.- Functions.- More Set Theory and Logic.- Boolean Algebras. Part 2: Numbers and Structures - Intuitive Arithmetics.- Real Numbers.- Totally Ordered Spaces.- Part 3: Elementary Real Functions - Real Polynomials.- Real Functions of One Real Variables.- Algebraic Functions.- Elementary Transcendental Functions.- Complex Numbers.- Enumerative Combinatorics.- Part 4: Geometry through Algebra - Vector Spaces.- Orthogonal Operators.- Actions \u0026amp; Representations.- Elementary Plane Geometry.- Metric Spaces.- Part 5: Appendices - Etymologies.- Index of names.- Main figures.- Glossary.- References.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415652868439,"sku":"9783030871765","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030871765.jpg?v=1730527665"},{"product_id":"foundations-of-software-science-and-computation-structures-25th-international-conference-fossacs-2022-held-as-part-of-the-european-joint-conferences-on-theory-and-practice-of-software-etaps-2022-munich-germany-april-2-7-2022-proceedings-9783030992521","title":"Foundations of Software Science and Computation","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. \u003c\/p\u003e  \u003cp\u003eThe 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e \u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":49415672398167,"sku":"9783030992521","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030992521.jpg?v=1730527737"},{"product_id":"dynamic-logic-new-trends-and-applications-4th-international-workshop-dali-2022-haifa-israel-july-31-august-1-2022-revised-selected-papers-9783031266218","title":"Dynamic Logic. New Trends and Applications: 4th","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book constitutes revised selected papers from the refereed proceedings of the 4th International Workshop on Dynamic Logic, DaLí 2022, held in Haifa, Israel, in July\/August 2022.\u003cbr\u003eThe 8 full papers presented in this volume were carefully reviewed and selected from 22 submissions. They deal with new trends and applications in the area of Dynamic Logic. \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFirst steps in updating knowing how.- Parametrized modal logic II: the unidimensional case.- Relating Kleene algebras.- Dynamic epistemic logic for budget-constrained agents.- Action models for coalition logic.- Quantum logic for observation of physical quantities.- Cautious distributed belief.-  A STIT logic of intentionality.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415703101783,"sku":"9783031266218","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031266218.jpg?v=1730527844"},{"product_id":"logic-and-its-applications-10th-indian-conference-icla-2023-indore-india-march-3-5-2023-proceedings-9783031266881","title":"Logic and Its Applications: 10th Indian","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eEdited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eBesides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA Note on the Ontology of Mathematics.- Boolean Functional Synthesis: From Under the Hood of Solvers.- Labelled Calculi for Lattice-based Modal Logics.- Two Ways to Scare a Gruffalo.- Determinacy Axioms and Large Cardinals.- Big ideas from logic for mathematics and computing education.- Modal Logic of Generalized Separated Topological Spaces.- Multiple-valued Semantics for Metric Temporal Logic.- Segment transit function of the induced path function of graphs and its first-order definability.- Fuzzy Free Logic with Dual Domain Semantics.- A New Dimension of Imperative Logic. -Quasi-Boolean based models in Rough Set theory: A case of Covering.- Labelled calculi for the logics of rough concepts.- An Infinity of Intuitionistic Connexive Logics.- Relational Semantics for Normal Topological Quasi-Boolean Logic.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415703134551,"sku":"9783031266881","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031266881.jpg?v=1730527844"},{"product_id":"formal-methods-teaching-5th-international-workshop-fmtea-2023-lubeck-germany-march-6-2023-proceedings-9783031275333","title":"Formal Methods Teaching: 5th International","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book constitutes the proceedings of the 5th International Workshop on Formal Methods Teaching, FMTea 2023, which was held in Lübeck, Germany, in March 2023.\u003cbr\u003eThe 7 full papers presented in this volume were carefully reviewed and selected from 10 submissions. FMTea 2023 aim is to support a worldwide improvement in learning Formal Methods, mainly by teaching but also via self-learning.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAutomated Exercise Generation for Satisfiability Checking.- Graphical Loop Invariant Based Programming.- A Gentle Introduction to Verification of Parameterized Reactive Systems.- Model Checking Concurrent Programs for Autograding in pseuCo Book.- Teaching TLA+ to Engineers at Microsoft.- Teaching and Training in Formalisation with B.- Teaching low-code Formal Methods with Coloured Petri Nets.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49415704641879,"sku":"9783031275333","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031275333.jpg?v=1730527847"},{"product_id":"logical-foundations-of-mathematics-and-computational-complexity-a-gentle-introduction-9783319001180","title":"Logical Foundations of Mathematics and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. \u003ci\u003eLogical Foundations of Mathematics and Computational Complexity\u003c\/i\u003e covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eEmphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eLogical Foundations of Mathematics and Computational Complexity\u003c\/i\u003e is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This monograph by the outstanding Czech logician Pavel Pudlák provides a broad but also deep survey of work in logic and computer science relevant to foundational issues, interpreted in a wide sense. … This is a fine overview of logic and complexity theory that can be confidently recommended to anybody who would like to orient themselves in an increasingly intricate and difficult field.” (Alasdair Urquhart, Philosophia Mathematica, Vol. 23 (3), October, 2015)\u003c\/p\u003e\u003cp\u003e“For the non-expert it offers indeed a ‘gentle introduction’ to logic that is well selected and excellently explained. And for the logician it certainly offers some of the best introductions to those topics outside their area of direct expertise. … it contains plenty of informal explanations, intuition and motivation. … It is truly a gift to the logic and wider communities … . This book is very enjoyable to read and I wish it all success.” (Olaf Beyersdorff, Mathematical Reviews, August, 2014)\u003c\/p\u003e\u003cp\u003e“It spans the historical, logical, and at times philosophical underpinnings of the theory of computational complexity. Students of mathematics seeking a transition to higher mathematics will find it helpful, as will mathematicians with expertise in other areas. … an excellent choice for a first text in studying complexity, or as a clarifying adjunct to any assigned text in this area. … a compact guide for graduate students with a need for or interest in computational complexity and its foundations.” (Tom Schulte, MAA Reviews, July, 2014)\u003c\/p\u003e“This book, exactly as indicated by its title, deals with the main philosophical, historical, logical and mathematical aspects … in a quite approachable and attractive way. … the prospective readers of this book are mathematicians with an interest in the foundations, philosophers with a good background in mathematics, and also philosophically minded scientists. Due to the author’s nice style, the book will be a very good choice for the first text in studying this subject.” (Branislav Boričić, zbMATH, Vol. 1270, 2013)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e​​​​​​​​​​Mathematician’s world.- Language, logic and computations.- Set theory.- Proofs of impossibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49417083617623,"sku":"9783319001180","price":112.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319001180.jpg?v=1730531583"},{"product_id":"theorie-des-ensembles-9783540340348","title":"Théorie des ensembles","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eLe Livre de Théorie des ensembles qui vient en tête du traité présente les fondements axiomatiques de la théorie des ensembles. 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