{"title":"Set theory Books","description":"","products":[{"product_id":"the-foundations-of-mathematics-9780198706434","title":"The Foundations of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe transition from school mathematics to university mathematics is seldom straightforward. Students are faced with a disconnect between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years'' experience of the potential difficulties involved, through teaching first-year undergraduates and researching the ways in which students and mathematicians think. The book explains the motivation behind abstract foundational material based on students'' experiences of school mathematics, and explicitly suggests ways students can make sense of formal ideas.This second edition takes a significant step forward by not only making the transition from intuitive to formal methods, but also by reversing the process- using structure theorems to prove that formal systems have visual and symbolic interpretations that enhance mathematical thinking. This is exemplified by a new chapter on the theory of groups. While the first edition extended counting to infinite cardinal numbers, the second also extends the real numbers rigorously to larger ordered fields. This links intuitive ideas in calculus to the formal epsilon-delta methods of analysis. The approach here is not the conventional one of ''nonstandard analysis'', but a simpler, graphically based treatment which makes the notion of an infinitesimal natural and straightforward. This allows a further vision of the wider world of mathematical thinking in which formal definitions and proof lead to amazing new ways of defining, proving, visualising and symbolising mathematics beyond previous expectations.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe writing is both rigorous and thorough, and the authors use compact presentations to support their explanations and proofs. Highly recommended. * N. W. Schillow, CHOICE *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI: THE INTUITIVE BACKGROUND; II: THE BEGINNINGS OF FORMALISATION; III: THE DEVELOPMENT OF AXIOMATIC SYSTEMS; IV: USING AXIOMATIC SYSTEMS; V: STRENGTHENING THE FOUNDATIONS","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732766929239,"sku":"9780198706434","price":23.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198706434.jpg?v=1719998308"},{"product_id":"discrete-quantum-walks-on-graphs-and-digraphs-9781009261685","title":"Discrete Quantum Walks on Graphs and Digraphs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDiscrete quantum walks are quantum analogues of classical random walks. They are an important tool in quantum computing and a number of algorithms can be viewed as discrete quantum walks, in particular Grover''s search algorithm. These walks are constructed on an underlying graph, and so there is a relation between properties of walks and properties of the graph. This book studies the mathematical problems that arise from this connection, and the different classes of walks that arise. Written at a level suitable for graduate students in mathematics, the only prerequisites are linear algebra and basic graph theory; no prior knowledge of physics is required. The text serves as an introduction to this important and rapidly developing area for mathematicians and as a detailed reference for computer scientists and physicists working on quantum information theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; 1. Grover search; 2. Two reflections; 3. Applications; 4. Averaging: 5. Covers and embeddings; 6. Vertex-face walks; 7. Shunts; 8. 1-Dimensional walks; References; Glossary; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738023407959,"sku":"9781009261685","price":60.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009261685.jpg?v=1791468916"},{"product_id":"an-invitation-to-model-theory-9781316615553","title":"An Invitation to Model Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eModel theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Part I. Languages and Structures: 1. Structures; 2. Terms; 3. Formulas; 4. Definable sets; 5. Substructures and quantifiers; Part II. Theories and Compactness: 6. Theories and axioms; 7. The complex and real fields; 8. Compactness and new constants; 9. Axiomatisable classes; 10. Cardinality considerations; 11. Constructing models from syntax; Part III. Changing Models: 12. Elementary substructures; 13. Elementary extensions; 14. Vector spaces and categoricity; 15. Linear orders; 16. The successor structure; Part IV. Characterising Definable Sets: 17. Quantifier elimination for DLO; 18. Substructure completeness; 19. Power sets and Boolean algebras; 20. The algebras of definable sets; 21. Real vector spaces and parameters; 22. Semi-algebraic sets; Part V. Types: 23. Realising types; 24. Omitting types; 25. Countable categoricity; 26. Large and small countable models; 27. Saturated models; Part VI. Algebraically Closed Fields: 28. Fields and their extensions; 29. Algebraic closures of fields; 30. Categoricity and completeness; 31. Definable sets and varieties; 32. Hilbert's Nullstellensatz; Bibliography; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738565194071,"sku":"9781316615553","price":30.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781316615553.jpg?v=1791470335"},{"product_id":"set-theory-and-foundations-of-mathematics-an-introduction-to-mathematical-logic-volume-i-set-theory-9789811201929","title":"Set Theory And Foundations Of Mathematics: An","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743275856215,"sku":"9789811201929","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811201929.jpg?v=1720064880"},{"product_id":"fundamentals-of-analysis-with-applications-9789811683824","title":"Fundamentals of Analysis with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743291945303,"sku":"9789811683824","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"fundamentals-of-analysis-with-applications-9789811683855","title":"Fundamentals of Analysis with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book serves as a textbook in real analysis. It focuses on the fundamentals of the structural properties of metric spaces and analytical properties of functions defined between such spaces. Topics include sets, functions and cardinality, real numbers, analysis on R, topology of the real line, metric spaces, continuity and differentiability, sequences and series, Lebesgue integration, and Fourier series. It is primarily focused on the applications of analytical methods to solving partial differential equations rooted in many important problems in mathematics, physics, engineering, and related fields. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Sets, Functions and Cardinality.- 2. The Real Numbers.- 3. Sequence and Series of Numbers.- 4. Analysis on R.- 5. Topology of the Real Line.- 6. Metric Spaces.- 7. Continuity and Differentiability.- 8. Sequences and Series of Functions.- 9. Lebesgue Integration.- 10. Fourier Series.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743292043607,"sku":"9789811683855","price":42.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811683855.jpg?v=1720064954"},{"product_id":"set-theory-and-the-continuum-hypothesis-9780486469218","title":"Set Theory and the Continuum Hypothesis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864735658327,"sku":"9780486469218","price":12.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486469218.jpg?v=1722273002"},{"product_id":"set-theory-and-logic-9780486638294","title":"Set Theory and Logic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe best introductory text we have seen.  Cosmos. Lucidly and gradually explains sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories. Its clarity makes this book excellent for self-study.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864739426647,"sku":"9780486638294","price":16.57,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486638294.jpg?v=1722273019"},{"product_id":"the-joy-of-set-9780691166148","title":"The Joy of SET","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHave you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is yes, then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mat\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"[A] model of mathematical exposition. The quality of writing is consistently high: clear but not condescending, humorous, chatty, and a genuine pleasure to read... I doubt it will be very long before I find something from [The Joy of SET] to use in one of my classes.\"--Mark Hunacek, MAA Reviews \"[The Joy of SET] shows how budding interest in mathematics can be fostered and developed... If [middle and high school teachers] ever try to enliven their classes or just interaction with curious students, this book is one they may depend on.\"--Alexander Bogomolny, Cut the Knot blog \"[A]mazing... What I love about The Joy of SET is that it is written in such a way that it can be read and enjoyed by both SET enthusiasts and someone that has never played SET before... Really and truly, there is enough math in this book to keep you busy for a lifetime! ... I definitely recommend this book.\"--Sarah Carter, Math Equals Love blog \"[The Joy of SET] takes readers on a fascinating journey into this seemingly simple card game... The book is in my view just the right way to talk about math as fun, and intellectually challenging.\"--Robert Harington, Scholarly Kitchen \"[A]s the authors convincingly demonstrate ... the mathematics behind SET actually goes very deep... [The Joy of SET] would make a fantastic resource for a middle school, high school, or undergraduate math club.\"--Brent Yorgey, Math Less Traveled blog \"This book, written by a mathematically inclined family, is the first and only work to explore the connection between the game and mathematics... [The Joy of SET] will attract those who play SET and those who want to explore mathematically related subjects.\"--Choice\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii  1 SET and You 1  2 Counting Fun! 27  3 Probability! 52  4 SET and Modular Arithmetic 72  5 SET and Geometry 98  Interlude: How to Improve at SET 136  6 More Combinatorics 149  7 Probability and Statistics 171  8 Vectors and Linear Algebra 197  9 Affine Geometry Plus 229  10 Computing and Simulations 256  Conclusion 288  Solutions to Exercises 289  Bibliography 303  Index 307","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865532150103,"sku":"9780691166148","price":22.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691166148.jpg?v=1722274422"},{"product_id":"the-joy-of-set-9780691192321","title":"The Joy of SET","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“A model of mathematical exposition. The quality of writing is consistently high: clear but not condescending, humorous, chatty, and a genuine pleasure to read.”\u003cb\u003e—Mark Hunacek, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e“The book shows how budding interest in mathematics can be fostered and developed.”\u003cb\u003e—Alexander Bogomolny, \u003ci\u003eCut the Knot\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e“What I love about \u003ci\u003eThe Joy of SET\u003c\/i\u003e is that it is written in such a way that it can be read and enjoyed by both SET enthusiasts and someone that has never played SET before.”\u003cb\u003e—Sarah Carter, \u003ci\u003eMath Equals Love\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e“As the authors convincingly demonstrate . . . the mathematics behind SET actually goes \u003ci\u003every deep\u003c\/i\u003e.\"\u003cb\u003e—Brent Yorgey, \u003ci\u003eMath Less Traveled\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e“\u003ci\u003eThe Joy of SET\u003c\/i\u003e uses a popular and very simple card game as a springboard for a whirlwind tour through probability, combinatorics, finite geometries, and experimental mathematics. Whether or not you play SET, you’ll find a lot of great math to play with in this book.”\u003cb\u003e—Jordan Ellenberg, author of \u003ci\u003eHow Not to Be Wrong: The Power of Mathematical Thinking\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865543553367,"sku":"9780691192321","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691192321.jpg?v=1722274478"},{"product_id":"naive-set-theory-9781781394670","title":"Naive Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Benediction Classics","offers":[{"title":"Default Title","offer_id":48868216635735,"sku":"9781781394670","price":20.54,"currency_code":"GBP","in_stock":true}]},{"product_id":"fixed-point-theory-and-its-applications-to-real-world-problems-9781536193367","title":"Fixed Point Theory and its Applications to Real","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping. The book \"Fixed Point Theory \u0026amp; its Applications to Real World Problems\" is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface; Dynamical Behavior of Generalized Logistic System Using Superior Fixed Point Feedback System; On A New Type of Lipschitz Mapping Pairs in Fixed Point Considerations and Applications; On Geometric Properties of Non-Unique Fixed Points in b−Metric Spaces; Fixed Point Theorem for Multivalued Mappings with Rational Expressions in Complete Partial Metric Spaces; Common Fixed-Point Theorems In Menger PM-Spaces with Nonlinear Generalized Type; Coincidence Point Theorems for Non-Expansive Type Mappings and an Application to Dynamic Programming; Some Stability and Data Dependence Results for Pseudo-Contractive Multivalued Mappings; Multivalued Geraghty Θ-Contractions and Applications to Fractional Differential Inclusions; Near Fixed Point, Near Fixed Interval Circle and Near Fixed Interval Disc in Metric Interval Space; Applications of Generalized α− Ćirić and α−Browder Contractions in Partial Metric Spaces; Fixed Point Theorems for Asymptotically Regular Maps in Partial Metric Spaces; Existence of Common Fixed Point in Quasi-Partial Metric with Applications; An Iterative Algorithm for Weak Contraction Mappings; Fixed Point Stability of Additive Functional Equations in Paranormed Spaces; Amiable Fixed Sets and Their Descriptive Proximities: An Introduction; Strong Coupled Fixed Points of Kannan Type and Reich Type Cyclic Coupled Mappings in S-Metric Spaces; A Common Fixed-Point Theorem for a Pair of Mappings in Fuzzy Metric Spaces with an Application; Coupled Common Fixed-Point Theorems for Geraghty Contraction Mappings Satisfying Mixed Weakly Monotone Property in Sb-Metric Space; Fixed Point Theorems for Multivalued Suzuki Type Z_R-Contraction in Relational Metric Space; w-Interpolative Hardy-Rogers Type Contractions on Quasi-Partial b-Metric Space; General Three-Step Iteration Process (nv) for Suzuki Generalized Nonexpansive Mappings; A Generalized Fixed-Point Theorem on Partial b-Metric Spaces; Fixed point to fixed disc and application in partial metric spaces; Index.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48886198272343,"sku":"9781536193367","price":163.19,"currency_code":"GBP","in_stock":false}]},{"product_id":"turbulence-from-first-principles-9781628084689","title":"Turbulence from First Principles","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents a non-traditional approach to the theory of turbulence. Its objective is to prove that Newtonian mechanics is fully equipped for the description of turbulent motions without the help of experimentally obtained closures. Turbulence is one of the most fundamental problems in theoretical physics that is still unsolved. The term \"unsolved\" here means that turbulence cannot be properly formulated (ie: reduced to standard mathematical procedure such as solving differential equations). In other words, it is not just a computational problem: prior to computations, a consistent mathematical model must be found. Although applicability of the Navier-Stokes equations as a model for fluid mechanics is not in question, the instability of their solutions for flows with supercritical Reynolds numbers raises a more general question: is Newtonian mechanics complete?","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887063576919,"sku":"9781628084689","price":146.24,"currency_code":"GBP","in_stock":false}]},{"product_id":"topics-in-measure-theory-and-real-analysis-9789078677208","title":"Topics In Measure Theory And Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Atlantis Press","offers":[{"title":"Default Title","offer_id":48889937035607,"sku":"9789078677208","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789078677208.jpg?v=1791482967"},{"product_id":"discrete-mathematics-a-concise-introduction-9783031304873","title":"Discrete Mathematics: A Concise Introduction","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. “Safe” – that is, paradox-free – informal set theory is introduced following on the heels of Russell’s Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor’s diagonalisation technique. Predicate logic “for the user” is introduced along with axioms and rules and extensive examples. Partial orders and the \u003ci\u003eminimal condition\u003c\/i\u003e are studied in detail with the latter shown to be equivalent to the \u003ci\u003einduction principle\u003c\/i\u003e. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of \u003ci\u003efunctions\u003c\/i\u003e \u003ci\u003eand\u003c\/i\u003e \u003ci\u003esets\u003c\/i\u003e. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics. \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eElementary Informal Set Theory.- Safe Set Theory.- Relations and Functions.- A Tiny Bit of Informal Logic.- Inductively Defined Sets and Structural Induction.- Recurrence Equations.- Trees and Graphs.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084755738967,"sku":"9783031304873","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031304873.jpg?v=1725553236"},{"product_id":"consequence-relations-an-introduction-to-the-lindenbaumtarski-method-oxford-logic-guides-9780192866417","title":"Consequence Relations An Introduction to the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, intended for advanced undergraduate and graduate students in mathematics and philosophy, as well as researchers in the field of mathematical and philosophical logic.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Introduction 2: Preliminaries 3: Sentential Formal Languages 4: Logical Consequences 5: Matrix Consequences 6: Unital Abstract Logics 7: Equational Consequence 8: Equational L-Consequence 9: Q-Consequence 10: Decidability Bibliography Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":49369139544407,"sku":"9780192866417","price":90.06,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192866417.jpg?v=1791454087"},{"product_id":"data-engineering-fuzzy-mathematics-in-systems-theory-and-data-analysis-9780471416562","title":"Data Engineering Fuzzy Mathematics in Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThere are many situations in science and engineering where complex output data from a given system is used to formulate a model of how that system operates, or to simulate its response to different inputs. Applications include control, decision theory, and the emerging fields of bioinformatics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"To cope with real world uncertainties and provide a philosophical and practical guide...several methodologies are presented...\" (SciTech Book News, Vol. 25, No. 4, December 2001)\u003cbr\u003e \u003cbr\u003e \"...certainly a book that should be in the library of any institution where research and advanced study in fuzzy systems are carried out.\" (Choice, Vol. 39, No. 7, March 2002)\u003cbr\u003e \u003cbr\u003e \"...well organized, easy to read, and self-contained.... I would recommend it to anyone interested in self-study of the basic ideas of fuzzy systems...\" (International Journal of General Systems, Vol. 31, No. 6, 2002)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.\u003cbr\u003e \u003cbr\u003e Acknowledgments.\u003cbr\u003e \u003cbr\u003e Introduction.\u003cbr\u003e \u003cbr\u003e System Analysis.\u003cbr\u003e \u003cbr\u003e Uncertainty Techniques.\u003cbr\u003e \u003cbr\u003e Learning from Data: System Identification.\u003cbr\u003e \u003cbr\u003e Propositions as Subsets of the Data Space.\u003cbr\u003e \u003cbr\u003e Fuzzy Systems and Identification.\u003cbr\u003e \u003cbr\u003e Random-Set Modelling and Identification.\u003cbr\u003e \u003cbr\u003e Certain Uncertainty.\u003cbr\u003e \u003cbr\u003e Fuzzy Inference Engines.\u003cbr\u003e \u003cbr\u003e Fuzzy Classification.\u003cbr\u003e \u003cbr\u003e Fuzzy Control.\u003cbr\u003e \u003cbr\u003e Fuzzy Mathematics.\u003cbr\u003e \u003cbr\u003e Summary.\u003cbr\u003e \u003cbr\u003e Appendices.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402590331223,"sku":"9780471416562","price":131.35,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471416562.jpg?v=1730480873"},{"product_id":"chow-rings-decomposition-of-the-diagonal-and-the-topology-of-families-9780691160504","title":"Chow Rings Decomposition of the Diagonal and the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. This title delves into arguments originating in Nori's work that have been further developed by others.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This dense, fascinating book by Voisin is a report of some of the exciting discoveries she has made in the quest of the secrets of algebraic cycles.\"--Alberto Collino, Zentralblatt MATH \"[An advanced] reader will find a rich collection of ideas as well as detailed machinery with which to attack difficult problems in the field. Any complex geometer interested in the interplay between algebraic cycles, Hodge theory and algebraic topology should have this book on his or her shelf.\"--C. A. M. Peters, Mathematical Reviews Clippings\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii 1Introduction 1 1.1 Decomposition of the diagonal and spread 3 1.2 The generalized Bloch conjecture 7 1.3 Decomposition of the small diagonal and application to the topology of families 9 1.4 Integral coefficients and birational invariants 11 1.5 Organization of the text 13 2Review of Hodge theory and algebraic cycles 15 2.1 Chow groups 15 2.2 Hodge structures 24 3Decomposition of the diagonal 36 3.1 A general principle 36 3.2 Varieties with small Chow groups 44 4Chow groups of large coniveau complete intersections 55 4.1 Hodge coniveau of complete intersections 55 4.2 Coniveau 2 complete intersections 64 4.3 Equivalence of generalized Bloch and Hodge conjectures for general complete intersections 67 4.4 Further applications to the Bloch conjecture on 0-cycles on surfaces 86 5On the Chow ring of K3 surfaces and hyper-Kahler manifolds 88 5.1 Tautological ring of a K3 surface 88 5.2 A decomposition of the small diagonal 96 5.3 Deligne's decomposition theorem for families of K3 surfaces 106 6Integral coefficients 123 6.1 Integral Hodge classes and birational invariants 123 6.2 Rationally connected varieties and the rationality problem 127 6.3 Integral decomposition of the diagonal and the structure of the Abel-Jacobi map 139 Bibliography 155 Index 163","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403803500887,"sku":"9780691160504","price":157.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691160504.jpg?v=1730484593"},{"product_id":"badiou-and-indifferent-being-a-critical-introduction-to-being-and-event-9781350015678","title":"Badiou and Indifferent Being A Critical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eWilliam Watkin\u003c\/b\u003e is Professor of Contemporary Literature and Philosophy at Brunel University, UK.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eA remarkable achievement and a distinctive contribution to our knowledge of Badiou’s thought. For all the skill, and sometimes brilliance, of previous explications, no-one had quite captured the tenor, the character or (a heretical word, perhaps) the feel of Badiou’s ontology; not, at least, in language. * Journal of Badiou Studies *\u003cbr\u003eWatkin’s is a very important book. Much of the commentary on Badiou has tended to move his politics to the centre of his thought. With meticulousness, clarity and rigour, Watkin works rather through Badiou’s philosophization of mathematics, liberating the philosopher \u003ci\u003equa \u003c\/i\u003ephilosopher, the thinker whose awesome achievement has been to recast and transform our understanding of a major set of traditional philosophical terms. This book returns us to what is most gripping about Badiou, his stark, courageous and deeply uncontemporary asceticism. -- Andrew Gibson, former Research Professor of Modern Literature and Theory, Royal Holloway, University of London, UK\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003ci\u003epreface\u003c\/i\u003e \u003ci\u003eacknowledgements\u003c\/i\u003e  Introduction: Subtractive Being; Nonrelationality; Indifference; Set Theory; Retroactive Axiomatic Reasoning; Transmissibility, Intelligibility and Communicability; Theory of the Subject  Chapter One: Being: The One and the Multiple How to Prove that the One Is-Not (Meditation One); The One as Operational Counts-as-One; The Ancient Problem of Classes; Situations and Structures; The Multiple; Presentation of Presentation; Reasoning on Being by Means of Axioms; How to Accept that Being Is-Not  Chapter Two: Being: Separation, Void, Mark Meditation Two; Set Theory and Aggregation as Collection (Meditation Three); Axiom of Separation; Notation and Self-Predication; The Pure Multiple is Real; The Void: Proper Name of Being (Meditation Four); The Void and Nothing; Void as Nomination; ZF+C: The Nine Axioms of Contemporary Set Theory (Meditation 5); Axiom of Extensionality; Axiom of Replacement or Substitution; The Void Set and In-Difference; Meditation Six: Aristotle; Conclusion: Pure Multiple and the Void  Chapter Three: Being and Excess Powerset Axiom (Meditation Seven); Point of Excess; Void as Name; Four Kinds of One-ness: One, Count-as-one, Unicity, forming-into-one; The State (Meditation Eight); Threat of the Void; Belonging, Inclusion and Parts; Typologies of Being; States and Indifference (Meditation Nine)  Chapter Four: Nature and Infinity Nature is Normal (Meditation Eleven); Transitive Sets: Cardinal and Ordinal (Meditation Twelve); Nature and Minimality; Nature and Intrication; The Inexistence of Nature; Potential and Actual Infinity; Proving the Actual Infinite; Doubling and Dedekind Infinites; Frege and Equinumerosity  Chapter Five: Infinity, Limit and Succession The Limit; Succession and Limit; The Upper or Maximal Limit; Succession; Infinite Thought: Problems of Procedure (Meditation Thirteen); In-Different Other: The Second Existential Seal; There is some infinity in natural multiples (Meditation Fourteen); Conclusion on Being  Chapter Six: The Event: History and Ultra-One Historical Singularities (Meditation Sixteen); Historical Singularities, and Evental Sites: Examples; Primal Ones and the Edge of the Void; Singularity vs. Normality; Self-Predication: The Matheme of the Event (Meditation Seventeen); The Problem of Naming; Axiom of Foundation (Meditation Eighteen); Implications of Foundation; Coda: Un-Relation  Chapter Seven: The Event, Intervention and Fidelity The Wager: yes or no (Meditation Twenty); Intervention; Seven Consequences of the Event; Axiom of Choice (Meditation Twenty Two); Choice is Indifferent; Due to Choice, Singularities Exist and they are Indifferent; Fidelity, Connection (Meditation Twenty Three)  Chapter Eight: The Generic Continuum Hypothesis: (Meditation Twenty-Seven); The Thought of the Generic (Meditation Thirty-One); Truth and Knowledge: The Indifference of Avoidance; Generic Procedure; The Matheme of the Indiscernible (Meditation Thirty-Three); Easton’s Theorem (Meditation Twenty-Six); Conditioning the Indiscernible; Indiscernible or Generic Subsets; The Existence of the Indiscernible (Meditation Thirty-Four); Extension; Is there a name for the discernible such that it can be said to exist?  Chapter Nine: Forcing: Truth and Subject Theory of the Subject (Meditation Thirty-Five); Subjectivization; Chance; Faith; Names; Forcing (Mediation Thirty-Six); Leibniz’s Identity of Indiscernibles (Meditation Thirty); The Proof of Forcing (Meditation Thirty-Six); From the Indiscernible to the Undecidable; Conclusion (Meditation Thirty-Seven);  \u003ci\u003ebibliography\u003c\/i\u003e \u003ci\u003eindex\u003c\/i\u003e","brand":"Bloomsbury Publishing PLC","offers":[{"title":"Default Title","offer_id":49407497765207,"sku":"9781350015678","price":26.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781350015678.jpg?v=1730499577"},{"product_id":"granular-computing-9781439886816","title":"Granular Computing","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eInformation granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. \u003cstrong\u003eGranular Computing: Analysis and Design of Intelligent Systems \u003c\/strong\u003epresents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices. \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eIntroduces the concepts of information granules, information granularity, and granular computing\u003c\/li\u003e\n\u003cli\u003ePresents the key formalisms of information granules\u003c\/li\u003e\n\u003cli\u003eBuilds on the concepts of information granules with discussion of higher-order and higher-type information granules\u003c\/li\u003e\n\u003cli\u003eDiscusses the operational concept of in\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Dr. Pedrycz is an internationally acclaimed authority in the granular computing area. ... I particularly appreciate his elegant writing style. This book is the first comprehensive treatise of the granular computing techniques and their application to the design of intelligent systems. ... As an application-oriented practitioner in computational intelligence systems, I think that this book will be a welcome and strongly needed addition to this field. I cannot think of any other expert worldwide more qualified than Prof. Pedycz to write such a book.\"\u003cbr\u003e—Emil M. Petriu, University of Ottawa, Canada\u003c\/p\u003e\n\u003cp\u003e\"This volume covers most of the interesting and important topics in granular computing. The contents may be well understood by senior or master course students in the field of computer science ... also a good textbook for engineers who are involved in developing so-called intelligent systems.\"\u003cbr\u003e—Kaoru Hirota, Tokyo Institute of Technology, Japan\u003c\/p\u003e\n\u003cp\u003e\"Dr. Pedrycz’s latest magnum opus ... breaks new ground in many directions. [It] takes an important step toward achievement of human-level machine intelligence—a principal goal of artificial intelligence (AI) since its inception. ... [This is] a remarkably well put together and reader-friendly collection of concepts and techniques, which constitute granular computing. ... [The book] combines extraordinary breadth with extraordinary depth. It contains a wealth of new ideas, and unfolds a vast panorama of concepts, methods, and applications. ... Dr. Pedrycz’s development and description of these concepts, techniques, and their applications is a truly remarkable achievement. ... must reading for all who are concerned with the design and application of intelligent systems.\"\u003cbr\u003e—From the Foreword by Lotfi A. Zadeh, University of California, Berkeley, USA\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eInformation Granularity, Information Granules, and Granular Computing. Key Formalisms for Representation of Information Granules and Processing Mechanisms. Information Granules of Higher Type and Higher Order, and Hybrid Information Granules. Representation of Information Granules. The Design of Information Granules. Optimal Allocation of Information Granularity: Building Granular Mappings. Granular Description of Data and Pattern Classification. Granular Models: Architectures and Development. Granular Time Series. From Models to Granular Models. Collaborative and Linguistic Models of Decision Making. Index.\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49408300646743,"sku":"9781439886816","price":195.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781439886816.jpg?v=1730502345"},{"product_id":"set-theoretical-aspects-of-real-analysis-9781482242010","title":"Set Theoretical Aspects of Real Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eSet Theoretical Aspects of Real Analysis\u003c\/strong\u003e is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eZF theory and some point sets on the real line. Countable versions of AC and real analysis. Uncountable versions of AC and Lebesgue nonmeasurable sets. The Continuum Hypothesis and Lebesgue nonmeasurable sets. Measurability properties of sets and functions. Radon measures and nonmeasurable sets. Real-valued step functions with strange measurability properties. Relationships between certain classical constructions of Lebesgue nonmeasurable sets. Measurability properties of Vitali sets. A relationship between the measurability and continuity of real-valued functions. A relationship between absolutely nonmeasurable functions and Sierpinski-Zygmund functions. Sums of absolutely nonmeasurable injective functions. A large group of absolutely nonmeasurable additive functions. Additive properties of certain classes of pathological functions. Absolutely nonmeasurable homomorphisms of commutative groups. Measurable and nonmeasurable sets with homogeneous sections. A combinatorial problem on translation invariant extensions of the Lebesgue measure. Countable almost invariant partitions of G-spaces. Nonmeasurable unions of measure zero sections of plane sets. Measurability properties of well-orderings. Appendices. Bibliography. Subject Index.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409114046807,"sku":"9781482242010","price":175.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781482242010.jpg?v=1730505488"},{"product_id":"a-concise-introduction-to-pure-mathematics-9781498722926","title":"A Concise Introduction to Pure Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAccessible to all students with a sound background in high school mathematics, \u003cstrong\u003eA Concise Introduction to Pure Mathematics, Fourth Edition\u003c\/strong\u003e presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as the theory of solving cubic equations; Eulerâs formula for the numbers of corners, edges, and faces of a solid object and the five Platonic solids; the use of prime numbers to encode and decode secret information; the theory of how to compare the sizes of two infinite sets; and the rigorous theory of limits and continuous functions.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eNew to the Fourth Edition\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e \u003cli\u003eTwo new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applications\u003c\/li\u003e \u003cli\u003eNew material on inequalities, counting methods, the inclusion-exclusion princi\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"In addition to preparing students to go on into mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. … This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck’s writing style is clear and easy to read. This is a book that could be read by a student on his or her own. … While there is a difference in mathematical education between the U.K. and the U.S., this book will serve both groups of students extremely well.\"\u003cbr\u003e—From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA\u003c\/p\u003e\n\u003cp\u003e\"Liebeck’s book stands out from the crowd of similar books by being short (as the title says, it is concise) and by trying to expose students to mathematical ideas beyond the basics of sets and logic. In addition to the pre-Analysis and pre-Algebra chapters, there are chapters on complex numbers, inequalities, some number theory and combinatorics, and the Platonic solids. Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for…applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups — and this book could help them learn all that.\"\u003cbr\u003e—Fernando Q. Gouvêa, \u003cem\u003eMAA Reviews, \u003c\/em\u003eJune 2016\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003ePraise for Previous Editions:\u003cbr\u003e\"\u003c\/strong\u003e\u003c\/p\u003e\n\u003cstrong\u003eIt would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. … A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering.\"\u003cbr\u003e—\u003cem\u003eComputing Reviews\u003c\/em\u003e, November 2011\u003c\/strong\u003e\u003cp\u003e\u003cstrong\u003e\"Now in an updated and expanded third edition, \u003cstrong\u003eA Concise Introduction to Pure Mathematics\u003c\/strong\u003e provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics … . Of special note is the inclusion of solutions to all of the odd-numbered exercises. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college-level mathematics curriculums, \u003cstrong\u003eA Concise Introduction to Pure Mathematics\u003c\/strong\u003e is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index.\"\u003cbr\u003e—\u003cem\u003eLibrary Bookwatch\u003c\/em\u003e, December 2010\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.\"\u003cbr\u003e—Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … .\"\u003cbr\u003e—Gerald A. Heuer, \u003cem\u003eZentralblatt MATH\u003c\/em\u003e, 2009\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"… a pleasure to read … a very welcome and highly accessible book.\"\u003cbr\u003e—Michael Ward, \u003cem\u003eThe Mathematical Gazette\u003c\/em\u003e, March 2007\u003c\/strong\u003e\u003c\/p\u003e\n\u003cbr\u003e\u003cp\u003e\"In addition to preparing students to go on into mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. … This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck’s writing style is clear and easy to read. This is a book that could be read by a student on his or her own. … While there is a difference in mathematical education between the U.K. and the U.S., this book will serve both groups of students extremely well.\"\u003cbr\u003e—From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA\u003c\/p\u003e\n\u003cp\u003e\"Liebeck’s book stands out from the crowd of similar books by being short (as the title says, it is concise) and by trying to expose students to mathematical ideas beyond the basics of sets and logic. In addition to the pre-Analysis and pre-Algebra chapters, there are chapters on complex numbers, inequalities, some number theory and combinatorics, and the Platonic solids. Students are taught how to understand and create proofs, but they are also given a glimpse of what it is all for…applied mathematicians also need to know about proofs, counting, inequalities, bounds, and even groups — and this book could help them learn all that.\"\u003cbr\u003e—Fernando Q. Gouvêa, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e \u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003ePraise for Previous Editions:\u003cbr\u003e\"\u003c\/strong\u003e\u003c\/p\u003e\n\u003cstrong\u003eIt would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. … A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering.\"\u003cbr\u003e—\u003cem\u003eComputing Reviews\u003c\/em\u003e, November 2011\u003c\/strong\u003e\u003cp\u003e\u003cstrong\u003e\"Now in an updated and expanded third edition, \u003cstrong\u003eA Concise Introduction to Pure Mathematics\u003c\/strong\u003e provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics … . Of special note is the inclusion of solutions to all of the odd-numbered exercises. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college-level mathematics curriculums, \u003cstrong\u003eA Concise Introduction to Pure Mathematics\u003c\/strong\u003e is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index.\"\u003cbr\u003e—\u003cem\u003eLibrary Bookwatch\u003c\/em\u003e, December 2010\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck’s book has in many different ways been among my most rewarding teaching experiences during the last decades.\"\u003cbr\u003e—Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world … .\"\u003cbr\u003e—Gerald A. Heuer, \u003cem\u003eZentralblatt MATH\u003c\/em\u003e, 2009\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003e\"… a pleasure to read … a very welcome and highly accessible book.\"\u003cbr\u003e—Michael Ward, \u003cem\u003eThe Mathematical Gazette\u003c\/em\u003e, March 2007\u003c\/strong\u003e\u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eSets and Proofs. Number Systems. Decimals. \u003ci\u003enth \u003c\/i\u003eRoots and Rational Powers. Inequalities. Complex Numbers. Polynomial Equations. Induction. Euler’s Formula and Platonic Solids. The Integers. Prime Factorization. More on Prime Numbers. Congruence of Integers. More on Congruence. Secret Codes. Counting and Choosing. More on Sets. Equivalence Relations. Functions. Permutations. Infinity. Introduction to Analysis: Bounds. More Analysis: Limits. Yet More Analysis: Continuity. Introduction to Abstract Algebra: Groups. Introduction to Abstract Algebra: More on Groups. Solutions to Odd-Numbered Exercises. Further Reading. Index of Symbols. Index.\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409282736471,"sku":"9781498722926","price":47.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498722926.jpg?v=1730506277"},{"product_id":"the-truth-value-algebra-of-type2-fuzzy-sets-9781498735278","title":"The Truth Value Algebra of Type2 Fuzzy Sets","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eType-2 fuzzy sets extend both ordinary and interval-valued fuzzy sets to allow distributions, rather than single values, as degrees of membership. Computations with these truth values are governed by the truth value algebra of type-2 fuzzy sets. The Truth Value Algebra of Type-2 Fuzzy Sets: Order Convolutions of Functions on the Unit Interval explores the fundamental properties of this algebra and the role of these properties in applications. Accessible to anyone with a standard undergraduate mathematics background, this self-contained book offers several options for a one- or two-semester course. It covers topics increasingly used in fuzzy set theory, such as lattice theory, analysis, category theory, and universal algebra. The book discusses the basics of the type-2 truth value algebra, its subalgebra of convex normal functions, and their applications. It also examines the truth value algebra from a more algebraic and axiomatic view.","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409285849431,"sku":"9781498735278","price":126.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498735278.jpg?v=1791472718"},{"product_id":"a-bridge-to-higher-mathematics-9781498775250","title":"A Bridge to Higher Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eA Bridge to Higher Mathematics\u003c\/em\u003e is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis is one of the shorter books for a course that introduces students to the concept of mathematical proofs. The brevity is due to the \"bare-bones\" nature of the treatment. The number of topics covered, the number of examples, and the number of exercises are not smaller than what appears in competing textbooks; what is shorter is the text that one finds between theorems, lemmas, examples, and exercises. Besides the topics found in similar textbooks (i.e., proof techniques, logic, set theory, relations, and functions), there are chapters on (very) elementary number theory, combinatorial counting techniques, and Peano axioms on the set of positive integers. Several chapters are devoted to the construction of various kinds of numbers, such as integers, rationals, real numbers, and complex numbers. Answers to around half the exercises are included at the end of the book, and a few have complete solutions. This reviewer finds the book more enjoyable than the average competing textbook.\u003c\/p\u003e\u003cp\u003e\u003cem\u003e \u003cbr\u003e\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003e--M. Bona, University of Florida\u003c\/em\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eElements of logic\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eTrue and false statements\u003c\/p\u003e\u003cp\u003eLogical connectives and truth tables\u003c\/p\u003e\u003cp\u003eLogical equivalence\u003c\/p\u003e\u003cp\u003eQuantifiers\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eProofs: Structures and strategies\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAxioms, theorems and proofs\u003c\/p\u003e\u003cp\u003eDirect proof\u003c\/p\u003e\u003cp\u003eContrapositive proof\u003c\/p\u003e\u003cp\u003eProof by equivalent statements\u003c\/p\u003e\u003cp\u003eProof by cases\u003c\/p\u003e\u003cp\u003eExistence proofs\u003c\/p\u003e\u003cp\u003eProof by counterexample\u003c\/p\u003e\u003cp\u003eProof by mathematical induction\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eElementary Theory of Sets. Functions\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAxioms for set theory\u003c\/p\u003e\u003cp\u003eInclusion of sets\u003c\/p\u003e\u003cp\u003eUnion and intersection of sets\u003c\/p\u003e\u003cp\u003eComplement, difference and symmetric difference of sets\u003c\/p\u003e\u003cp\u003eOrdered pairs and the Cartersian product\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eFunctions\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eDefinition and examples of functions\u003c\/p\u003e\u003cp\u003eDirect image, inverse image\u003c\/p\u003e\u003cp\u003eRestriction and extension of a function\u003c\/p\u003e\u003cp\u003eOne-to-one and onto functions\u003c\/p\u003e\u003cp\u003eComposition and inverse functions\u003c\/p\u003e\u003cp\u003e*Family of sets and the axiom of choice\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eRelations\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eGeneral relations and operations with relations\u003c\/p\u003e\u003cp\u003eEquivalence relations and equivalence classes\u003c\/p\u003e\u003cp\u003eOrder relations\u003c\/p\u003e\u003cp\u003e*More on ordered sets and Zorn's lemma\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAxiomatic theory of positive integers\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003ePeano axioms and addition\u003c\/p\u003e\u003cp\u003eThe natural order relation and subtraction\u003c\/p\u003e\u003cp\u003eMultiplication and divisibility\u003c\/p\u003e\u003cp\u003eNatural numbers\u003c\/p\u003e\u003cp\u003eOther forms of induction\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eElementary number theory\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eAboslute value and divisibility of integers\u003c\/p\u003e\u003cp\u003eGreatest common divisor and least common multiple\u003c\/p\u003e\u003cp\u003eIntegers in base 10 and divisibility tests\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCardinality. Finite sets, infinite sets\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eEquipotent sets\u003c\/p\u003e\u003cp\u003eFinite and infinite sets\u003c\/p\u003e\u003cp\u003eCountable and uncountable sets\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCounting techniques and combinatorics\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eCounting principles\u003c\/p\u003e\u003cp\u003ePigeonhole principle and parity\u003c\/p\u003e\u003cp\u003ePermutations and combinations\u003c\/p\u003e\u003cp\u003eRecursive sequences and recurrence relations\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eThe construction of integers and rationals\u003c\/strong\u003e \u003c\/p\u003e\u003cp\u003eDefinition of integers and operations\u003c\/p\u003e\u003cp\u003eOrder relation on integers\u003c\/p\u003e\u003cp\u003eDefinition of rationals, operations and order\u003c\/p\u003e\u003cp\u003eDecimal representation of rational numbers\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eThe construction of real and complex numbers\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003eThe Dedekind cuts approach\u003c\/p\u003e\u003cp\u003eThe Cauchy sequences approach\u003c\/p\u003e\u003cp\u003eDecimal representation of real numbers\u003c\/p\u003e\u003cp\u003eAlgebraic and transcendental numbers\u003c\/p\u003e\u003cp\u003eComples numbers\u003c\/p\u003e\u003cp\u003eThe trigonometric form of a complex number\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409296335191,"sku":"9781498775250","price":76.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498775250.jpg?v=1730506323"},{"product_id":"logic-colloquium-99-lecture-notes-in-logic-17-9781568811994","title":"Logic Colloquium '99: Lecture Notes in Logic 17","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The other articles cover current reseach topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e… The collection gives a good picture of the situation in logic at the millenium.-C.W. Kilmister, \u003cem\u003eThe Mathematical Gazette\u003c\/em\u003e, July 2005\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49410249654615,"sku":"9781568811994","price":74.09,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781568811994.jpg?v=1791474073"},{"product_id":"model-theory-of-fields-lecture-notes-in-logic-5-second-edition-9781568812816","title":"Model Theory of Fields: Lecture Notes in Logic 5,","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction to the Model Theory of Fields 2. Model Theory of Differential Fields 3. Differential Algebraic Groups and the Number of Countable Differentially Closed Fields 4. Some Model Theory of Separably Closed Fields","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49410249916759,"sku":"9781568812816","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781568812816.jpg?v=1791474074"},{"product_id":"logic-in-tehran-proceedings-of-the-workshop-and-conference-on-logic-algebra-and-arithmetic-held-october-18-22-2003-lecture-notes-in-logic-26-9781568812953","title":"Logic in Tehran: Proceedings of the Workshop and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis proceedings volume contains research papers in mathematical logic, especially in model theory and its applications to algebra and formal theories of arithmetic. Other papers address interpretability theory, computable analysis, modal logic, and the history of mathematical logic in Iran. The conference was held in Tehran, Iran, in October 2003, with the expressed purpose of bringing together researchers with connections to Iranian logicians and promoting further research in mathematical logic in Iran.","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49410249982295,"sku":"9781568812953","price":47.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781568812953.jpg?v=1791474074"},{"product_id":"nonlinear-stochastic-integrators-equations-and-flows-9782881247330","title":"Nonlinear Stochastic Integrators, Equations and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHighly technical monograph in which the authors, writing on the basis of their own recent research for the benefit of expert readers, describe a general theory of stochastic integration equations. First published in 1990.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction, Nonlinear Stochastic Integrators, Stochastic Calculus, Dependence on the initial Conditions and Flows.","brand":"Gordon \u0026 Breach Science Publishers SA","offers":[{"title":"Default Title","offer_id":49415542669655,"sku":"9782881247330","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9782881247330.jpg?v=1730527259"},{"product_id":"descriptive-theory-of-sets-and-functions-functional-analysis-in-semi-ordered-spaces-9782884490122","title":"Descriptive Theory of Sets and Functions.","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the extension of Hilbert space.","brand":"Gordon and Breach","offers":[{"title":"Default Title","offer_id":49415543226711,"sku":"9782884490122","price":453.63,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9782884490122.jpg?v=1730527264"},{"product_id":"q-rung-orthopair-fuzzy-sets-theory-and-applications-9789811914485","title":"q-Rung Orthopair Fuzzy Sets: Theory and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book collects chapters which discuss interdisciplinary solutions to complex problems by using different approaches in order to save money, time and resources. The book presents the results on the recent advancements in artificial intelligence, computational intelligence, decision-making problems, emerging problems and practical achievements in the broad knowledge management field. \u003ci\u003eq\u003c\/i\u003e-ROFS is one of the hot topics for all the researchers, industrialists as well as academicians. This book is of interest to professionals and researchers working in the field of decision making and computational intelligence, as well as postgraduate and undergraduate students studying applications of fuzzy sets.\u003c\/p\u003e  \u003cp\u003eThe book helps solve different kinds of the decision-making problems such as medical diagnosis, pattern recognition, construction problems and technology selection under the uncertain fuzzy environment. Containing 19 chapters, the book begins by giving a topology of the \u003ci\u003eq\u003c\/i\u003e-ROFSs and their applications. It then progresses in a logical fashion, dedicating a chapter to each approach, including the generalized information measures for \u003ci\u003eq\u003c\/i\u003e-ROFSs, implementation of \u003ci\u003eq\u003c\/i\u003e-ROFSs to medical diagnosis, inventory model, multi-attribute decision-making and approaches to real-life industrial problems such as green campus transportation, social responsibility evaluation pattern and extensions of the \u003ci\u003eq\u003c\/i\u003e-ROFSs.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eq-rung orthopair fuzzy Supra Topological application in Data mining process.- q-Rung Orthopair Fuzzy Soft Topology with Multi-Attribute Decision-Making.- Decision-Making on Patients’ medical based on a q-Rung Orthopair Fuzzy Max-Min-Max Composite Relation.- Soergel Distance Measures for q-Rung Orthopair Fuzzy Sets and Their Applications.- TOPSIS Techniques on q-Rung Orthopair Fuzzy Sets and Its Extensions.- Knowledge Measure-based q-Rung Orthopair Fuzzy Inventory Model.- Higher Type q-rung Orthopair Fuzzy Sets: Interval Analysis.- Evidence-Based Cloud Vendor Assessment with Generalized Orthopair Fuzzy Information and Partial Weight Data.- Supplier Selection Process Based on CODAS Method using q-Rung Orthopair Fuzzy Information.- Group Decision-Making Framework with Generalized Orthopair Fuzzy 2-Tuple Linguistic Information.- 3PL Service Provider Selection with Q Rung Orthopair Fuzzy Based CODAS Method.- An Integrated Proximity Indexed Value and Q-Rung Orthopair Fuzzy Decision-Making Model for Prioritization of Green Campus Transportation.- Platform-Based Corporate Social Responsibility Evaluation with Three-Way Group Decisions Under Q-Rung Orthopair Fuzzy Environment.- MARCOS Technique by Using q-Rung Orthopair Fuzzy Sets for Evaluating the Performance of Insurance Companies in Terms of Healthcare Services.- Interval Complex q-rung Orthopair Fuzzy Aggregation Operators and Their Applications in Cite Selection of Electric Vehicle.- A Novel Fermatean Fuzzy Analytic Hierarchy Process Proposition and Its Usage for Supplier Selection Problem in Industry 4.0 Transition.- Pentagonal q-Rung Orthopair Numbers and Their Applications.- q-Rung Orthopair Fuzzy Soft Sets Based Multi-Criteria Decision-Making.- Development of Heronian Mean Based Aggregation Operators Under Interval-Valued Dual Hesitant q-Rung Orthopair Fuzzy Environments for Multicriteria Decision-Making.\u003cbr\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":49427843678551,"sku":"9789811914485","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811914485.jpg?v=1730565865"},{"product_id":"naive-set-theory-9780486814872","title":"Naive Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis classic by one of the 20th century''s most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":49525447229783,"sku":"9780486814872","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486814872.jpg?v=1731860538"},{"product_id":"how-to-prove-it-9781108439534","title":"How to Prove It","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text''s third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed ''scratch work'' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this boo\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'Not only does this book help students learn how to prove results, it highlights why we care so much. It starts in the introduction with some simple conjectures and gathering data, quickly disproving the first but amassing support for the second. Will that pattern persist? How can these observations lead us to a proof? The book is engagingly written, and covers - in clear and great detail - many proof techniques. There is a wealth of good exercises at various levels. I've taught problem solving before (at The Ohio State University and Williams College), and this book has been a great addition to the resources I recommend to my students.' Steven J. Miller, Williams College, Massachusetts\u003cbr\u003e'This book is my go-to resource for students struggling with how to write mathematical proofs.  Beyond its plentiful examples, Velleman clearly lays out the techniques and principles so often glossed over in other texts.' Rafael Frongillo, University of Colorado, Boulder\u003cbr\u003e'I've been using this book religiously for the last eight years. It builds a strong foundation in proof writing and creates the axiomatic framework for future higher-level mathematics courses. Even when teaching more advanced courses, I recommend students to read chapter 3 (Proofs) since it is, in my opinion, the best written exposition of proof writing techniques and strategies. This third edition brings a new chapter (Number Theory), which gives the instructor a few more topics to choose from when teaching a fundamental course in mathematics. I will keep using it and recommending it to everyone, professors and students alike.' Mihai Bailesteanu, Central Connecticut State University\u003cbr\u003e'Professor Velleman sets himself the difficult task of bridging the gap between algorithmic and proof-based mathematics. By focusing on the basic ideas, he succeeded admirably. Many similar books are available, but none are more treasured by beginning students. In the Third Edition, the constant pursuit of excellence is further reinforced.' Taje Ramsamujh, Florida International University\u003cbr\u003e'Proofs are central to mathematical development. They are the tools used by mathematicians to establish and communicate their results. The developing mathematician often learns what constitutes a proof and how to present it by osmosis. How to Prove It aims at changing that. It offers a systematic introduction to the development, structuring, and presentation of logical mathematical arguments, i.e. proofs. The approach is based on the language of first-order logic and supported by proof techniques in the style of natural deduction. The art of proving is exercised with naive set theory and elementary number theory throughout the book. As such, it will prove invaluable to first-year undergraduate students in mathematics and computer science.' Marcelo Fiore, University of Cambridge\u003cbr\u003e'Overall, this is an engagingly-written and effective book for illuminating thinking about and building a careful foundation in proof techniques. I could see it working in an introduction to proof course or a course introducing discrete mathematics topics alongside proof techniques. As a self-study guide, I could see it working as it so well engages the reader, depending on how able they are to navigate the cultural context in some examples.' Peter Rowlett, LMS Newsletter\u003cbr\u003e'Altogether this is an ambitious and largely very successful introduction to the writing of good proofs, laced with many good examples and exercises, and with a pleasantly informal style to make the material attractive and less daunting than the length of the book might suggest. I particularly liked the many discussions of fallacious or incomplete proofs, and the associated challenges to readers to untangle the errors in proofs and to decide for themselves whether a result is true.' Peter Giblin, University of Liverpool, The Mathematical Gazette\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Number theory; 8. Infinite sets.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":49528815583575,"sku":"9781108439534","price":35.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108439534.jpg?v=1731873126"},{"product_id":"sorting-wonder-readers-early-level-9781429678704","title":"Sorting Wonder Readers Early Level","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Capstone Press","offers":[{"title":"Default Title","offer_id":49529790923095,"sku":"9781429678704","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"axiomatic-set-theory-dover-books-on-mathematics-9780486616308","title":"Axiomatic Set Theory Dover Books on Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eGeared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":49909362622807,"sku":"9780486616308","price":13.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486616308.jpg?v=1738271573"},{"product_id":"introduction-to-ramsey-spaces-9780691145426","title":"Introduction to Ramsey Spaces","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eRamsey theory is an area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. This book presents a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Winner of the Shoenfield Prize, Association for Symbolic Logic\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction 1  Chapter 1. Ramsey Theory: Preliminaries 3  1.1 Coideals 3  1.2 Dimensions in Ramsey Theory 5  1.3 Higher Dimensions in Ramsey Theory 10  1.4 Ramsey Property and Baire Property 20      Chapter 2. Semigroup Colorings 27  2.1 Idempotents in Compact semigroups 27  2.2 The Galvin-Glazer Theorem 30  2.3 Gowers's Theorem 34  2.4 A Semigroup of Subsymmetric Ultrafilters 38  2.5 The Hales-Jewett Theorem 41  2.6 Partial Semigroup of Located Words 46      Chapter 3. Trees and Products 49  3.1 Versions of the Halpern-Lauchli Theorem 49  3.2 A Proof of the Halpern-Lauchli Theorem 55  3.3 Products of Finite Sets 57      Chapter 4. Abstract Ramsey Theory 63  4.1 Abstract Baire Property 63  4.2 The Abstract Ramsey Theorem 68  4.3 Combinatorial Forcing 76  4.4 The Hales-Jewett Space 83  4.5 Ramsey Spaces of Infinite Block Sequences of Located Words 89      Chapter 5. Topological Ramsey Theory 93  5.1 Topological Ramsey Spaces 93  5.2 Topological Ramsey Spaces of Infinite Block Sequences of Vectors 99  5.3 Topological Ramsey Spaces of Infinite Sequences of Variable Words 105  5.4 Parametrized Versions of Rosenthal Dichotomies 111  5.5 Ramsey Theory of Superperfect Subsets of Polish Spaces 117  5.6 Dual Ramsey Theory 121  5.7 A Ramsey Space of Infinite-Dimensional Vector Subspaces of FN 127      Chapter 6. Spaces of Trees 135  6.1 A Ramsey Space of Strong Subtrees 135  6.2 Applications of the Ramsey Space of Strong Subtrees 138  6.3 Partition Calculus on Finite Powers of the Countable Dense Linear Ordering 143  6.4 A Ramsey Space of Increasing Sequences of Rationals 149  6.5 Continuous Colorings on Q[k] 152  6.6 Some Perfect Set Theorems 158  6.7 Analytic Ideals and Points in Compact Sets of the First Baire Class 165      Chapter 7. Local Ramsey Theory 179  7.1 Local Ellentuck Theory 179  7.2 Topological Ultra-Ramsey Spaces 190  7.3 Some Examples of Selective Coideals on N 194  7.4 Some Applications of Ultra-Ramsey Theory 198  7.5 Local Ramsey Theory and Analytic Topologies on N 202  7.6 Ultra-Hales-Jewett Spaces 207  7.7 Ultra-Ramsey Spaces of Block Sequences of Located Words 212  7.8 Ultra-Ramsey Space of Infinite Block Sequences of Vectors 215      Chapter 8. Infinite Products of Finite Sets 219  8.1 Semicontinuous Colorings of Infinite Products of Finite Sets 219  8.2 Polarized Ramsey Property 224  8.3 Polarized Partition Calculus 231      Chapter 9. Parametrized Ramsey Theory 237  9.1 Higher Dimensional Ramsey Theorems  Parametrized by Infinite Products of Finite Sets 237  9.2 Combinatorial Forcing Parametrized by Infinite Products of Finite Sets 243  9.3 Parametrized Ramsey Property 248  9.4 Infinite-Dimensional Ramsey Theorem Parametrized by Infinite Products of Finite Sets 254      Appendix 259  Bibliography 271  Subject Index 279  Index of Notation 285","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49922420900183,"sku":"9780691145426","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"beyond-first-order-model-theory-volume-i-9781498753975","title":"Beyond First Order Model Theory Volume I","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eModel theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAbstract elementary classes. Generalized logics in set theory. Topological methods in abstract model theory. Randomizations of structures. First Order logics with dependent sorts. Applications of infinitary logics.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":50578120573271,"sku":"9781498753975","price":175.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781498753975.jpg?v=1791472727"},{"product_id":"logic-colloquium-2000-hardcover-lecture-notes-in-logic-19-9781568812526","title":"Logic Colloquium 2000 (hardcover): Lecture Notes","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities. The presentations include tutorials and research articles from some of the world's preeminent logicians. Three long articles are based on tutorials given at the meeting, and present accessible expositions of devloping research in three active areas of logic: model theory, computability, and set theory. The eleven subsequent articles cover seperate research topics in all areas of mathematical logic, including: aspects in Computer Science, Proof Theory, Set Theory, Model Theory, Computability Theory, and aspects of Philosophy.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eTutorials; Model Theory and Geometry; Notions of Computability at Higher Types I; The Continuum Hypothesis; Participant Photographs; Articles; Bounded Forcing Axioms and the Size of the Continuum; Hilbert's Wide Program; Rigidity Conjectures; Metapredicative and Explicit Mahlo: a Proof-Theoretic Perspective; A Two-Dimensional Tree Ideal; Psychology Looks Hopefully to Logic; Russell's Logics; Partitioning Pairs of Uncountable Sets; Aspects of the Turing Jump; Liouville Functions; Analytic and Pseudo-Analytic Structures","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":50578193613143,"sku":"9781568812526","price":40.84,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781568812526.jpg?v=1791474074"},{"product_id":"logic-colloquium-99-lecture-notes-in-logic-17-9781568812038","title":"Logic Colloquium '99: Lecture Notes in Logic 17","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA compilation of papers presented at the 1999 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '99 includes surveys and research articles from some of the world's preeminent logicians. Two long articles are based on tutorials given at the meeting and present accessible expositions of current research in two active areas of logic, geometric model theory and descriptive set theory of group actions. The other articles cover current reseach topics in all areas of mathematical logic, including logic in computer science, proof theory, set theory, model theory, computability theory, and philosophy.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e… The collection gives a good picture of the situation in logic at the millenium.-C.W. Kilmister, \u003cem\u003eThe Mathematical Gazette\u003c\/em\u003e, July 2005\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":50578194006359,"sku":"9781568812038","price":40.84,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781568812038.jpg?v=1791474073"},{"product_id":"elements-of-set-theory-9780122384400","title":"Elements of Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eContents Preface  List of Symbols  Chapter 1 Introduction       Baby Set Theory       Sets—An Informal View      Classes      Axiomatic Method       Notation       Historical Notes  Chapter 2 Axioms and Operations      Axioms       Arbitrary Unions and Intersections       Algebra of Sets       Epilogue       Review Exercises  Chapter 3 Relations and Functions      Ordered Pairs      Relations       n-Ary Relations       Functions       Infinite Cartesian Products      Equivalence Relations       Ordering Relations       Review Exercises  Chapter 4 Natural Numbers       Inductive Sets       Peano's Postulates       Recursion on ?       Arithmetic       Ordering on ?      Review Exercises  Chapter 5 Construction of the Real Numbers      Integers       Rational Numbers       Real Numbers       Summaries       Two  Chapter 6 Cardinal Numbers and the Axiom of Choice      Equinumerosity       Finite Sets       Cardinal Arithmetic       Ordering Cardinal Numbers       Axiom of Choice       Countable Sets       Arithmetic of Infinite Cardinals       Continuum Hypothesis  Chapter 7 Orderings and Ordinals      Partial Orderings       Well Orderings       Replacement Axioms       Epsilon-Images       Isomorphisms       Ordinal Numbers       Debts Paid       Rank  Chapter 8 Ordinals and Order Types      Transfinite Recursion Again       Alephs       Ordinal Operations       Isomorphism Types       Arithmetic of Order Types       Ordinal Arithmetic  Chapter 9 Special Topics      Well-Founded Relations      Natural Models       Cofinality  Appendix Notation, Logic, and Proofs  Selected References for Further Study List of Axioms Index","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":51017534964055,"sku":"9780122384400","price":54.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780122384400.jpg?v=1750773867"},{"product_id":"irrationality-and-transcendence-in-number-theory-9780367628758","title":"Irrationality and Transcendence in Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003eIrrationality and Transcendence in Number Theory \u003c\/i\u003e\u003c\/b\u003etells the story of irrational numbers from their discovery in the days of Pythagoras to the ideas behind the work of Baker and Mahler on transcendence in the 20th century. It focuses on themes of irrationality, algebraic and transcendental numbers, continued fractions, approximation of real numbers by rationals, and relations between automata and transcendence. This book serves as a guide and introduction to number theory for advanced undergraduates and early postgraduates. Readers are led through the developments in number theory from ancient to modern times. The book includes a wide range of exercises, from routine problems to surprising and thought-provoking extension material.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFeatures\u003c\/b\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eUses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation\u003c\/li\u003e\n\u003cli\u003eSuitable as a primary textbook for\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"Exceptionally informative, impressively organized and presented, \u003cem\u003eIrrationality and Transcendence in Number Theory\u003c\/em\u003e is an ideal selection as a curriculum textbook.\"\u003cbr\u003e\u003cstrong\u003e- \u003cem\u003eMidwest Books Review\u003c\/em\u003e\u003c\/strong\u003e\u003cbr\u003e\"This excellent book not only helps fill a substantial gap in the undergraduate mathematics literature, but it does so in a way that most students will, I think, find interesting, inviting and accessible. \u003cbr\u003e[. . .] This material is, of course, very nontrivial, but Angell goes to great lengths to make it accessible. He writes slowly and clearly and spends a lot of time motivating results. As previously noted, he also includes background Appendices in each chapter.\u003cbr\u003eThere are other useful pedagogical features. Each chapter ends with an extensive collection of exercises, most of them non-routine; a 20-page section at the end of the book offers hints to these. The book also contains a five-page bibliography (one that, surprisingly, omits the Burger\/Tubbs book mentioned earlier) that directs a reader to useful sources. \u003cbr\u003eThe subject matter of this book is interesting and beautiful and deserves to be made accessible to well-prepared senior undergraduates. Angell has done an excellent job in helping to do so.\"\u003cbr\u003e\u003cstrong\u003e- \u003c\/strong\u003e\u003cem\u003e\u003cstrong\u003eMAA Reviews\u003c\/strong\u003e\u003c\/em\u003e \u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003e1. Introduction.\u003c\/strong\u003e 1.1. Irrational Surds. 1.2. Irrational Decimals. 1.3. Irrationality of the Exponential Constant. 1.4. Other Results, and Some Open Questions. Exercises. Appendix: Some Elementary Number Theory. \u003cstrong\u003e2. Hermite’s Method.\u003c\/strong\u003e 2.1. Irrationality of \u003ci\u003eer. \u003c\/i\u003e2.2. Irrationality of \u003ci\u003eπ. \u003c\/i\u003e2.3. Irrational values of trigonometric functions. Exercises. Appendix: Some Results of Elementary Calculus.\u003cstrong\u003e 3. Algebraic \u0026amp; Transcendental Numbers.\u003c\/strong\u003e 3.1. Definitions and Basic Properties. 3.2. Existence of Transcendental Numbers. 3.3. Approximation of Real Numbers by Rationals. 3.4. Irrationality of (3) : a sketch. Exercises. Appendix 1: Countable and Uncountable Sets. Appendix 2: The Mean Value Theorem. Appendix 3: The Prime Number Theorem. \u003cstrong\u003e4. Continued Fractions.\u003c\/strong\u003e Definition and Basic Properties. 4.2. Continued Fractions of Irrational Numbers. 4.3. Approximation Properties of Convergents. 4.4. Two important Approximation Problems. 4.5. A \"Computational\" Test for Rationality. 4.6. Further Approximation Properties of Convergents. 4.7. Computing the Continued Fraction of an Algebraic Irrational. 4.8. The Continued Fraction of \u003ci\u003ee. \u003c\/i\u003eExercises. Appendix 1: A Property of Positive Fractions. Appendix 2: Simultaneous Equations with Integral Coefficients. Appendix 3: Cardinality of Sets of Sequences. Appendix 4: Basic Musical Terminology. \u003cstrong\u003e5. Hermite’s Method for Transcendence.\u003c\/strong\u003e 5.1. Transcendence of \u003ci\u003ee.\u003c\/i\u003e 5.2. Transcendence of \u003ci\u003eπ. 5.3. \u003c\/i\u003eSome more Irrationality Proofs. 5.4. Transcendence of ea .5.5. Other Results. Exercises. Appendix 1: Roots and Coefficients of Polynomials. Appendix 2: Some Real and Complex Analysis. Appendix 3: Ordering Complex Numbers. \u003cstrong\u003e6. Automata and Transcendence.\u003c\/strong\u003e 6.1. Deterministic Finite Automata. 6.2 Mahler’s Transcendence Proof. 6.3 A More General Transcendence Result. 6.4. A Transcendence Proof for the Thue Sequence. 6.5. Automata and Functional Equations. 6.6. Conclusion. Exercises. Appendix 1: Alphabets, Languages and DFAs. Appendix 2: Some Results of Complex Analysis. Appendix 3: A Result on Linear Equations.\u003cstrong\u003e 7. Lambert’s Irrationality Proofs.\u003c\/strong\u003e 7.1. Generalised Continued Fractions. 7.2. Further Continued Fractions. Exercises. Appendix: Some Results from Elementary Algebra and Calculus. Hints for Exercises. Bibliography. Index. \u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":51017989521751,"sku":"9780367628758","price":45.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780367628758.jpg?v=1791457960"},{"product_id":"classic-set-theory-9780412606106","title":"Classic Set Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDesigned for undergraduate students of set theory, this book presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. It aims to give students a grounding to the results of set theory as well as to tackle significant problems that arise from the theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eINTRODUCTION\u003cbr\u003eOutline of the book\u003cbr\u003eAssumed knowledge\u003cbr\u003e\u003cbr\u003eTHE REAL NUMBERS\u003cbr\u003eIntroduction\u003cbr\u003eDedekind's construction\u003cbr\u003eAlternative constructions\u003cbr\u003eThe rational numbers\u003cbr\u003e\u003cbr\u003eTHE NATURAL NUMBERS\u003cbr\u003eIntroduction\u003cbr\u003eThe construction of the natural numbers\u003cbr\u003eArithmetic\u003cbr\u003eFinite sets\u003cbr\u003e\u003cbr\u003eTHE ZERMELO-FRAENKEL AXIOMS\u003cbr\u003eIntroduction\u003cbr\u003eA formal language\u003cbr\u003eAxioms 1 to 3\u003cbr\u003eAxioms 4 to 6\u003cbr\u003eAxioms 7 to 9\u003cbr\u003e\u003cbr\u003eCARDINAL (Without the Axiom of Choice)\u003cbr\u003eIntroduction\u003cbr\u003eComparing Sizes\u003cbr\u003eBasic properties of ˜ and =\u003cbr\u003eInfinite sets without AC-countable sets\u003cbr\u003eUncountable sets and cardinal arithmetic without AC\u003cbr\u003e\u003cbr\u003eORDERED SETS\u003cbr\u003eIntroduction\u003cbr\u003eLinearly ordered sets\u003cbr\u003eOrder arithmetic\u003cbr\u003eWell-ordered sets\u003cbr\u003e\u003cbr\u003eORDINAL NUMBERS\u003cbr\u003eIntroduction\u003cbr\u003eOrdinal numbers\u003cbr\u003eBeginning ordinal arithmetic\u003cbr\u003eOrdinal arithmetic\u003cbr\u003eThe Às\u003cbr\u003e\u003cbr\u003eSET THEORY WITH THE AXIOM OF CHOICE\u003cbr\u003eIntroduction\u003cbr\u003eThe well-ordering principle\u003cbr\u003eCardinal arithmetic and the axiom of choice\u003cbr\u003eThe continuum hypothesis\u003cbr\u003e\u003cbr\u003eBIBLIOGRAPHY\u003cbr\u003eINDEX","brand":"Taylor \u0026 Francis Ltd","offers":[{"title":"Default Title","offer_id":51018099294551,"sku":"9780412606106","price":75.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780412606106.jpg?v=1750775627"},{"product_id":"set-theory-an-introduction-to-independence-proofs-9780444868398","title":"Set Theory An Introduction To Independence Proofs","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eThe Foundations of Set Theory. Infinitary Combinatorics. The Well-Founded Sets. Easy Consistency Proofs. Defining Definability. The Constructible Sets. Forcing. Iterated Forcing. Bibliography. Indexes.","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":51018241933655,"sku":"9780444868398","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780444868398.jpg?v=1750776136"},{"product_id":"introduction-to-set-theory-revised-and-expanded-9780824779153","title":"Introduction to Set Theory Revised and Expanded","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"The book remains an excellent text for a senior undergraduate or first-year graduate level course. There is sufficient material for instructors of widely differing views to assemble one-semester courses. . ..the chapter on the axiom of choice is particularly strong. \"\u003cbr\u003e---Mathematical Reviews \u003cbr\u003e\". . .a fine text. . ..The proofs are both elegant and readable. \"\u003cbr\u003e---American Mathematical Monthly \u003cbr\u003e\". . .offers many benefits including. . .interesting applications of abstract set theory to real analysis. . .enriching standard classroom material. \"\u003cbr\u003e---L'Enseignement mathematique \u003cbr\u003e\". . .an excellent and much needed book. . .Especially valuable are a number of remarks sprinkled throughout the text which afford a glimpse of further developments. \"\u003cbr\u003e---The Mathematical Intelligencer \u003cbr\u003e\"The authors show that set theory is powerful enough to serve as an underlying framework for mathematics by using it to develop the beginnings of the theory of natural, rational, and real numbers. \"\u003cbr\u003e---Quarterly Review of Applied Mathematics \u003cbr\u003e\". . .In the third edition, Chapter 11 has been expanded, and four new chapters have been added. \"\u003cbr\u003e---Mathematical Reviews\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eSets; relations, functions and orderings; natural numbers; finite, countable and uncountable sets; cardinal numbers; ordinal numbers; alephs; the axiom of choice; arithmetic of cardinal numbers; sets of real numbers; filters and ultrafilters; combinatorial set theory; large cardinals; the axiom of foundation; the axiomatic set theory.","brand":"CRC Press","offers":[{"title":"Default Title","offer_id":51018478125399,"sku":"9780824779153","price":96.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780824779153.jpg?v=1791467771"},{"product_id":"philosophical-uses-of-categoricity-arguments-9781009432924","title":"Philosophical Uses of Categoricity Arguments","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis Element addresses the categoricity arguments that have been more effective in historical cases that reflect philosophically on internal mathematical matters than in recent questions of pre-theoretic metaphysics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction; 2. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 3. Dedekind in 'Was sind und was sollen die Zahlen?' (1888); 4. Kreisel in 'Informal rigor and incompleteness proofs' (1967) and 'Two notes on the foundations of set theory'(1969); 5. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 6. Parsons in 'The uniqueness of the natural numbers' (1990) and 'Mathematical induction' (2008); 7. Conclusion; References.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":51018639638871,"sku":"9781009432924","price":21.54,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781009432924.jpg?v=1750777617"},{"product_id":"the-language-of-symmetry-9781032303949","title":"The Language of Symmetry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cem\u003eThe Language of Symmetry \u003c\/em\u003eis a re-assessment of the structure and reach of symmetry, by an interdisciplinary group of specialists from the arts, humanities, and sciences at Oxford University.\u003c\/p\u003e\u003cp\u003eIt explores, amongst other topics:\u003c\/p\u003e\u003cul\u003e \u003cli\u003eorder and chaos in the formation of planetary systems\u003c\/li\u003e \u003cli\u003eentropy and symmetry in physics\u003c\/li\u003e \u003cli\u003egroup theory, fractals, and self-similarity\u003c\/li\u003e \u003cli\u003esymmetrical structures in western classical music\u003c\/li\u003e \u003cli\u003ehow biological systems harness disorder to create order\u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003eThis book aims to open up the scope of interdisciplinary work in the study of symmetry and is intended for scholars of any background - whether it be science, arts, or philosophy.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. 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