Set theory Books
Gordon and Breach Descriptive Theory of Sets and Functions.
Book SynopsisThis 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.
£325.00
John Wiley & Sons Inc Data Engineering Fuzzy Mathematics in Systems
Book SynopsisThere 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.Trade Review"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) "...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) "...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)Table of ContentsPreface. Acknowledgments. Introduction. System Analysis. Uncertainty Techniques. Learning from Data: System Identification. Propositions as Subsets of the Data Space. Fuzzy Systems and Identification. Random-Set Modelling and Identification. Certain Uncertainty. Fuzzy Inference Engines. Fuzzy Classification. Fuzzy Control. Fuzzy Mathematics. Summary. Appendices. Index.
£131.35
Wiley Fuzzy Cluster Analysis Methods for Classification
Book SynopsisFuzzy clustering, which combines fuzzy logic and cluster analysis techniques, has experienced a spur of interest in recent years owing to its important applications in image recognition. This revised, updated, and expanded translation of the German book deals with the ideas and algorithms of fuzzy clustering and their applications.Table of ContentsIntroduction. Basic Concepts. Classical Fuzzy Clustering Algorithms. Linear and Ellipsoidal Prototypes Shell Prototypes. Polygonal Object Boundaries. Cluster Estimation Models. Cluster Validity. Rule Generation with Clustering. Appendix. Bibliography.
£164.66
Harvard University Press Understanding the Infinite
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£32.36
Princeton University Press Chow Rings Decomposition of the Diagonal and the
Book SynopsisProvides 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.Trade Review"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 ClippingsTable of ContentsPreface 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
£148.75
Princeton University Press The Joy of SET
Book SynopsisHave 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 matTrade Review"[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."--ChoiceTable of ContentsPreface 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
£22.50
Princeton University Press The Joy of SET
Book SynopsisTrade Review“A model of mathematical exposition. The quality of writing is consistently high: clear but not condescending, humorous, chatty, and a genuine pleasure to read.”—Mark Hunacek, MAA Reviews“The book shows how budding interest in mathematics can be fostered and developed.”—Alexander Bogomolny, Cut the Knot“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.”—Sarah Carter, Math Equals Love“As the authors convincingly demonstrate . . . the mathematics behind SET actually goes very deep."—Brent Yorgey, Math Less Traveled“The Joy of SET 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.”—Jordan Ellenberg, author of How Not to Be Wrong: The Power of Mathematical Thinking
£16.19
Society for Industrial and Applied Mathematics (SIAM) Nonlocal Integral Equation Continuum Models
£50.40
Birkhauser Verlag AG A.P. Morse’s Set Theory and Analysis
Book SynopsisThis volume explores A.P. Morse’s (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse’s works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse’s publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor’s commentary serves to outline Morse’s goals, give informal explanations of Morse’s formal language, and compare Morse’s often unique approaches to more traditional approaches. Minor corrections to Morse’s previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor’s introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse’s methods.A.P. Morse’s Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse’s unique perspective and in the history of mathematics will also find this book to be of interest.Table of ContentsPreface.- Editor's Introduction.- Language and Inference.- Logic.- Set Theory.- Elementary Analysis.- Metrics.- Measure.- Linear Measure and Total Variation.- Integration.- Product Measures.- Web Derivatives.- Classical Differentiation.- The Construction of Definition.- The Consistency of the Axiom of Size.- Suggested Reading.- Publications of A.P. Morse.- Errata to A Theory of Sets, Second Edition.- Integration with Respect to Addor Functions.- The Henstock-Kurzweil Integral.
£93.49
Springer International Publishing AG Discrete Mathematics: A Concise Introduction
Book SynopsisThis 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 minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. 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. Table of ContentsElementary 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.
£33.24
Springer Verlag, Singapore Fundamentals of Analysis with Applications
Book SynopsisThis 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.Table of Contents1. 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.
£38.24
Springer Verlag, Singapore q-Rung Orthopair Fuzzy Sets: Theory and
Book SynopsisThis 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. q-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. The 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 q-ROFSs and their applications. It then progresses in a logical fashion, dedicating a chapter to each approach, including the generalized information measures for q-ROFSs, implementation of q-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 q-ROFSs.Table of Contentsq-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.
£67.49
Taylor & Francis Ltd Beyond First Order Model Theory Volume II
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£128.25
Taylor & Francis Ltd Logic of Arithmetic
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£58.89
Taylor & Francis Ltd Lectures on Mathematical Logic Volume II
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£58.89
Taylor & Francis Ltd Variational Problems in Topology The Geometry of Length Area and Volume
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£56.04
Taylor & Francis Ltd Bornologies and Lipschitz Analysis
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£80.74
Taylor & Francis Ltd Architecture of Mathematics
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£45.99
Taylor & Francis Ltd Irrationality and Transcendence in Number Theory
Book SynopsisIrrationality and Transcendence in Number Theory tells 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.Features Uses techniques from widely diverse areas of mathematics, including number theory, calculus, set theory, complex analysis, linear algebra, and the theory of computation Suitable as a primary textbook forTrade Review"Exceptionally informative, impressively organized and presented, Irrationality and Transcendence in Number Theory is an ideal selection as a curriculum textbook."- Midwest Books Review"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. [. . .] 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.There 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. The 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."- MAA Reviews Table of Contents1. Introduction. 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. 2. Hermite’s Method. 2.1. Irrationality of er. 2.2. Irrationality of π. 2.3. Irrational values of trigonometric functions. Exercises. Appendix: Some Results of Elementary Calculus. 3. Algebraic & Transcendental Numbers. 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. 4. Continued Fractions. 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 e. Exercises. 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. 5. Hermite’s Method for Transcendence. 5.1. Transcendence of e. 5.2. Transcendence of π. 5.3. Some 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. 6. Automata and Transcendence. 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. 7. Lambert’s Irrationality Proofs. 7.1. Generalised Continued Fractions. 7.2. Further Continued Fractions. Exercises. Appendix: Some Results from Elementary Algebra and Calculus. Hints for Exercises. Bibliography. Index.
£45.99
Taylor & Francis Ltd Set Theoretical Aspects of Real Analysis
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£43.69
Taylor & Francis Ltd Philosophy of Mathematics
Book SynopsisThe philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge.With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic.Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, conTrade Review"The philosophically minded mathematician will find every penny and every second engaged with this book well spent." - Firdous Ahmad Mala, The Mathematical IntelligencerTable of Contents1. Introduction 2. Mathematical Preliminaries 3. Platonism 4. Intuitionism 5. Logicism 6. Formalism 7. Gödel’s Incompleteness Theorem and Computability 8. The Church-Turing Thesis 9. Infinity 10. Supertasks 11. Models, Completeness, and Skolem’s Paradox 12. Axiom of Choice 13. Naturalism 14. Structuralism 15. Yablo’s Paradox 16. Mathematical Pluralism 17. Does Mathematics Need More Axioms? 18. Mathematical Nominalism
£80.74
Taylor & Francis Ltd The Language of Symmetry
Book SynopsisThe Language of Symmetry is 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.It explores, amongst other topics: order and chaos in the formation of planetary systems entropy and symmetry in physics group theory, fractals, and self-similarity symmetrical structures in western classical music how biological systems harness disorder to create order This 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.Table of Contents1. Planetary Systems: From Symmetry to Chaos. 2. Entropy and Symmetry in the Universe. 3. Darkness, Light, and how Symmetry might relate Them. Self-Similar 4. Self-Similarity. 5 The Language of Symmetry in Music. 6. The Interdependence of Order and Disorder: How Complexity arises in the Living and the Inanimate Universe. 7. A Philosophers Perspective on the Harnessing of Stochasticity. 8. Postscript: A Dialogue between Denis Noble and Benedict Rattigan. 9. Appendix: A Response to Professor Nobles Paper: Ordered disorder to drive Physiology.
£23.99
Taylor & Francis Ltd The Baseball Mysteries
The Baseball Mysteries: Challenging Puzzles for Logical Detectives is a book of baseball puzzles, logical baseball puzzles. To jump in, all you need is logic and a casual fan's knowledge of the game. The puzzles are solved by reasoning from the rules of the game and a few facts.The logic in the puzzles is like legal reasoning. A solution must argue from evidence (the facts) and law (the rules). Unlike legal arguments, however, a solution must reach an unassailable conclusion.There are many puzzle books. But there's nothing remotely like this book. The puzzles here, while rigorously deductive, are firmly attached to actual events, to struggles that are reported in the papers every day.The puzzles offer a unique and scintillating connection between abstract logic and gritty reality.Actually, this book offers the reader an unlimited number of puzzles. Once you've solved a few of the challenges here, every boxscore you see in the pap
£23.99
Cambridge University Press Sets for Mathematics
Book SynopsisIn this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra. Starting with intuitive descriptions of mathematically and physically common phenomena, it leads up to a precise specification of the Category of Sets. Suitable for advanced undergraduates and beginning graduate students.Trade Review"...the categorical approach to mathematics has never been presented with greater conviction than it has in this book. The authors show that the use of categories in analyzing the set concept is not only natural, but inevitable." Mathematical Reviews"To learn set theory this way means not having to relearn it later.... Recommended." ChoiceTable of ContentsForeword; 1. Abstract sets and mappings; 2. Sums, monomorphisms and parts; 3. Finite inverse limits; 4. Colimits, epimorphisms and the axiom of choice; 5. Mapping sets and exponentials; 6. Summary of the axioms and an example of variable sets; 7. Consequences and uses of exponentials; 8. More on power sets; 9. Introduction to variable sets; 10. Models of additional variation; Appendices; Bibliography.
£44.64
Cambridge University Press Lectures in Logic and Set Theory Volume I Mathematical Logic Volume 1 Mathematical Logic 82 Cambridge Studies in Advanced Mathematics Series Number 82
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£45.59
Cambridge University Press Lectures in Logic and Set Theory 83 Cambridge Studies in Advanced Mathematics Series Number 83
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£59.84
Cambridge University Press Numbers Sets and Axioms
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£47.49
Cambridge University Press LMS 128 Descriptive Set Theory London Mathematical Society Lecture Note Series Series Number 128
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£53.99
Cambridge University Press Organizational Learning from Performance Feedback A Behavioral Perspective on Innovation and Change
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£122.55
Cambridge University Press Set Theory Logic and their Limitations
Book SynopsisThis is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and GÃdel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.Trade Review' … written by an excellent mathematician … I very much like the way the author explains things.' European Mathematical SocietyTable of ContentsMathematical induction; 1. Sets and classes; 2. Relations and functions; 3. Cardinals; 4. Ordinals; 5. The axiom of choice; 6. Finite cardinals and alephs; 7. Propositional logic; 8. First order logic; 9. Facts from recursion theory; 10. Limitative results; Appendix: Skolem's paradox.
£41.79
Cambridge University Press LMS 220 Algebraic Set Theory London Mathematical Society Lecture Note Series Series Number 220
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£53.43
Cambridge University Press Set Theory for the Working Mathematician 39 London Mathematical Society Student Texts Series Number 39
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£116.85
Cambridge University Press Case Studies in Neuroanesthesia and Neurocritical Care Case Studies in Neurology
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£100.70
Cambridge University Press The Foundations of Mathematics in the Theory of Sets 82 Encyclopedia of Mathematics and its Applications Series Number 82
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£122.55
Cambridge University Press Descriptive Set Theory and Dynamical Systems 277 London Mathematical Society Lecture Note Series Series Number 277
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£62.99
Cambridge University Press Philosophical Uses of Categoricity Arguments
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£47.49
Cambridge University Press The Theory of Countable Borel Equivalence Relations
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£99.00
Cambridge University Press Basic Category Theory 143 Cambridge Studies in
Book SynopsisAssuming little mathematical background, this short introduction to category theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. Suitable for independent study or as a course book, it gives extensive explanations of the key concepts along with hundreds of examples and exercises.Table of ContentsNote to the reader; Introduction; 1. Categories, functors and natural transformations; 2. Adjoints; 3. Interlude on sets; 4. Representables; 5. Limits; 6. Adjoints, representables and limits; Appendix: proof of the General Adjoint Functor Theorem; Glossary of notation; Further reading; Index.
£47.49
Cambridge University Press Set Theory A First Course Cambridge Mathematical Textbooks
Book SynopsisSet theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.Trade Review'… Cunningham neglects no opportunity to make the subject as accessible as possible. The mathematical development is rigorous, as it should be, but not excessively so. Although he starts from zero, that is not to say the book is easy, but any difficulty that arises is in the nature of the subject, and is no fault of the author's. Throughout the book, he offers many appropriate examples (or non-examples), and provides numerous and diverse exercises, which often prove results that are later used in the body of the text, drawing the reader into the subject.' Frederic Green, ACM SIGACT News'This book fulfills its stated goals: 'The textbook is suitable for a broad range of readers, from undergraduate to graduate students, who desire a better understanding of the fundamental topics in set theory that may have been, or will be, overlooked in their other mathematics courses'.' Shoshana Friedman, MathSciNetTable of Contents1. Introduction; 2. Basic set building axioms and operations; 3. Relations and functions; 4. The natural numbers; 5. On the size of sets; 6. Transfinite recursion; 7. The axiom of choice (revisited); 8. Ordinals; 9. Cardinals.
£45.59
Cambridge University Press Lectures on Infinitary Model Theory
Book SynopsisThis book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic. Connections between infinitary model theory and other branches of mathematical logic, and applications to algebra and algebraic geometry are both comprehensively explored.Table of ContentsIntroduction; Part I. Classical Results in Infinitary Model Theory: 1. Infinitary languages; 2. Back and forth; 3. The space of countable models; 4. The model existence theorem; 5. Hanf numbers and indiscernibles; Part II. Building Uncountable Models: 6. Elementary chains; 7. Vaught counterexamples; 8. Quasinimal excellence; Part III. Effective Considerations: 9. Effective descriptive set theory; 10. Hyperarithmetic sets; 11. Effective aspects of Lω1,ω; 12. Spectra of Vaught counterexamples; Appendix A. N1-free abelian groups; Appendix B. Admissibility; References; Index.
£105.45
Cambridge University Press The BanachTarski Paradox
Book SynopsisThe BanachTarski Paradox is the most surprising result in mathematics. This new edition of a classic book offers a comprehensive, accessible presentation, with many related results, especially connections to non-Euclidean geometry, to squaring the circle, and even to some art by Escher. This material is suited to projects for undergraduates or masters students.Trade Review'The new edition of The Banach–Tarski Paradox, by Grzegorz Tomkowicz and Stan Wagon, is a welcome revisiting and extensive reworking of the first edition of the book. Whether you are new to the topic of paradoxical decompositions, or have studied the phenomenon for years, this book has a lot to offer. I recommend buying two copies of the book, one for the office and one for the home, because studying the book carefully (perhaps in a series of working seminars) will be worthwhile, and casually browsing through the book in your spare time will be simply a lot of fun.' Joseph Rosenblatt, Department Chair, Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis'This is the second edition of this classic and comprehensive monograph on paradoxical decompositions. What adds to the special appeal of this topic is the diversity of methods and the connection to several fields including set theory, group theory, measure theory, geometry, algebra, and discrete mathematics. The previous edition of this book stimulated a large amount of research. The present volume also includes these developments and furthermore discusses the solutions to some of the problems that were solved in the past thirty years, including the realization of the Banach–Tarski paradox with pieces having the Baire property and Tarski's circle squaring problem.' Miklos Laczkovich, University College London'Wagon's classic book on the Banach–Tarski paradox has been updated with Tomkowicz to include major advances over the last thirty years. It remains the definitive source for both newcomers to the subject and experts who want to broaden their knowledge. The book provides a basic introduction to the field with clear exposition and important historical background. It includes complete proofs of the Banach–Tarski paradox and related results. It continues with an extensive survey of more advanced topics. This is far and away the best resource for beginners and experts on the strangest result in all of mathematics.' Matthew Foreman, University of California, Irvine'Several spectacular results have been proved since the first edition of this book … All these results and problems are presented in a penetrating and lucid way in this new edition.' Jan Mycielski, University of Colorado, Boulder, from the ForewordReview of previous edition: '… a readable and stimulating book.' Ward Henson, American Scientist'In 1985 Stan Wagon wrote The Banach-Tarski Paradox, which not only became the classic text on paradoxical mathematics, but also provided vast new areas for research. The new second edition, co-written with Grzegorz Tomkowicz, a Polish mathematician who specializes in paradoxical decompositions, exceeds any possible expectation I might have had for expanding a book I already deeply treasured. The meticulous research of the original volume is still there, but much new research has also been included … I should also mention that this book is beautifully illustrated.' John J. Watkins, MAA Reviews'For some people the book will be over by page 36, because by then one has seen full treatments of the results of Hausdorff and of Banach and Tarski. These people are short-sighted; there is much fascinating mathematics to be learned from the further developments. As the recent result of Marks and Unger shows, there is probably still much to discover. Indeed, the book contains some very interesting questions that still await solution.' Klaas Pieter Hart, Mathematical ReviewsTable of ContentsPart I. Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures: 1. Introduction; 2. The Hausdorff paradox; 3. The Banach–Tarski paradox: duplicating spheres and balls; 4. Hyperbolic paradoxes; 5. Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition; 6. Higher dimensions; 7. Free groups of large rank: getting a continuum of spheres from one; 8. Paradoxes in low dimensions; 9. Squaring the circle; 10. The semigroup of equidecomposability types; Part II: Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions: 11. Transition; 12. Measures in groups; 13. Applications of amenability; 14. Growth conditions in groups and supramenability; 15. The role of the axiom of choice.
£37.04
Cambridge University Press How to Prove It
Book SynopsisProofs 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 booTrade Review'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'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'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'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'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'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'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 GazetteTable of Contents1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Number theory; 8. Infinite sets.
£85.49
Capstone Press Sorting Wonder Readers Early Level
Book Synopsis
£6.99
