Mathematical foundations Books
Cambridge University Press LMS 110 Introduction Theory of Surreal Numb London Mathematical Society Lecture Note Series Series Number 110
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£65.02
Cambridge University Press Varieties of Constructive Mathematics
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£55.91
Cambridge University Press Stable Domination and Independence in Algebraically Closed Valued Fields 30 Lecture Notes in Logic Series Number 30
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£35.14
Cambridge University Press Notes on Logic and Set Theory
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£41.79
Cambridge University Press Stone Spaces 3 Cambridge Studies in Advanced Mathematics Series Number 3
Book SynopsisOver the last 45 years, Boolean theorem has been generalized and extended in several different directions and its applications have reached into almost every area of modern mathematics; but since it lies on the frontiers of algebra, geometry, general topology and functional analysis, the corpus of mathematics which has arisen in this way is seldom seen as a whole. In order to give a unified treatment of this rather diverse body of material, Dr Johnstone begins by developing the theory of locales (a lattice-theoretic approach to 'general topology without points' which has achieved some notable results in the past ten years but which has not previously been treated in book form). This development culminates in the proof of Stone's Representation Theorem.Table of ContentsPreface; Advice to the reader; Introduction; 1. Preliminaries; 2. Introduction to locales; 3. Compact Hausdorff spaces; 4. Continuous real-valued functions; 5. Representations of rings; 6. Profiniteness and duality; 7. Continuous lattices; Bibliography; Index of categories; Index of other symbols; Index of definitions.
£43.69
Cambridge University Press LMS 108 Some Topics in Graph Thry London Mathematical Society Lecture Note Series Series Number 108
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£50.99
Cambridge University Press LMS 166 Surveys Combinatorics 91 London Mathematical Society Lecture Note Series Series Number 166
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£58.99
Cambridge University Press Categories and Computer Science 28 Cambridge Computer Science Texts Series Number 28
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£76.95
Cambridge University Press Categories and Computer Science 28 Cambridge Computer Science Texts Series Number 28
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£37.99
Cambridge University Press The Petersen Graph 7 Australian Mathematical Society Lecture Series Series Number 7
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£52.60
Cambridge University Press Handbook of Categorical Algebra Volume 1 Basic Category Theory Encyclopedia of Mathematics and its Applications Series Number 50
Book SynopsisA Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various 'refinements' of the fundamental concepts of category and functor.Trade Review"...Not only is this the most comprehensive book ever written on category theory, it is by far the best written...What the author has understood is that one cannot understand this subject without lots of examples..." Gian-Carlo Rota, The Bulletin of Mathematics Books"...these volumes will be of enormous value to graduate students in pure or applied category theory." Martin Hyland, Mathematical ReviewsTable of ContentsIntroduction; 1. The language of categories; 2. Limits; 3. Adjoint functors; 4. Generators and projectives; 5. Categories of fractions; 6. Flat functors and Cauchy completeness; 7. Bicategories and distributors; 8. Internal category theory; Bibliography; Index.
£152.95
Cambridge University Press Handbook of Categorical Algebra Volume 2 Categories and Structures Encyclopedia of Mathematics and its Applications Series Number 51
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£173.85
Cambridge University Press Handbook of Categorical Algebra Volume 3 Sheaf Theory Encyclopedia of Mathematics and its Applications Series Number 52
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£185.25
Cambridge University Press LMS 191 Finite Geometries London Mathematical Society Lecture Note Series Series Number 191
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£61.71
Cambridge University Press LMS 187 Surveys Combinatorics 1993 London Mathematical Society Lecture Note Series Series Number 187
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£55.09
Cambridge University Press Combinatorial Games TicTacToe Theory 114 Encyclopedia of Mathematics and its Applications Series Number 114
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£152.95
Cambridge University Press Higher Operads Higher Categories 298 London
Book SynopsisHigher-dimensional category theory draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. This is the first book on the subject and lays its foundations, appealing to graduate students and researchers who wish to become acquainted with this modern branch of mathematics.Table of ContentsPart I. Background: 1. Classical categorical structures; 2. Classical operads and multicategories; 3. Notions of monoidal category; Part II. Operads. 4. Generalized operads and multicategories: basics; 5. Example: fc-multicategories; 6. Generalized operads and multicategories: further theory; 7. Opetopes; Part III. n-categories: 8. Globular operads; 9. A definition of weak n-category; 10. Other definitions of weak n-category; Appendices: A. Symmetric structures; B. Coherence for monoidal categories; C. Special Cartesian monads; D. Free multicategories; E. Definitions of trees; F. Free strict n-categories; G. Initial operad-with-contraction.
£88.21
Cambridge University Press Iterative Solution Methods
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£75.99
Cambridge University Press Advances in Linear Logic 222 London Mathematical Society Lecture Note Series Series Number 222
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£65.86
Cambridge University Press Dynamical Systems and Semisimple Groups
Book SynopsisAssuming only a basic knowledge of manifolds theory, algebra, and measure theory, this 1998 book is a systematic and largely self-contained introduction to Margulis-Zimmer theory. It should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.Trade ReviewReview of the hardback: 'This text might well become a standard one …'. G. Pilz, Internationale Mathematische NachrichtenTable of ContentsPreface; 1. Topological dynamics; 2. Ergodic theory - part I; 3. Smooth actions and Lie theory; 4. Algebraic actions; 5. The classical groups; 6. Geometric structures; 7. Semisimple Lie groups; 8. Ergodic theory - part II; 9. Oseledec's theorem; 10. Rigidity theorems; Appendix: Lattices in SL(n, R); References; Index.
£105.45
Cambridge University Press An Introduction to Mathematical Reasoning Numbers Sets and Functions
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£94.99
Cambridge University Press Lie Groups Lie Algebras Cohomology and some Applications in Physics
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£69.17
Cambridge University Press An Introduction to Mathematical Reasoning Numbers
Book SynopsisThe purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. This is achieved by exploring set theory, combinatorics and number theory, topics which include many fundamental ideas which are part of the tool kit of any mathematician. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. Over 250 problems include questions to interest and challenge the most able student as well as plenty of routine exercises to help familiarize the reader with the basic ideas.Trade Review'The book is written with understanding of the needs of students …' European Mathematical SocietyTable of ContentsPart I. Mathematical Statements and Proofs: 1. The language of mathematics; 2. Implications; 3. Proofs; 4. Proof by contradiction; 5. The induction principle; Part II. Sets and Functions: 6. The language of set theory; 7. Quantifiers; 8. Functions; 9. Injections, surjections and bijections; Part III. Numbers and Counting: 10. Counting; 11. Properties of finite sets; 12. Counting functions and subsets; 13. Number systems; 14. Counting infinite sets; Part IV. Arithmetic: 15. The division theorem; 16. The Euclidean algorithm; 17. Consequences of the Euclidean algorithm; 18. Linear diophantine equations; Part V. Modular Arithmetic: 19. Congruences of integers; 20. Linear congruences; 21. Congruence classes and the arithmetic of remainders; 22. Partitions and equivalence relations; Part VI. Prime Numbers: 23. The sequence of prime numbers; 24. Congruence modulo a prime; Solutions to exercises.
£33.24
Cambridge University Press LMS 241 Surveys Combinatorics 97 London Mathematical Society Lecture Note Series Series Number 241
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£69.99
Cambridge University Press Completeness and Basis Properties of Sets of Special Functions
Book SynopsisThis tract presents an exposition of methods for testing sets of special functions for completeness and basis properties, mostly in L2 and L2 spaces. The emphasis on methods of testing and their applications will also interest scientists and engineers engaged in fields such as the sampling theory of signals in electrical engineering and boundary value problems in mathematical physics.Table of ContentsPreface; 1. Foundations; 2. Orthogonal sequences; 3. Non-orthogonal sequences; 4. Differential and integral operators; Appendix; Bibliography; Subject index.
£36.87
Cambridge University Press The Principles of Mathematics Revisited
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£25.64
Cambridge University Press Practical Foundations of Mathematics 59 Cambridge Studies in Advanced Mathematics Series Number 59
Book SynopsisPractical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.Trade ReviewReview of the hardback: 'This is a fascinating and rewarding book … each chapter has several pages of subtle, provocative and imaginative exercises. In summary, it is a magnificent compilation of ideas and techniques: it is a mine of (well-organised) information suitable for the graduate student and experienced researcher alike.' Roy Dyckhoff, Bulletin of the London Mathematical SocietyTable of Contents1. First order reasoning; 2. Types and induction; 3. Posets and lattices; 4. Cartesian closed categories; 5. Limits and colimits; 6. Structural recursion; 7. Adjunctions; 8. Algebra with dependent types; 9. The quantifiers.
£144.40
Cambridge University Press Surveys in Combinatorics 1999 267 London Mathematical Society Lecture Note Series Series Number 267
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£65.86
Cambridge University Press Essential Mathematics for Political and Social Research
Book SynopsisThis 2006 book was the first of its kind to specifically address the comprehensive introduction to the mathematical principles needed by modern social scientists. The material introduces basic mathematical principles necessary to do analytical work in the social sciences. The core purpose is to present fundamental notions in standard notation and standard language.Trade Review"Ultimately, math is a language, and Jeff Gill's new book is a comprehensive guide to its grammar, syntax, and vocabulary. The book covers essential topics for advanced social science research and will be an excellent teaching, reference, and self-study tool." --Scott Desposato, University of California, San Diego"The body of topics that Gill covers is both appropriate and desirable for any primer in mathematics. The use of substantive examples is really outstanding, and makes this a uniquely attractive commodity for political science faculty who would be teaching a mathematical research/methods class over the course of a semester." --Alan Wiseman, Ohio State UniversityTable of Contents1. The basics; 2. Analytic geometry; 3. Linear algebra: vectors, matrices and operations; 4. Linear algebra continued: matrix structure; 5. Elementary scalar calculus; 6. Additional topics in scalar and vector calculus; 7. Probability theory; 8. Random variables; 9. Markov chains.
£41.79
Cambridge University Press Model Theory with Applications to Algebra and Analysis Volume 1 London Mathematical Society Lecture Note Series Series Number 349
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£50.99
Cambridge University Press Model Theory With Applications To Algebra And Analysis
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£65.86
Cambridge University Press Kurt Gdel and the Foundations of Mathematics Horizons of Truth
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£107.35
Cambridge University Press New Perspectives in Algebraic Combinatorics
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£122.55
Cambridge University Press Model Theory Algebra and Geometry 39 Mathematical Sciences Research Institute Publications Series Number 39
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£105.45
Cambridge University Press Recent Trends in Combinatorics
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£104.50
Cambridge University Press Random Matrix Models and their Applications
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£122.55
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.
£109.25
Cambridge University Press Mathematical Constants
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£151.05
Cambridge University Press Combinatorics of Symmetric Designs 5 New Mathematical Monographs Series Number 5
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£133.95
Cambridge University Press Categorical Foundations Special Topics in Order Topology Algebra and Sheaf Theory 97 Encyclopedia of Mathematics and its Applications Series Number 97
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£122.55
Cambridge University Press Spectral Generalizations of Line Graphs On Graphs with Least Eigenvalue 2 314 London Mathematical Society Lecture Note Series Series Number 314
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£65.86
Cambridge University Press Dependence Logic A New Approach to Independence Friendly Logic 70 London Mathematical Society Student Texts Series Number 70
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£116.85
Cambridge University Press A Primer of Infinitesimal Analysis
Book SynopsisOne of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new edition basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, literally, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the âœinfinitesimalâ methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.Trade Review'This might turn out to be a boring, shallow book review: I merely LOVED the book...the explanations are so clear, so considerate; the author must have taught the subject many times, since he anticipates virtually every potential question, concern, and misconception in a student's or reader's mind.' MAA Reviews'John Bell has done a first rate job in presenting an elementary introduction to this fascinating subject ... I recommend it highly.' J. P. Mayberry, British Journal for the Philosophy of ScienceTable of ContentsIntroduction; 1. Basic features of smooth worlds; 2. Basic differential calculus; 3. First applications of the differential calculus; 4. Applications to physics; 5. Multivariable calculus and applications; 6. The definite integral: Higher order infinitesimals; 7. Synthetic geometry; 8. Smooth infinitesimal analysis as an axiomatic system; Appendix; Models for smooth infinitesimal analysis.
£52.24
Cambridge University Press Introduction to Coalgebra Towards Mathematics of States and Observation 59 Cambridge Tracts in Theoretical Computer Science Series Number 59
Book SynopsisThis is the first mature and accessible introduction to coalgebra, providing clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. It will be of interest to mathematicians, computer scientists, mathematical physicists and even economists.Trade Review'The book is very carefully written, its many examples are discussed usually in great detail, expressing patiently the salient features to be exhibited. This applies to the usually fairly detailed proofs as well. Another treasure trove is the collection of most instructive exercises, of which there are plenty … This admirable book sets the standard for the work on set-based coalgebras for many years to come. It can be used for reference, and it is equally usable as a textbook.' Ernst-Erich Doberkat, Zentralblatt MATHTable of Contents1. Motivation; 2. Coalgebras of polynomial functors; 3. Bisimulations; 4. Logic, lifting and finality; 5. Monads, comonads and distributive laws; 6. Invariants and assertions; References; Definition and symbol index; Subject index.
£133.95
Cambridge University Press Kurt Godel and the Foundations of Mathematics Horizons Of Truth
Book SynopsisThis volume commemorates the life, work and foundational views of Kurt Gödel by exploring the impact of his work on current research and its future implications not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science.Trade Review'This is a very useful volume that brings together aspects of Gödel's work that relates to logic and mathematics …' The Mathematical IntelligencerTable of ContentsPart I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity, and Hilbert's program Solomon Feferman; 7. Computation and intractability: echoes of Kurt Gödel Christos H. Papadimitriou; 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland; 9. Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel's remarkable excursion into cosmology Wolfgang Rindler; 10. Physical unknowables Karl Svozil; Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work: 11. Gödel and physics John D. Barrow; 12. Gödel, Thomas Aquinas, and the unknowability of God Denys A. Turner; 13. Gödel's mathematics of philosophy Piergiorgio Odifreddi; 14. Gödel's ontological proof and its variants Petr Hájek; 15. The Gödel theorem and human nature Hilary Putnam; 16. Gödel, the mind, and the laws of physics Roger Penrose; Part III. New Frontiers - Beyond Gödel's Work in Mathematics and Symbolic Logic: 17. Gödel's functional interpretation and its use in current mathematics Ulrich Kohlenbach; 18. My forty years on his shoulders Harvey M. Friedman; 19. My interaction with Kurt Gödel: the man and his work Paul J. Cohen; 20. The transfinite universe W. Hugh Woodin; 21. The Gödel phenomena in mathematics: a modern view Avi Wigderson.
£56.99
Cambridge University Press The Combination of Observations
Book SynopsisFirst published in 1931, this book is the second edition of a 1917 original. The text provides an account of the method of least squares, aiming to obtain the best interpretation of the results of experiment without consideration of the way in which these results are obtained.Table of Contents1. Errors of observation; 2. The law of error; 3. The case of one unknown; 4. Observations of a different weight; 5. The general problem of the adjustment of indirect observations involving several unknown quantities; 6. Evaluation of the most probable values of the unknowns, their weights and probable errors; 7. The adjustment of conditioned observations; 8. The rejection of observations; 9. Alternatives to the normal law of errors; 10. Correlation; 11. Harmonic analysis; 12. The periodogram; Appendices; Index.
£27.99
McGraw-Hill Education - Europe Aleks 360 18 Weeks for Basic College Math with
Book Synopsis
£125.16
Pearson Education (US) Student Solutions Manual for Finite Mathematics
Book Synopsis Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming. He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University. David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an emeritus professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC. Table of Contents 1. Linear Equations and Straight Lines 2. Matrices 3. Linear Programming, A Geometric Approach 4. The Simplex Method 5. Sets and Counting 6. Probability 7. Probability and Statistics 8. Markov Processes 9. The Theory of Games 10. The Mathematics of Finance 11. Logic Appendix A. Areas Under the Standard Normal Curve Appendix B. The TI-83/84 Plus Graphing Calculators Appendix C. Spreadsheet Fundamentals Appendix D. Wolfram Alpha Answers to Odd-Numbered Exercises Index
£68.00
