Mathematical foundations Books
Cambridge University Press Semimodular Lattices Theory and Applications 73 Encyclopedia of Mathematics and its Applications Series Number 73
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£50.95
Cambridge University Press Algebraic Theories A Categorical Introduction to General Algebra 184 Cambridge Tracts in Mathematics Series Number 184
Book SynopsisFirst up-to-date treatment of the categorical view of sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry, and mathematical physics. A stimulating read for graduate students and researchers in category theory, general algebra, theoretical computer science and algebraic topology.Trade Review'The book is very well written and made as self-contained as it is reasonable for the intended audience of graduate students and researchers.' Zentralblatt MATHTable of ContentsForeword F. W. Lawvere; Introduction; Preliminaries; Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories; 2. Sifted and filtered colimits; 3. Reflexive coequalizers; 4. Algebraic categories as free completions; 5. Properties of algebras; 6. A characterization of algebraic categories; 7. From filtered to sifted; 8. Canonical theories; 9. Algebraic functors; 10. Birkhoff's variety theorem; Part II. Concrete Algebraic Categories: 11. One-sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of Σ-algebras; 14. S-sorted algebraic categories; Part III. Selected Topics: 15. Morita equivalence; 16. Free exact categories; 17. Exact completion and reflexive-coequalizer completion; 18. Finitary localizations of algebraic categories; A. Monads; B. Abelian categories; C. More about dualities for one-sorted algebraic categories; Summary; Bibliography; Index.
£105.45
Cambridge University Press A Students Guide to Data and Error Analysis
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£66.50
Cambridge University Press Recent Trends in Combinatorics
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£35.14
Cambridge University Press A Students Guide to Data and Error Analysis
Book SynopsisAll students taking laboratory courses within the physical sciences and engineering will benefit from this book, whilst researchers will find it an invaluable reference. This concise, practical guide brings the reader up-to-speed on the proper handling and presentation of scientific data and its inaccuracies. It covers all the vital topics with practical guidelines, computer programs (in Python), and recipes for handling experimental errors and reporting experimental data. In addition to the essentials, it also provides further background material for advanced readers who want to understand how the methods work. Plenty of examples, exercises and solutions are provided to aid and test understanding, whilst useful data, tables and formulas are compiled in a handy section for easy reference.Trade Review"Overall, this would be a nice text or reference to accompany a short course in statistics for undergraduate science or engineering..also useful for researchers desiring a primer or review...Recommended." - CHOICETable of ContentsPart I. Data and Error Analysis: 1. Introduction; 2. The presentation of physical quantities with their inaccuracies; 3. Errors: classification and propagation; 4. Probability distributions; 5. Processing of experimental data; 6. Graphical handling of data with errors; 7. Fitting functions to data; 8. Back to Bayes: knowledge as a probability distribution; Answers to exercises; Part II. Appendices: A1. Combining uncertainties; A2. Systematic deviations due to random errors; A3. Characteristic function; A4. From binomial to normal distributions; A5. Central limit theorem; A6. Estimation of the varience; A7. Standard deviation of the mean; A8. Weight factors when variances are not equal; A9. Least squares fitting; Part III. Python Codes; Part IV. Scientific Data: Chi-squared distribution; F-distribution; Normal distribution; Physical constants; Probability distributions; Student's t-distribution; Units.
£25.64
Cambridge University Press Model Theory Algebra and Geometry 39 Mathematical Sciences Research Institute Publications Series Number 39
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£39.89
Cambridge University Press The Logic of Quantum Mechanics Volume 15 Encyclopedia of Mathematics and its Applications Series Number 15
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£55.09
Cambridge University Press Random Matrix Models and their Applications 40 Mathematical Sciences Research Institute Publications Series Number 40
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£45.59
Cambridge University Press Brouwers Cambridge Lectures on Intuitionism
Book SynopsisOriginally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics in intuitionism such as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work.Table of ContentsFrontispiece L. E. J. Brouwer; Editorial preface; 1. Historical introduction and fundamental notions; 2. General properties of species, spread directions, spreads and spaces; 3. Order; 4. Precision analysis of the continuum; 5. The bunch theorem; Appendix; Notes; References; Index.
£37.37
Cambridge University Press New Perspectives in Algebraic Combinatorics 38 Mathematical Sciences Research Institute Publications Series Number 38
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£39.89
Cambridge University Press Combinatorial Games TicTacToe Theory 114 Encyclopedia of Mathematics and its Applications Series Number 114
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£69.99
Cambridge University Press Combinatorics
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£55.09
Cambridge University Press LMS 23 Parallelisms London Mathematical Society Lecture Note Series Series Number 23
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£45.16
Cambridge University Press LMS 38 Surveys in Combinatorics 79 London Mathematical Society Lecture Note Series Series Number 38
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£61.71
Cambridge University Press Surveys in Combinatorics Invited Papers for the Ninth British Combinatorial Conference 1983 82 London Mathematical Society Lecture Note Series Series Number 82
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£45.16
Cambridge University Press LMS 87 Surveys in Set Theory London Mathematical Society Lecture Note Series Series Number 87
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£61.71
Cambridge University Press LMS 47 Coding the Universe London Mathematical Society Lecture Note Series Series Number 47
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£74.13
Cambridge University Press Finite Geometries and Designs Proceedings of the Second Isle of Thorns Conference 1980 49 London Mathematical Society Lecture Note Series Series Number 49
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£50.95
Cambridge University Press Combinatorics Proceedings of the Eighth British Combinatorial Conference University College Swansea 1981
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£55.09
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