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Books > Science & Mathematics > Mathematics > Mathematical foundations > General

Errors, Blunders, and Lies - How to Tell the Difference (Paperback): David S. Salsburg Errors, Blunders, and Lies - How to Tell the Difference (Paperback)
David S. Salsburg
R1,029 R903 Discovery Miles 9 030 Save R126 (12%) Ships in 10 - 15 working days

We live in a world that is not quite "right." The central tenet of statistical inquiry is that Observation = Truth + Error because even the most careful of scientific investigations have always been bedeviled by uncertainty. Our attempts to measure things are plagued with small errors. Our attempts to understand our world are blocked by blunders. And, unfortunately, in some cases, people have been known to lie. In this long-awaited follow-up to his well-regarded bestseller, The Lady Tasting Tea, David Salsburg opens a door to the amazing widespread use of statistical methods by looking at historical examples of errors, blunders and lies from areas as diverse as archeology, law, economics, medicine, psychology, sociology, Biblical studies, history, and war-time espionage. In doing so, he shows how, upon closer statistical investigation, errors and blunders often lead to useful information. And how statistical methods have been used to uncover falsified data. Beginning with Edmund Halley's examination of the Transit of Venus and ending with a discussion of how many tanks Rommel had during the Second World War, the author invites the reader to come along on this easily accessible and fascinating journey of how to identify the nature of errors, minimize the effects of blunders, and figure out who the liars are.

Categories for the Working Mathematician (Hardcover, 2nd ed. 1978): Saunders MacLane Categories for the Working Mathematician (Hardcover, 2nd ed. 1978)
Saunders MacLane
R1,487 R1,403 Discovery Miles 14 030 Save R84 (6%) Ships in 9 - 15 working days

Categories for the Working Mathematician provides an array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including two new chapters on topics of active interest. One is on symmetric monoidal categories and braided monoidal categories and the coherence theorems for them. The second describes 2-categories and the higher dimensional categories which have recently come into prominence. The bibliography has also been expanded to cover some of the many other recent advances concerning categories.

Handbook of Categorical Algebra: Volume 3, Sheaf Theory (Hardcover, Volume 3, Sheaf Theory): Francis Borceux Handbook of Categorical Algebra: Volume 3, Sheaf Theory (Hardcover, Volume 3, Sheaf Theory)
Francis Borceux
R5,878 R5,360 Discovery Miles 53 600 Save R518 (9%) Ships in 12 - 17 working days

This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.

Handbook of Categorical Algebra: Volume 2, Categories and Structures (Hardcover, Volume 2, Categories and Structures): Francis... Handbook of Categorical Algebra: Volume 2, Categories and Structures (Hardcover, Volume 2, Categories and Structures)
Francis Borceux
R5,030 Discovery Miles 50 300 Ships in 12 - 17 working days

The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.

Handbook of Categorical Algebra: Volume 1, Basic Category Theory (Hardcover, Volume 1, Basic Category Theory): Francis Borceux Handbook of Categorical Algebra: Volume 1, Basic Category Theory (Hardcover, Volume 1, Basic Category Theory)
Francis Borceux
R4,427 Discovery Miles 44 270 Ships in 12 - 17 working days

A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate students with a good background in mathematics. Volume 1 is devoted to general concepts. 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.

Finite Geometries and Combinatorics (Paperback): F. de Clerck, J. Hirschfeld Finite Geometries and Combinatorics (Paperback)
F. de Clerck, J. Hirschfeld
R1,580 Discovery Miles 15 800 Ships in 12 - 17 working days

Finite geometry and combinatorics is the art of counting any phenomena that can be described by a diagram. Everyday life is full of applications; from telephones to compact disc players, from the transmission of confidential information to the codes on any item on supermarket shelves. This is a collection of thirty-five articles on covering topics such as finite projective spaces, generalized polygons, strongly regular graphs, diagram geometries and polar spaces. Included here are articles from many of the leading practitioners in the field including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results and the growing use of computer algebra packages in this area is also demonstrated.

Surveys in Combinatorics, 1993 (Paperback): K. Walker Surveys in Combinatorics, 1993 (Paperback)
K. Walker
R1,353 Discovery Miles 13 530 Ships in 12 - 17 working days

This volume is comprised of the invited lectures given at the 14th British Combinatorial Conference. The lectures survey many topical areas of current research activity in combinatorics and its applications, and also provide a valuable overview of the subject, for both mathematicians and computer scientists.

The Petersen Graph (Paperback, New): D. A. Holton, J. Sheehan The Petersen Graph (Paperback, New)
D. A. Holton, J. Sheehan
R1,547 Discovery Miles 15 470 Ships in 12 - 17 working days

The Petersen graph occupies an important position in the development of several areas of modern graph theory because it often appears as a counter-example to important conjectures. In this account, the authors examine those areas, using the prominent role of the Petersen graph as a unifying feature. Topics covered include: vertex and edge colourability (including snarks), factors, flows, projective geometry, cages, hypohamiltonian graphs, and symmetry properties such as distance transitivity. The final chapter contains a mixture of other topics in which the Petersen graph has played its part. Undergraduate students should profit from reading this book as there are few prerequisite skills involved, and it could be used for a second course in graph theory. At the same time, the authors have also included a number of unsolved problems as well as topics of recent study. It should, therefore, also be useful as a reference for graph theorists.

Quick Arithmetic - A Self-Teaching Guide (Hardcover, 3rd ed.): Robert A. Carman, Marilyn J. Carman Quick Arithmetic - A Self-Teaching Guide (Hardcover, 3rd ed.)
Robert A. Carman, Marilyn J. Carman
R818 R696 Discovery Miles 6 960 Save R122 (15%) Ships in 10 - 15 working days

Master math at your own pace
Does working with numbers often frustrate you? Do you need to brush up on your basic math skills? Do you feel math stands between you and your career goals, or a better grade at school?
Quick Arithmetic, Third Edition is the quickest and easiest way to teach yourself the basic math skills you need to advance on the job or in school. Using cartoons and a clear writing style, this practical guide provides a fresh start for learning or reviewing how to work with whole numbers, fractions, decimals, and percentages. The book's proven self-teaching approach allows you to work at your own pace and learn only the material you need. Previews and objectives at the beginning of each section help you determine your particular needs, while self-tests, practice problems, and a final exam let you measure your progress and reinforce what you've learned.
For anyone who has ever felt intimidated by a page of numbers, Quick Arithmetic, Third Edition has the answers

Gorenstein Dimensions (Paperback, 2000 ed.): Lars W. Christensen Gorenstein Dimensions (Paperback, 2000 ed.)
Lars W. Christensen
R1,637 Discovery Miles 16 370 Ships in 10 - 15 working days

This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content.
Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.

Applications of Categories in Computer Science - Proceedings of the London Mathematical Society Symposium, Durham 1991... Applications of Categories in Computer Science - Proceedings of the London Mathematical Society Symposium, Durham 1991 (Paperback, New)
M. P. Fourman, P. T. Johnstone, A.M. Pitts
R1,680 Discovery Miles 16 800 Ships in 12 - 17 working days

Category theory and related topics of mathematics have been increasingly applied to computer science in recent years. This book contains selected papers from the London Mathematical Society Symposium on the subject which was held at the University of Durham. Participants at the conference were leading computer scientists and mathematicians working in the area and this volume reflects the excitement and importance of the meeting. All the papers have been refereed and represent some of the most important and current ideas. Hence this book will be essential to mathematicians and computer scientists working in the applications of category theory.

Surveys in Combinatorics, 1991 (Paperback): A. D. Keedwell Surveys in Combinatorics, 1991 (Paperback)
A. D. Keedwell
R1,678 Discovery Miles 16 780 Ships in 12 - 17 working days

This volume contains nine invited papers that survey many areas of current research in combinatorics both on the theoretical and practical side. Several papers may be regarded as summarizing our present state of knowledge in a particular topic.

Prime Numbers and the Riemann Hypothesis (Paperback): Barry Mazur, William Stein Prime Numbers and the Riemann Hypothesis (Paperback)
Barry Mazur, William Stein
R709 Discovery Miles 7 090 Ships in 12 - 17 working days

Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis.

Basketball Data Science - With Applications in R (Hardcover): Paola Zuccolotto, Marica Manisera Basketball Data Science - With Applications in R (Hardcover)
Paola Zuccolotto, Marica Manisera
R3,889 Discovery Miles 38 890 Ships in 12 - 17 working days

Using data from one season of NBA games, Basketball Data Science: With Applications in R is the perfect book for anyone interested in learning and applying data analytics in basketball. Whether assessing the spatial performance of an NBA player's shots or doing an analysis of the impact of high pressure game situations on the probability of scoring, this book discusses a variety of case studies and hands-on examples using a custom R package. The codes are supplied so readers can reproduce the analyses themselves or create their own. Assuming a basic statistical knowledge, Basketball Data Science with R is suitable for students, technicians, coaches, data analysts and applied researchers. Features: * One of the first books to provide statistical and data mining methods for the growing field of analytics in basketball. * Presents tools for modelling graphs and figures to visualize the data. * Includes real world case studies and examples, such as estimations of scoring probability using the Golden State Warriors as a test case. * Provides the source code and data so readers can do their own analyses on NBA teams and players.

Derived Equivalences for Group Rings (Paperback, 1998 ed.): Steffen Koenig Derived Equivalences for Group Rings (Paperback, 1998 ed.)
Steffen Koenig; Contributions by B. Keller, M. Linckelmann; Alexander Zimmermann; Contributions by J Rickard, …
R1,541 Discovery Miles 15 410 Ships in 10 - 15 working days

A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Brou 's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure." The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.

Wavelets, Approximation, and Statistical Applications (Paperback, New): Wolfgang Hardle, Gerard Kerkyacharian, Dominique... Wavelets, Approximation, and Statistical Applications (Paperback, New)
Wolfgang Hardle, Gerard Kerkyacharian, Dominique Picard, Alexander Tsybakov
R3,266 Discovery Miles 32 660 Ships in 10 - 15 working days

The mathematical theory of ondelettes (wavelets) was developed by Yves Meyer and many collaborators about 10 years ago. It was designed for ap proximation of possibly irregular functions and surfaces and was successfully applied in data compression, turbulence analysis, image and signal process ing. Five years ago wavelet theory progressively appeared to be a power ful framework for nonparametric statistical problems. Efficient computa tional implementations are beginning to surface in this second lustrum of the nineties. This book brings together these three main streams of wavelet theory. It presents the theory, discusses approximations and gives a variety of statistical applications. It is the aim of this text to introduce the novice in this field into the various aspects of wavelets. Wavelets require a highly interactive computing interface. We present therefore all applications with software code from an interactive statistical computing environment. Readers interested in theory and construction of wavelets will find here in a condensed form results that are somewhat scattered around in the research literature. A practioner will be able to use wavelets via the available software code. We hope therefore to address both theory and practice with this book and thus help to construct bridges between the different groups of scientists. This te. xt grew out of a French-German cooperation (Seminaire Paris Berlin, Seminar Berlin-Paris). This seminar brings together theoretical and applied statisticians from Berlin and Paris. This work originates in the first of these seminars organized in Garchy, Burgundy in 1994."

Metamathematics of First-Order Arithmetic (Paperback, Softcover reprint of the original 1st ed. 1993): Petr Hajek, Pavel Pudlak Metamathematics of First-Order Arithmetic (Paperback, Softcover reprint of the original 1st ed. 1993)
Petr Hajek, Pavel Pudlak
R3,561 Discovery Miles 35 610 Ships in 10 - 15 working days

People have always been interested in numbers, in particular the natural numbers. Of course, we all have an intuitive notion of what these numbers are. In the late 19th century mathematicians, such as Grassmann, Frege and Dedekind, gave definitions for these familiar objects. Since then the development of axiomatic schemes for arithmetic have played a fundamental role in a logical understanding of mathematics. There has been a need for some time for a monograph on the metamathematics of first-order arithmetic. The aim of the book by Hajek and Pudlak is to cover some of the most important results in the study of a first order theory of the natural numbers, called Peano arithmetic and its fragments (subtheories). The field is quite active, but only a small part of the results has been covered in monographs. This book is divided into three parts. In Part A, the authors develop parts of mathematics and logic in various fragments. Part B is devoted to incompleteness. Part C studies systems that have the induction schema restricted to bounded formulas (Bounded Arithmetic). One highlight of this section is the relation of provability to computational complexity. The study of formal systems for arithmetic is a prerequisite for understanding results such as Godel's theorems. This book is intended for those who want to learn more about such systems and who want to follow current research in the field. The book contains a bibliography of approximately 1000 items."

A Set Theory Workbook (Paperback, 1998 ed.): Iain Adamson A Set Theory Workbook (Paperback, 1998 ed.)
Iain Adamson
R1,435 Discovery Miles 14 350 Ships in 10 - 15 working days

This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.

Green Functors and G-sets (Paperback, 1997 ed.): Serge Bouc Green Functors and G-sets (Paperback, 1997 ed.)
Serge Bouc
R1,953 Discovery Miles 19 530 Ships in 10 - 15 working days

This book provides a definition of Green functors for a finite group G, and of modules over it, in terms of the category of finite G-sets. Some classical constructions, such as the associated categroy or algebra, have a natural interpretation in that framework. Many notions of ring theory can be extended to Green functors (opposite Green functor, bimodules, Morita theory, simple modules, centres, ...). There are moreover connections between Green functors for different groups, given by functors associated to bisets. Intended for researchers and students in representation theory of finite groups it requires only basic algebra and category theory, though knowledge of the classical examples of Mackey functors is probably preferable

Design Theory (Paperback, Revised): D.R. Hughes, F. Piper Design Theory (Paperback, Revised)
D.R. Hughes, F. Piper
R1,215 Discovery Miles 12 150 Ships in 12 - 17 working days

Design theory has grown to be a subject of considerable interest in mathematics, not only in itself, but for its connections to other fields such as geometry, group theory, graph theory and coding theory. This textbook, first published in 1985, is intended to be an accessible introduction to the subject for advanced undergraduate and beginning graduate students which should prepare them for research in design theory and its applications. The first four chapters of the book are designed to be the core of any course in the subject, while the remaining chapters can be utilized in more advanced or longer courses. The authors assume some knowledge of linear algebra for the first half of the book, but for the second half, students need further background in algebra.

Triangulated Categories in the Representation of Finite Dimensional Algebras (Paperback): Dieter Happel Triangulated Categories in the Representation of Finite Dimensional Algebras (Paperback)
Dieter Happel
R1,547 R1,024 Discovery Miles 10 240 Save R523 (34%) Ships in 12 - 17 working days

Happel presents an introduction to the use of triangulated categories in the study of representations of finit-dimensional algeras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite=dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and iterated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.

Category Theory and Computer Science - 7th International Conference, CTCS'97, Santa Margherita Ligure Italy, September... Category Theory and Computer Science - 7th International Conference, CTCS'97, Santa Margherita Ligure Italy, September 4-6, 1997, Proceedings (Paperback, 1997 ed.)
Eugenio Moggi, Giuseppe Rosolini
R1,580 Discovery Miles 15 800 Ships in 10 - 15 working days

This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997.
Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.

Ideal Spaces (Paperback, 1997 ed.): Martin Vath Ideal Spaces (Paperback, 1997 ed.)
Martin Vath
R1,360 Discovery Miles 13 600 Ships in 10 - 15 working days

Ideal spaces are a very general class of normed spaces of measurable functions, which includes e.g. Lebesgue and Orlicz spaces. Their most important application is in functional analysis in the theory of (usual and partial) integral and integro-differential equations. The book is a rather complete and self-contained introduction into the general theory of ideal spaces. Some emphasis is put on spaces of vector-valued functions and on the constructive viewpoint of the theory (without the axiom of choice). The reader should have basic knowledge in functional analysis and measure theory.

The Logical Writings of Karl Popper (Hardcover, 1st ed. 2022): David Binder, Thomas Piecha, Peter Schroeder-Heister The Logical Writings of Karl Popper (Hardcover, 1st ed. 2022)
David Binder, Thomas Piecha, Peter Schroeder-Heister
R1,279 Discovery Miles 12 790 Ships in 9 - 15 working days

This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

Varieties of Constructive Mathematics (Paperback): Douglas Bridges, Fred Richman Varieties of Constructive Mathematics (Paperback)
Douglas Bridges, Fred Richman
R1,366 Discovery Miles 13 660 Ships in 12 - 17 working days

This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.

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