Introduction to the Analysis of Metric Spaces

Author: John R. Giles,John Robilliard Giles

Publisher: Cambridge University Press

ISBN: 9780521359283

Category: Mathematics

Page: 257

View: 2793

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Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.
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Introduction to the Analysis of Normed Linear Spaces

Author: J. R. Giles,John Robilliard Giles

Publisher: Cambridge University Press

ISBN: 9780521653756

Category: Mathematics

Page: 280

View: 8363

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This text is ideal for a basic course in functional analysis for senior undergraduate and beginning postgraduate students. John Giles provides insight into basic abstract analysis, which is now the contextual language of much modern mathematics. Although it is assumed that the student has familiarity with elementary real and complex analysis, linear algebra, and the analysis of metric spaces, the book does not assume a knowledge of integration theory or general topology. Its central theme concerns structural properties of normed linear spaces in general, especially associated with dual spaces and continuous linear operators on normed linear spaces. Giles illustrates the general theory with a great variety of example spaces.
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Lectures on Real Analysis

Author: Finnur Lárusson

Publisher: Cambridge University Press

ISBN: 1139511041

Category: Mathematics

Page: N.A

View: 8370

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This is a rigorous introduction to real analysis for undergraduate students, starting from the axioms for a complete ordered field and a little set theory. The book avoids any preconceptions about the real numbers and takes them to be nothing but the elements of a complete ordered field. All of the standard topics are included, as well as a proper treatment of the trigonometric functions, which many authors take for granted. The final chapters of the book provide a gentle, example-based introduction to metric spaces with an application to differential equations on the real line. The author's exposition is concise and to the point, helping students focus on the essentials. Over 200 exercises of varying difficulty are included, many of them adding to the theory in the text. The book is perfect for second-year undergraduates and for more advanced students who need a foundation in real analysis.
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Notes on Counting: An Introduction to Enumerative Combinatorics

Author: Peter J. Cameron

Publisher: Cambridge University Press

ISBN: 1108417361

Category: Mathematics

Page: N.A

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Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield-Pólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.
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Neverending Fractions

An Introduction to Continued Fractions

Author: Jonathan Borwein,Alf van der Poorten,Jeffrey Shallit,Wadim Zudilin

Publisher: Cambridge University Press

ISBN: 0521186498

Category: Mathematics

Page: 224

View: 3364

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This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.
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AI 2002: Advances in Artificial Intelligence

15th Australian Joint Conference on Artificial Intelligence, Canberra, Australia, December 2-6, 2002, Proceedings

Author: Bob McKay,John Slaney

Publisher: Springer

ISBN: N.A

Category: Artificial intelligence

Page: 730

View: 931

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This book constitutes the refereed proceedings of the 15th Australian Joint Conference on Artificial Intelligence, AI 2002, held in Canberra, Australia in December 2002. The 62 revised full papers and 12 posters presented were carefully reviewed and selected from 117 submissions. The papers are organized in topical sections on natural language and information retrieval, knowledge representation and reasoning, deduction, learning theory, agents, intelligent systems. Bayesian reasoning and classification, evolutionary algorithms, neural networks, reinforcement learning, constraints and scheduling, neural network applications, satisfiability reasoning, machine learning applications, fuzzy reasoning, and case-based reasoning.
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