Introduction to the Analysis of Normed Linear Spaces

Author: J. R. Giles
Publisher: Cambridge University Press
ISBN: 0521653754
Release Date: 2000-03-13
Genre: Mathematics

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.

Introduction to the Analysis of Metric Spaces

Author: John R. Giles
Publisher: Cambridge University Press
ISBN: 0521359287
Release Date: 1987-09-03
Genre: Mathematics

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.

Lectures on Real Analysis

Author: Finnur Lárusson
Publisher: Cambridge University Press
ISBN: 9781107026780
Release Date: 2012-06-07
Genre: Mathematics

A rigorous introduction to real analysis for undergraduates. Concise yet comprehensive, it includes a gentle introduction to metric spaces.

Notes on Counting An Introduction to Enumerative Combinatorics

Author: Peter J. Cameron
Publisher: Cambridge University Press
ISBN: 9781108279321
Release Date: 2017-06-21
Genre: Mathematics

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.

Neverending Fractions

Author: Jonathan Borwein
Publisher: Cambridge University Press
ISBN: 9780521186490
Release Date: 2014-07-03
Genre: Mathematics

This introductory text covers a variety of applications to interest every reader, from researchers to amateur mathematicians.


Author: Amir-Homayoon Najmi
Publisher: JHU Press
ISBN: 9781421405599
Release Date: 2012-03-27
Genre: Mathematics

Najmi’s primer will be an indispensable resource for those in computer science, the physical sciences, applied mathematics, and engineering who wish to obtain an in-depth understanding and working knowledge of this fascinating and evolving field.

An Introduction to Banach Space Theory

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 9781461206033
Release Date: 2012-12-06
Genre: Mathematics

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Publicationes mathematicae

Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet
ISBN: UCSD:31822020281788
Release Date: 1988
Genre: Mathematics


ISBN: UOM:39015079402478
Release Date: 2000
Genre: Best books

Foundations of Convex Geometry

Author: W. A. Coppel
Publisher: Cambridge University Press
ISBN: 0521639700
Release Date: 1998-03-05
Genre: Mathematics

This book on the foundations of Euclidean geometry aims to present the subject from the point of view of present day mathematics, taking advantage of all the developments since the appearance of Hilbert's classic work. Here real affine space is characterised by a small number of axioms involving points and line segments making the treatment self-contained and thorough, many results being established under weaker hypotheses than usual. The treatment should be totally accessible for final year undergraduates and graduate students, and can also serve as an introduction to other areas of mathematics such as matroids and antimatroids, combinatorial convexity, the theory of polytopes, projective geometry and functional analysis.

A Course in Modern Analysis and Its Applications

Author: Graeme Laurence Cohen
Publisher: Cambridge University Press
ISBN: 0521526272
Release Date: 2003-06-30
Genre: Mathematics

An advanced 2003 undergraduate text on mathematical analysis designed for pure or applied mathematicians, covering theory as well as applications.

Quantum Groups

Author: Ross Street
Publisher: Cambridge University Press
ISBN: 9781139461443
Release Date: 2007-01-18
Genre: Mathematics

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.