Sets Sequences and Mappings

Author: Kenneth Anderson
Publisher: Courier Corporation
ISBN: 9780486158129
Release Date: 2012-11-14
Genre: Mathematics

This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition.

LOGIC SETS AND THE TECHNIQUES OF MATHEMATICAL PROOFS

Author: Brahima MBODJE, Ph.D.
Publisher: Author House
ISBN: 9781463429669
Release Date: 2011-06-30
Genre: Education

As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov
Publisher: Courier Corporation
ISBN: 0486406830
Release Date: 1999
Genre: Mathematics

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

A Course in Advanced Calculus

Author: Robert S. Borden
Publisher: Courier Corporation
ISBN: 9780486150383
Release Date: 2012-09-11
Genre: Mathematics

An excellent undergraduate text examines sets and structures, limit and continuity in En, measure and integration, differentiable mappings, sequences and series, applications of improper integrals, more. Problems with tips and solutions for some.

Theory of Sets

Author: Erich Kamke
Publisher: Courier Corporation
ISBN: 0486601412
Release Date: 1950
Genre: Mathematics

Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." ? School Science and Mathematics.

Elements of the Theory of Functions

Author: Konrad Knopp
Publisher: Courier Dover Publications
ISBN: 9780486165608
Release Date: 2016-10-05
Genre: Mathematics

Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.

Convex Functions

Author: Jonathan M. Borwein
Publisher: Cambridge University Press
ISBN: 9781139811095
Release Date: 2010-01-14
Genre: Mathematics

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Introduction to Topology

Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 0486663523
Release Date: 1990
Genre: Mathematics

Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

Analysis in Euclidean Space

Author: Kenneth Hoffman
Publisher: Courier Corporation
ISBN: 9780486135847
Release Date: 2013-01-16
Genre: Mathematics

Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.

Introduction to Abstract Analysis

Author: Marvin E. Goldstein
Publisher: Courier Corporation
ISBN: 9780486799919
Release Date: 2014-10-27
Genre: Mathematics

Concise text prepares readers to pursue abstract analysis in the literature of pure mathematics. Detailed, easy-to-follow proofs and examples illustrate topics including real numbers, vector and metric spaces, infinite series, and other concepts. 1969 edition.