Cover image for A primer of abstract mathematics
A primer of abstract mathematics
Ash, Robert B.
Personal Author:
Publication Information:
Washington, DC : Mathematical Association of America, [1998]

Physical Description:
x, 181 pages ; 26 cm.
General Note:
Includes index.
Subject Term:
Format :


Call Number
Material Type
Home Location
Central Library QA162 .A84 1998 Adult Non-Fiction Non-Fiction Area

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The purpose of this book is to prepare the reader for coping with abstract mathematics. The intended audience is both students taking a first course in abstract algebra who feel the need to strengthen their background, and those from a more applied background who need some experience in dealing with abstract ideas. Learning any area of abstract mathematics requires not only ability to write formally but also to think intuitively about what is going on and to describe that process clearly and cogently in ordinary English. Ash tries to aid intuition by keeping proofs short and as informal as possible, and using concrete examples as illustration. Thus it is an ideal textbook for an audience with limited experience in formalism and abstraction. A number of expository innovations are included, for example, an informal development of set theory which teaches students all the basic results for algebra in one chapter.

Reviews 1

Choice Review

Ash presents topics from discrete mathematics and linear algebra; the discrete topics include elementary logic, some combinatorics, some number theory, and some set theory. The treatment of linear algebra includes, principally, the Jordan canonical form and some associated ideas. A small selection of exercises accompanies each topic. The style of the book and its mathematical approach are very casual and informal, perhaps too much so for its stated purpose, which is to prepare the reader for further work in abstract mathematics. A more complete treatment of these topics with the same general purpose can also be found in The Keys to Advanced Mathematics, by Daniel Solow (CH, Dec'95); How To Prove It: A Structured Approach, by Daniel J. Velleman (CH, Jun'95); and Mathematical Thinking: Problem-Solving and Proofs, by John P. D'Angelo and Douglas B. West (1997). General readers; lower-division undergraduates. M. Henle; Oberlin College

Table of Contents

1 Logic and foundations
2 Counting
3 Elementary number theory
4 Some highly informal set theory
5 Linear algebra
6 Theory of linear operators
Appendix: an application of linear algebra

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