Proofs and Fundamentals: A First Course in Abstract Mathematics

Ethan D. Bloch

ISBN 10: 0817641114 / ISBN 13: 9780817641115

Published by Birkhäuser Boston, 2000

About this Item

In a hardcover with green titles to spine and white titles to front. No dust jacket. 445 pp. The book is in very good condition. There is minor shelf-wear to the extremities of the cover, the top corner of the back board is bruised and the spine lightly tanned. The binding is tight. There is a number and price to the top corner of the front paste down. Otherwise the pages are clean and unmarked. Seller Inventory # 913284

Bibliographic Details

Title: Proofs and Fundamentals: A First Course in ...

Publisher: Birkhäuser Boston

Publication Date: 2000

Binding: Hardcover

Condition: Very Good

Dust Jacket Condition: No Jacket

Edition: 1st Edition

About this title

Synopsis:

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

From the Back Cover:

This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis.

This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations.

A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised.

Reviews of the first edition:

This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course.
―Zentralblatt Math

'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better.
―MAA Online