Proofs and Fundamentals: A First Course in Abstract Mathematics - Hardcover

Hardcover

ISBN 10: 3764341114 ISBN 13: 9783764341114

Synopsis

This text is designed as a "transition" textbook to introduce undergraduates to the writing of vigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. It serves as a bridge between computational courses, e.g. calculus, and more theoretical, proofs-oriented courses such as linear devoted to the proper writing of proofs and over 400 problem sets, which are mostly proofs rather than example problems. Because of the exposition and choice of topics this book should be of interest for classroom use as well as for the general reader who wants to gain a deeper understanding of the language of mathematics. The material of this text was chosen because it is needed in the advanced mathematics curriculum, yet it is often not taught in any other course at the level of calculus or below.

About this title

Review

From the book reviews:

“The contents of the book is organized in three parts ... . this is a nice book, which also this reviewer has used with profit in his teaching of beginner students. It is written in a highly pedagogical style and based upon valuable didactical ideas.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 174, 2014)

“Books in this category are meant to teach mathematical topics and techniques that will become valuable in more advanced courses. This book meets these criteria. ... This book is well suited as a textbook for a transitional course between calculus and more theoretical courses. I also recommend it for academic libraries.” (Edgar R. Chavez, ACM Computing Reviews, February, 2012)

“This is an improved edition of a good book that can serve in the undergraduate curriculum as a bridge between computationally oriented courses like calculus and more abstract courses like algebra.” (Teun Koetsier, Zentralblatt MATH, Vol. 1230, 2012)

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

Edition details

• ISBN 10: 3764341114
• ISBN 13: 9783764341114
• Binding: Hardcover
• Language: English