Valentin Deaconu, Donald C. Pfaff

Chapman and Hall/CRC

Published
December 5, 2016

Textbook
- 204 Pages
- 37 B/W Illustrations

ISBN 9781498775250 - CAT# K29670

Series: Textbooks in Mathematics

**For Instructors** Request Inspection Copy

**For Librarians** Available on Taylor & Francis eBooks >>

was $96.95

USD^{$}77^{.56}

SAVE *~*$19.39

Add to Wish List

FREE Standard Shipping!

*A Bridge to Higher Mathematics* is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought.

The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems.

The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof.

The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof.

For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star.

All these materials are optional, depending on the instructor and the goals of the course.

We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.

Request an

e-inspection copy

e-inspection copy