A Transition to Proof : An Introduction to Advanced Mathematics book cover
1st Edition

A Transition to Proof
An Introduction to Advanced Mathematics

ISBN 9780367201579
Published April 2, 2019 by Chapman and Hall/CRC
462 Pages 39 B/W Illustrations

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Book Description

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively.

The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof.


  • The text is aimed at transition courses preparing students to take analysis
  • Promotes creativity, intuition, and accuracy in exposition
  • The language of proof is established in the first two chapters, which cover logic and set theory
  • Includes chapters on cardinality and introductory topology

Table of Contents

Symbolic Logic


Introduction to Proofs

Mathematical Induction




Introduction to Topology

Properties of the Real Number System

Proof Writing Tips

Selected Solutions and Hints

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Dr. Neil R. Nicholson is Associate Professor of Mathematics at North Central College. He holds a Ph.D. in Mathematics from The University of Iowa, specializing in knot theory. His research interests have consistently been topics accessible to undergraduates; collaborating with them on original research is a fundamental goal of his professional development. In 2015, he earned the Clarence F. Dissinger Award for Junior Faculty Teaching at North Central College. He serves as the Faculty Athletic Representative to the NCAA for North Central College.