A Transition to Proof

An Introduction to Advanced Mathematics

Neil R. Nicholson

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English

CRC Press
21 January 2023

Calculus & mathematical analysis

Series: Textbooks in Mathematics

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.

Features:

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

By: Neil R. Nicholson
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 453g
ISBN: 9781032475721
ISBN 10: 1032475722
Series: Textbooks in Mathematics
Pages: 464
Publication Date: 21 January 2023
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Paperback
Publisher's Status: Active

Symbolic Logic Sets Introduction to Proofs Mathematical Induction Relations Functions Cardinality Introduction to Topology Properties of the Real Number System Proof Writing Tips Selected Solutions and Hints

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.