A Transition to Proof: An Introduction to Advanced Mathematics

ISBN-13: 9781032475721 / Angielski / Miękka / 2023 / 464 str.

Neil R. Nicholson

Opis

The fundamental tool of theoretical mathematics is mathematical proof. Any claim or justification a mathematician makes must be proven. This book is designed for a reader who wants to learn what exactly a mathematical proof is, how they are constructed, and how to go about writing one.

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

Spis treści

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

O autorze

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.