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Bibliographic Details

Title: Exploring the Infinite: An Introduction to Proof and Analysis (Textbooks in Mathematics)
Publisher: Chapman and Hall/CRC
Publication Date: 2016
Language: English
ISBN 10: 1498704492
ISBN 13: 9781498704496
Binding: Hardcover
Condition: Good

About this title

Synopsis

Exploring the Infinite addresses the trend toward

a combined transition course and introduction to analysis course. It

guides the reader through the processes of abstraction and log-

ical argumentation, to make the transition from student of mathematics to

practitioner of mathematics.

This requires more than knowledge of the definitions of mathematical structures,

elementary logic, and standard proof techniques. The student focused on only these

will develop little more than the ability to identify a number of proof templates and

to apply them in predictable ways to standard problems.

This book aims to do something more; it aims to help readers learn to explore

mathematical situations, to make conjectures, and only then to apply methods

of proof. Practitioners of mathematics must do all of these things.

The chapters of this text are divided into two parts. Part I serves as an introduction

to proof and abstract mathematics and aims to prepare the reader for advanced

course work in all areas of mathematics. It thus includes all the standard material

from a transition to proof" course.

Part II constitutes an introduction to the basic concepts of analysis, including limits

of sequences of real numbers and of functions, infinite series, the structure of the

real line, and continuous functions.

Features

Two part text for the combined transition and analysis course

New approach focuses on exploration and creative thought

Emphasizes the limit and sequences

Introduces programming skills to explore concepts in analysis

Emphasis in on developing mathematical thought

Exploration problems expand more traditional exercise sets

About the Author

Jennifer Halfpap is an Associate Professor in the Department of Mathematical Sciences at the University of Montana, Missoula, USA. She is also the Associate Chair of the department, directing the Graduate Program.

"About this title" may belong to another edition of this title.

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