Description 
1 online resource (xiv, 406 pages) 
Series 
Undergraduate texts in mathematics, 01726056 

Undergraduate texts in mathematics.

Contents 
What's Mathematics?  Let's Play a Game!  What's the Name of the Game?  How to Make a Statement?  What's True in Mathematics?  Famous Classical Theorems  Recent Progress in Mathematics  How to Solve It?  Let's Be Logical!  Setting Examples  Quantifier Mechanics  Mathematical Structures  Working in the Fields (and Other Structures)  Universal Proofs  The Domino Effect  More Domino Games  Existential Proofs  A Cornucopia of Famous Problems  Advanced Math for Beginners  Good Relations  Order, Please!  Let's Be Functional!  Infinite Delights  Number Systems Systematically  Games Are Valuable! 
Summary 
This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse. The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader. With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible. This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less wellknown questions that remain open for future mathematicians. Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independentstudy and research projects 
Analysis 
Mathematics 

Logic, Symbolic and mathematical 
Notes 
Also has print version 
Bibliography 
Includes bibliographical references and index 
Subject 
Mathematics.


Mathematics  Authorship.


Logic, Symbolic and mathematical.


Algebra, Abstract.

Form 
Electronic book

ISBN 
1461466350 (print) 

1461466369 (electronic bk.) 

9781461466352 (print) 

9781461466369 (electronic bk.) 
