An Invitation to Abstract Mathematics

An Invitation to Abstract Mathematics by Béla Bajnok.

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...

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Bibliographic Details
Main Author: Bajnok, Béla (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2013.
Edition:1st ed. 2013.
Series:Undergraduate Texts in Mathematics,
Springer eBook Collection.
Subjects:
Mathematics.
History.
Mathematical logic.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Preface to Instructors
  • Preface to Students
  • Acknowledgments
  • I What's Mathematics
  • 1 Let's Play a Game!
  • 2 What's the Name of the Game?
  • 3 How to Make a Statement?- 4 What's True in Mathematics?
  • 5 Famous Classical Theorems
  • 6 Recent Progress in Mathematics
  • II How to Solve It?
  • 7 Let's be Logical!
  • 8 Setting Examples
  • 9 Quantifier Mechanics
  • 10 Mathematical Structures
  • 11 Working in the Fields (and Other Structures)
  • 12 Universal Proofs
  • 13 The Domino Effect
  • 14 More Domino Games
  • 15 Existential Proofs
  • 16 A Cornucopia of Famous Problems
  • III Advanced Math for Beginners
  • 17 Good Relations
  • 18 Order, Please!
  • 19 Let's be Functional!
  • 20 Now That's the Limit!
  • 21 Sizing It Up
  • 22 Infinite Delights
  • 23 Number Systems Systematically
  • 24 Games Are Valuable!
  • IV. Appendices
  • A. Famous Conjectures in Mathematics
  • B The Foundations of Set Theory
  • C All Games Considered
  • D Top 40 List of Math Theorems. - Index.

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