An Invitation to Abstract Mathematics - Béla Bajnok

An Invitation to Abstract Mathematics

(Autor)

Buch | Softcover
406 Seiten
2015 | 2013 ed.
Springer-Verlag New York Inc.
978-1-4899-9560-5 (ISBN)
53,49 inkl. MwSt
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Presenting historical perspective and notes on important figures in mathematics, covering current activity in the mathematical community, and raising famous and lesser-known questions, this book shows that abstract mathematics is a vibrant, dynamic enterprise.
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 well-known 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 independent-study and research projects.

Béla Bajnok is a native of Hungary, and he remains greatly influenced by the excellent education he received there. He currently holds the endowed position of Alumni Chair Professor at Gettysburg College. He is also the recipient of the Mathematical Association of America's 2012 James P. Crawford EPADEL Teaching Award.

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.

Erscheint lt. Verlag 15.6.2015
Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo 45 Tables, black and white; XIV, 406 p.
Verlagsort New York
Sprache englisch
Maße 155 x 235 mm
Gewicht 6321 g
Themenwelt Mathematik / Informatik Mathematik Allgemeines / Lexika
Mathematik / Informatik Mathematik Geschichte der Mathematik
Mathematik / Informatik Mathematik Logik / Mengenlehre
Schlagworte abstract mathematics • bridge course • cardinalities • decision trees • infinity • Logic • Mathematical Proof • mathematics milestones • Number Systems • prime number theorem • pythagoream theorem • set theory • Surreal numbers • transition course
ISBN-10 1-4899-9560-9 / 1489995609
ISBN-13 978-1-4899-9560-5 / 9781489995605
Zustand Neuware
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