An Invitation to Abstract Mathematics. 2nd ed. 2020

種類:

電子ブック

責任表示:

by Béla Bajnok

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Bajnok, Béla.
• SpringerLink (Online service)

シリーズ名:

Undergraduate Texts in Mathematics ;

ISBN:

9783030561741 [3030561747]    

注記:

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? -- A Ten Famous Conjectures.-B Ten Famous Theorems -- II The Foundations of Mathematics -- 5 Let's Be Logical! -- 6 Setting Examples -- 7 Quantifier Mechanics -- 8 Let's Be Functional! -- C The Foundations of Set Theory -- III How to Prove It -- 9 Universal Proofs -- 10 The Domino Theory -- 11 More Domino Games -- 12 Existential Proofs -- D Ten Famous Problems -- IV Advanced Math for Beginners -- 13 Mathematical Structures -- 14 Working in the Fields (and Other Structures) -- 15 Group Work -- 16 Good Relations -- 17 Order, Please! -- 18 Now That's the Limit! -- 19 Sizing It Up -- 20 Infinite Delights -- 21 Number Systems Systematically -- 22 Games Are Valuable! -- E Graphic Content -- F All Games Considered -- G A Top Forty List of Math Theorems.
This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the la

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