Introduction to proof through number theory
著者
書誌事項
Introduction to proof through number theory
（The Sally series, . Pure and applied undergraduate texts ; 61）
American Mathematical Society, c2023
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Lighten up about mathematics! Have fun. If you read this book, you will have to endure bad math puns and jokes and out-of-date pop culture references. You'll learn some really cool mathematics to boot. In the process, you will immerse yourself in living, thinking, and breathing logical reasoning. We like to call this proofs, which to some is a bogey word, but to us it is a boogie word. You will learn how to solve problems, real and imagined. After all, math is a game where, although the rules are pretty much set, we are left to our imaginations to create. Think of this book as blueprints, but you are the architect of what structures you want to build. Make sure you lay a good foundation, for otherwise your buildings might fall down. To help you through this, we guide you to think and plan carefully. Our playground consists of basic math, with a loving emphasis on number theory. We will encounter the known and the unknown. Ancient and modern inquirers left us with elementary-sounding mathematical puzzles that are unsolved to this day. You will learn induction, logic, set theory, arithmetic, and algebra, and you may one day solve one of these puzzles.
目次
Evens, odds, and primes: A taste of number theory
Mathematical induction
Logic: Implications, contrapositives, contradictions, and quantifiers
The Euclidean algorithm and its consequences
Sets and functions
Modular arithmetic
Counting finite sets
Congruence class arithmetic, groups, and fields
Bibliography
Index
「Nielsen BookData」 より