論理と証明を通じた離散数学入門（テキスト） Introduction to Discrete Mathematics via Logic and Proof (Undergraduate Texts in Mathematics)

Jongsma, Calvin

Springer Nature Switzerland AG（2019/12発売）

• 製本 Hardcover:ハードカバー版／ページ数 482 p.
• 言語 ENG
• 商品コード 9783030253578
• DDC分類 511.1

Full Description

This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades.

Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include:

Mathematical and structural induction
Set theory
Combinatorics
Functions, relations, and ordered sets
Boolean algebra and Boolean functions
Graph theory

Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.

Contents

Preface.- List of Notations.- 1. Propositional Logic.- 2. First-Order Logic.- 3. Mathematical Induction and Arithmetic.- 4. Basic Set Theory and Combinatorics.- 5. Set Theory and Infinity.- 6. Functions and Equivalence Relations.- 7. Posets, Lattices, and Boolean Algebra.- 8. Topics in Graph Theory.- A. Inference Rules for PL and FOL.- Index.