Introduction to proofs and proof strategies

著者

    • Fuchs, Shay

書誌事項

Introduction to proofs and proof strategies

Shay Fuchs

（Cambridge mathematical textbooks）

Cambridge University Press, 2023

  • : pbk.

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注記

Includes index

内容説明・目次

内容説明

Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.

目次

  • Contents
  • Preface
  • Part I. Core Material
  • 1. Numbers, Quadratics and Inequalities
  • 2. Sets, Functions and the Field Axioms
  • 3. Informal Logic and Proof Strategies
  • 4. Mathematical Induction
  • 5. Bijections and Cardinality
  • 6. Integers and Divisibility
  • 7. Relations
  • Part II. Additional Topics
  • 8. Elementary Combinatorics
  • 9. Preview of Real Analysis - Limits and Continuity
  • 10. Complex Numbers
  • 11. Preview of Linear Algebra
  • Notes
  • References
  • Index.

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