A Logical Introduction to Proof

  • Daniel W. Cunningham

Table of contents

  1. Front Matter
    Pages i-xv
  2. Daniel W. Cunningham
    Pages 1-28
  3. Daniel W. Cunningham
    Pages 29-60
  4. Daniel W. Cunningham
    Pages 61-98
  5. Daniel W. Cunningham
    Pages 99-141
  6. Daniel W. Cunningham
    Pages 143-168
  7. Daniel W. Cunningham
    Pages 169-207
  8. Daniel W. Cunningham
    Pages 209-237
  9. Daniel W. Cunningham
    Pages 239-291
  10. Daniel W. Cunningham
    Pages 293-340
  11. Back Matter
    Pages 341-356

About this book

Introduction

A Logical Introduction to Proof is a unique textbook that uses a logic-first approach to train and guide undergraduates through a transition or “bridge” course  between calculus and advanced mathematics courses.  The author’s approach  prepares the student for the rigors required in future mathematics courses and is appropriate for majors in mathematics, computer science, engineering, as well as other applied mathematical sciences. It may also be beneficial as a supplement for students at the graduate level who need guidance or reference for writing proofs.   Core topics covered are logic, sets, relations, functions, and induction, where logic is the instrument for analyzing the structure of mathematical assertions and is a tool for composing mathematical proofs. Exercises are given at the end of each section within a chapter.

Chapter 1 focuses on propositional logic while Chapter 2 is devoted to the logic of quantifiers. Chapter 3 methodically presents the key strategies that are used in mathematical proofs; each presented as a proof diagram. Every proof strategy is carefully illustrated by a variety of mathematical theorems concerning the natural, rational, and real numbers. Chapter 4 focuses on mathematical induction and concludes with a proof of the fundamental theorem of arithmetic. Chapters 5 through 7 introduce students to the essential concepts that appear in all branches of mathematics. Chapter 8 introduces the basic structures of abstract algebra: groups, rings, quotient groups, and quotient rings. Finally, Chapter 9 presents proof strategies that explicitly show students how to deal with the fundamental definitions that they will encounter in real analysis, followed by numerous examples of proofs that use these strategies.  The appendix provides a useful summary of strategies for dealing with proofs.

Keywords

Assumption Strategies Logic used in mathematical proofs Proof Diagrams Proof Strategies Proof strategies that help students compose proofs

Authors and affiliations

  • Daniel W. Cunningham
    • 1
  1. 1., Mathematics DepartmentBuffalo State CollegeBuffaloUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-3631-7
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-3630-0
  • Online ISBN 978-1-4614-3631-7
  • About this book