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  • © 2013

A Logical Introduction to Proof

  • Identifies the important topics in logic that mathematicians use in their proofs

  • Methodically presents the key strategies used in mathematical proofs

  • Each proof strategy is illustrated by a variety of theorems concerning the natural, rational and real numbers

  • An introduction to group theory and real analysis that presents proof strategies for dealing with the core concepts introduced in these subjects

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
  2. Propositional Logic

    • Daniel W. Cunningham
    Pages 1-28
  3. Predicate Logic

    • Daniel W. Cunningham
    Pages 29-60
  4. Proof Strategies and Diagrams

    • Daniel W. Cunningham
    Pages 61-98
  5. Mathematical Induction

    • Daniel W. Cunningham
    Pages 99-141
  6. Set Theory

    • Daniel W. Cunningham
    Pages 143-168
  7. Functions

    • Daniel W. Cunningham
    Pages 169-207
  8. Relations

    • Daniel W. Cunningham
    Pages 209-237
  9. Core Concepts in Abstract Algebra

    • Daniel W. Cunningham
    Pages 239-291
  10. Core Concepts in Real Analysis

    • Daniel W. Cunningham
    Pages 293-340
  11. Back Matter

    Pages 341-356

About this book

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

Reviews

From the reviews:

“Cunningham (Buffalo State, SUNY) focuses on the strategies for different proof techniques. … The well-written text is consistent in its focus, which should help students. The book includes sufficient, appropriate exercises. … contains ample notes to guide students through most of the exercises. Whether used for a course or as a reference for students learning proof techniques, this book is certainly worthy of consideration. Summing Up: Highly recommended. Lower-division undergraduates through graduate students.” (J. R. Burke, Choice, Vol. 51 (1), September, 2013)

Authors and Affiliations

  • , Mathematics Department, Buffalo State College, Buffalo, USA

    Daniel W. Cunningham

Bibliographic Information

  • Book Title: A Logical Introduction to Proof

  • Authors: Daniel W. Cunningham

  • DOI: https://doi.org/10.1007/978-1-4614-3631-7

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2013

  • Hardcover ISBN: 978-1-4614-3630-0Published: 19 September 2012

  • Softcover ISBN: 978-1-4899-9099-0Published: 15 October 2014

  • eBook ISBN: 978-1-4614-3631-7Published: 19 September 2012

  • Edition Number: 1

  • Number of Pages: XVI, 356

  • Topics: Mathematics, general, Mathematical Logic and Foundations

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access