Proofs and Fundamentals

A First Course in Abstract Mathematics

  • Ethan D. Bloch
Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Proofs

    1. Front Matter
      Pages 1-1
  3. PROOFS

    1. Ethan D. Bloch
      Pages 3-45
    2. Ethan D. Bloch
      Pages 47-88
  4. Fundamentals

    1. Front Matter
      Pages 89-89
  5. FUNDAMENTALS

    1. Ethan D. Bloch
      Pages 91-128
    2. Ethan D. Bloch
      Pages 129-169
    3. Ethan D. Bloch
      Pages 171-194
    4. Ethan D. Bloch
      Pages 195-248
  6. Extras

    1. Front Matter
      Pages 249-249
  7. EXTRAS

    1. Ethan D. Bloch
      Pages 251-322
    2. Ethan D. Bloch
      Pages 323-340
  8. Back Matter
    Pages 341-359

About this book

Introduction

This textbook is designed to introduce undergraduates to the writing of rigorous mathematical proofs, and to fundamental mathematical ideas such as sets, functions, relations, and cardinality. The book serves as a bridge between computational courses such as calculus and more theoretical courses such as linear algebra, abstract algebra, and real analysis.

This second edition has been significantly enhanced, while maintaining the balance of topics and careful writing of the previous edition. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences, and suggests avenues for independent student explorations.

A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised.

Reviews of the first edition:

This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course.
—Zentralblatt Math

'Proofs and Fundamentals' has many strengths. One notable strength is its excellent organization... There are large exercise sets throughout the book... the exercises are well integrated with the text and vary appropriately from easy to hard... Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better.
—MAA Online

Keywords

Cardinality Formal Logic Introduction to Proofs

Authors and affiliations

  • Ethan D. Bloch
    • 1
  1. 1., Department of MathematicsBard CollegeAnnandale-on-HudsonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7127-2
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7126-5
  • Online ISBN 978-1-4419-7127-2
  • Series Print ISSN 0172-6056
  • About this book