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Proofs and Fundamentals

A First Course in Abstract Mathematics

  • Ethan D. Bloch
Textbook

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Proofs

    1. Front Matter
      Pages 1-1
    2. Ethan D. Bloch
      Pages 3-54
    3. Ethan D. Bloch
      Pages 55-103
  3. Fundamentals

    1. Front Matter
      Pages 105-105
    2. Ethan D. Bloch
      Pages 107-133
    3. Ethan D. Bloch
      Pages 135-176
    4. Ethan D. Bloch
      Pages 177-201
    5. Ethan D. Bloch
      Pages 203-248
  4. Extras

    1. Front Matter
      Pages 249-249
    2. Ethan D. Bloch
      Pages 251-321
    3. Ethan D. Bloch
      Pages 323-362
    4. Ethan D. Bloch
      Pages 363-373
  5. Back Matter
    Pages 375-424

About this book

Introduction

In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for­ mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces­ sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se.

Keywords

abstract mathematics adopted-textbook NY ksa logic proofs algebra cardinality Counting Division Equivalence function homomorphism linear algebra Mathematica mathematical induction mathematical proof mathematics Permutation proof

Authors and affiliations

  • Ethan D. Bloch
    • 1
  1. 1.Department of Mathematics and Computer ScienceBard CollegeAnnandale-on-HudsonUSA

Bibliographic information

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