# Proofs and Fundamentals

## A First Course in Abstract Mathematics

Textbook

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

### 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

1. 1.Department of Mathematics and Computer ScienceBard CollegeAnnandale-on-HudsonUSA

### Bibliographic information

• Book Title Proofs and Fundamentals
• Book Subtitle A First Course in Abstract Mathematics
• Authors Ethan D. Bloch
• DOI https://doi.org/10.1007/978-1-4612-2130-2
• Copyright Information Birkhäuser Boston 2003
• Publisher Name Birkhäuser Boston
• eBook Packages
• Hardcover ISBN 978-0-8176-4111-5
• Softcover ISBN 978-1-4612-7426-1
• eBook ISBN 978-1-4612-2130-2
• Edition Number 1
• Number of Pages XXI, 424
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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