**Pure and Applied Undergraduate Texts**

Volume: 3;
2004;
424 pp;
Hardcover

MSC: Primary 00;

Print ISBN: 978-0-8218-4789-3

Product Code: AMSTEXT/3

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

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**Electronic ISBN: 978-1-4704-1116-9
Product Code: AMSTEXT/3.E**

List Price: $76.00

AMS Member Price: $60.80

MAA Member Price: $68.40

# A Discrete Transition to Advanced Mathematics

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*Bettina Richmond; Thomas Richmond*

As the title indicates, this book is intended for courses aimed at
bridging the gap between lower-level mathematics and advanced mathematics.
The text provides a careful introduction to techniques for writing proofs
and a logical development of topics based on intuitive understanding of
concepts. The authors utilize a clear writing style and a wealth of
examples to develop an understanding of discrete mathematics and critical
thinking skills. While including many traditional topics, the text offers
innovative material throughout. Surprising results are used to motivate
the reader. The last three chapters address topics such as continued
fractions, infinite arithmetic, and the interplay among Fibonacci numbers,
Pascal's triangle, and the golden ratio, and may be used for independent
reading assignments. The treatment of sequences may be used to introduce
epsilon-delta proofs. The selection of topics provides flexibility for the
instructor in a course designed to spark the interest of students through
exciting material while preparing them for subsequent proof-based courses.

The book includes a large number of problems of varying difficulty. A student
manual with solutions to selected problems is available electronically:
www.ams.org/bookstore/pspdf/amstext-3-solutions.pdf.

An instructor's manual for this title is available electronically. Please
send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate students interested in becoming mathematicians.

#### Reviews & Endorsements

This nice text is a welcome addition to existing literature on discrete mathematics, mathematical reasoning and proofs, and similar topics.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## A Discrete Transition to Advanced Mathematics

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Preface iii4 free
- Contents v6 free
- 1 Sets and Logic 110 free
- 2 Proofs 4958
- 3 Number Theory 7786
- 4 Combinatorics 123132
- 5 Relations 163172
- 6 Functions and Cardinality 197206
- 7 Graph Theory 231240
- 8 Sequences 273282
- 9 Fibonacci Numbers and Pascal's Triangle 331340
- 10 Continued Fractions 377386
- Answers or Hints for Selected Exercises 409418
- Bibliography 419428
- Index 421430
- Back Cover Back Cover1434