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A Discrete Transition to Advanced Mathematics
 
Bettina Richmond Western Kentucky University, Bowling Green, KY
Thomas Richmond Western Kentucky University, Bowling Green, KY
Now available in new edition: AMSTEXT/63
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A Discrete Transition to Advanced Mathematics
Bettina Richmond Western Kentucky University, Bowling Green, KY
Thomas Richmond Western Kentucky University, Bowling Green, KY
Now available in new edition: AMSTEXT/63
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 32004; 424 pp
    MSC: Primary 00

    Now available in Second Edition: AMSTEXT/63

    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.

    Ancillaries:

    Readership

    Undergraduate students interested in becoming mathematicians.

  • Table of Contents
     
     
    • Cover
    • Preface
    • Contents
    • 1. Sets and Logic
    • 2. Proofs
    • 3. Number Theory
    • 4. Combinatorics
    • 5. Relations
    • 6. Functions and Cardinality
    • 7. Graph Theory
    • 8. Sequences
    • 9. Fibonacci Numbers and Pascal’s Triangle
    • 10. Continued Fractions
    • Answers or Hints for Selected Exercises
    • Bibliography
    • Index
    • Back Cover
  • Reviews
     
     
    • This nice text is a welcome addition to existing literature on discrete mathematics, mathematical reasoning and proofs, and similar topics.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 32004; 424 pp
MSC: Primary 00

Now available in Second Edition: AMSTEXT/63

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.

Ancillaries:

Readership

Undergraduate students interested in becoming mathematicians.

  • Cover
  • Preface
  • Contents
  • 1. Sets and Logic
  • 2. Proofs
  • 3. Number Theory
  • 4. Combinatorics
  • 5. Relations
  • 6. Functions and Cardinality
  • 7. Graph Theory
  • 8. Sequences
  • 9. Fibonacci Numbers and Pascal’s Triangle
  • 10. Continued Fractions
  • Answers or Hints for Selected Exercises
  • Bibliography
  • Index
  • Back Cover
  • This nice text is a welcome addition to existing literature on discrete mathematics, mathematical reasoning and proofs, and similar topics.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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