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A Discrete Transition to Advanced Mathematics: Second Edition
 
Thomas Richmond Western Kentucky University, Bowling Green, KY
Softcover ISBN:  978-1-4704-7204-7
Product Code:  AMSTEXT/63
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7427-0
Product Code:  AMSTEXT/63.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7204-7
eBook: ISBN:  978-1-4704-7427-0
Product Code:  AMSTEXT/63.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Click above image for expanded view
A Discrete Transition to Advanced Mathematics: Second Edition
Thomas Richmond Western Kentucky University, Bowling Green, KY
Softcover ISBN:  978-1-4704-7204-7
Product Code:  AMSTEXT/63
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-7427-0
Product Code:  AMSTEXT/63.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-7204-7
eBook ISBN:  978-1-4704-7427-0
Product Code:  AMSTEXT/63.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 632023; 523 pp
    MSC: Primary 00

    This is a Revised Edition of: AMSTEXT/3

    This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity.

    Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio.

    A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout, featuring:

    • A new chapter on combinatorial geometry;
    • An expanded treatment of the combinatorics of indistinguishable objects;
    • New sections on the inclusion-exclusion principle and circular permutations;
    • Over 365 new exercises.
    Ancillaries:

    Readership

    Undergraduate students who need a strong conceptual foundation for higher mathematical thinking.

  • Table of Contents
     
     
    • Copyright
    • Contents
    • Preface
    • Preface to the Second Edition
    • Chapter 1. Sets and Logic
    • 1.1. Sets
    • 1.2. Set Operations
    • 1.3. Partitions
    • 1.4. Logic and Truth Tables
    • 1.5. Quantifiers
    • 1.6. Implications
    • Chapter 2. Proofs
    • 2.1. Proof Techniques
    • 2.2. Mathematical Induction
    • 2.3. The Pigeonhole Principle
    • Chapter 3. Number Theory
    • 3.1. Divisibility
    • 3.2. The Euclidean Algorithm
    • 3.3. The Fundamental Theorem of Arithmetic
    • 3.4. Divisibility Tests
    • 3.5. Number Patterns
    • Chapter 4. Combinatorics
    • 4.1. Getting from Point A to Point B
    • 4.2. The Fundamental Principle of Counting
    • 4.3. A Formula for the Binomial Coefficients
    • 4.4. Permutations with Indistinguishable Objects
    • 4.5. Combinations with Indistinguishable Objects
    • 4.6. The Inclusion-Exclusion Principle
    • 4.7. Circular Permutations
    • 4.8. Probability
    • Chapter 5. Relations
    • 5.1. Relations
    • 5.2. Equivalence Relations
    • 5.3. Partial Orders
    • 5.4. Quotient Spaces
    • Chapter 6. Functions and Cardinality
    • 6.1. Functions
    • 6.2. Inverse Relations and Inverse Functions
    • 6.3. Cardinality of Infinite Sets
    • 6.4. An Order Relation for Cardinal Numbers
    • Chapter 7. Graph Theory
    • 7.1. Graphs
    • 7.2. Matrices, Digraphs, and Relations
    • 7.3. Shortest Paths in Weighted Graphs
    • 7.4. Trees
    • Chapter 8. Sequences
    • 8.1. Sequences
    • 8.2. Finite Differences
    • 8.3. Limits of Sequences of Real Numbers
    • 8.4. Some Convergence Properties
    • 8.5. Infinite Arithmetic
    • 8.6. Recurrence Relations
    • Chapter 9. Fibonacci Numbers and Pascal’s Triangle
    • 9.1. Pascal’s Triangle
    • 9.2. The Fibonacci Numbers
    • 9.3. The Golden Ratio
    • 9.4. Fibonacci Numbers and the Golden Ratio
    • 9.5. Pascal’s Triangle and the Fibonacci Numbers
    • Chapter 10. Combinatorial Geometry in the Plane
    • 10.1. Polygons and Convex Sets
    • 10.2. Pick’s Theorem
    • 10.3. Irrational Approximations of 𝜋
    • 10.4. Cotes’s Theorem (optional)
    • 10.5. Tiling and Visibility
    • 10.6. Covering Properties and Geometry of Point Sets
    • 10.7. Linear Algebra and Packing the Plane
    • 10.8. Helly’s Theorem
    • Chapter 11. Continued Fractions
    • 11.1. Finite Continued Fractions
    • 11.2. Convergents of a Continued Fraction
    • 11.3. Infinite Continued Fractions
    • 11.4. Applications of Continued Fractions
    • Answers or Hints for Selected Exercises
    • Bibliography
    • Index
  • 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
    Accessibility – to request an alternate format of an AMS title
Volume: 632023; 523 pp
MSC: Primary 00

This is a Revised Edition of: AMSTEXT/3

This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity.

Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio.

A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout, featuring:

  • A new chapter on combinatorial geometry;
  • An expanded treatment of the combinatorics of indistinguishable objects;
  • New sections on the inclusion-exclusion principle and circular permutations;
  • Over 365 new exercises.
Ancillaries:

Readership

Undergraduate students who need a strong conceptual foundation for higher mathematical thinking.

  • Copyright
  • Contents
  • Preface
  • Preface to the Second Edition
  • Chapter 1. Sets and Logic
  • 1.1. Sets
  • 1.2. Set Operations
  • 1.3. Partitions
  • 1.4. Logic and Truth Tables
  • 1.5. Quantifiers
  • 1.6. Implications
  • Chapter 2. Proofs
  • 2.1. Proof Techniques
  • 2.2. Mathematical Induction
  • 2.3. The Pigeonhole Principle
  • Chapter 3. Number Theory
  • 3.1. Divisibility
  • 3.2. The Euclidean Algorithm
  • 3.3. The Fundamental Theorem of Arithmetic
  • 3.4. Divisibility Tests
  • 3.5. Number Patterns
  • Chapter 4. Combinatorics
  • 4.1. Getting from Point A to Point B
  • 4.2. The Fundamental Principle of Counting
  • 4.3. A Formula for the Binomial Coefficients
  • 4.4. Permutations with Indistinguishable Objects
  • 4.5. Combinations with Indistinguishable Objects
  • 4.6. The Inclusion-Exclusion Principle
  • 4.7. Circular Permutations
  • 4.8. Probability
  • Chapter 5. Relations
  • 5.1. Relations
  • 5.2. Equivalence Relations
  • 5.3. Partial Orders
  • 5.4. Quotient Spaces
  • Chapter 6. Functions and Cardinality
  • 6.1. Functions
  • 6.2. Inverse Relations and Inverse Functions
  • 6.3. Cardinality of Infinite Sets
  • 6.4. An Order Relation for Cardinal Numbers
  • Chapter 7. Graph Theory
  • 7.1. Graphs
  • 7.2. Matrices, Digraphs, and Relations
  • 7.3. Shortest Paths in Weighted Graphs
  • 7.4. Trees
  • Chapter 8. Sequences
  • 8.1. Sequences
  • 8.2. Finite Differences
  • 8.3. Limits of Sequences of Real Numbers
  • 8.4. Some Convergence Properties
  • 8.5. Infinite Arithmetic
  • 8.6. Recurrence Relations
  • Chapter 9. Fibonacci Numbers and Pascal’s Triangle
  • 9.1. Pascal’s Triangle
  • 9.2. The Fibonacci Numbers
  • 9.3. The Golden Ratio
  • 9.4. Fibonacci Numbers and the Golden Ratio
  • 9.5. Pascal’s Triangle and the Fibonacci Numbers
  • Chapter 10. Combinatorial Geometry in the Plane
  • 10.1. Polygons and Convex Sets
  • 10.2. Pick’s Theorem
  • 10.3. Irrational Approximations of 𝜋
  • 10.4. Cotes’s Theorem (optional)
  • 10.5. Tiling and Visibility
  • 10.6. Covering Properties and Geometry of Point Sets
  • 10.7. Linear Algebra and Packing the Plane
  • 10.8. Helly’s Theorem
  • Chapter 11. Continued Fractions
  • 11.1. Finite Continued Fractions
  • 11.2. Convergents of a Continued Fraction
  • 11.3. Infinite Continued Fractions
  • 11.4. Applications of Continued Fractions
  • Answers or Hints for Selected Exercises
  • Bibliography
  • Index
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
Accessibility – to request an alternate format of an AMS title
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