
A Discrete Transition to Advanced Mathematics
American Mathematical Society (Publisher)
2nd Edition
Published on 19. November 2023
Book
Paperback/Softback
503 pages
978-1-4704-7204-7 (ISBN)
Description
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. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.
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. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.
More details
Series
Edition
Second Edition
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Edition type
New edition
Dimensions
Height: 254 mm
Width: 178 mm
Weight
435 gr
ISBN-13
978-1-4704-7204-7 (9781470472047)
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Schweitzer Classification
Persons
Bettina Richmond, and Thomas Richmond, Western Kentucky University, Bowling Green, KY.
Content
Sets and logic
Proofs
Number theory
Combinatorics
Relations
Functions and cardinality
Graph theory
Sequences
Fibonacci numbers and Pascal's triangle
Combinatorial geometry in the plane
Continued fractions
Answers or hints for selected exercises
Bibliography
Proofs
Number theory
Combinatorics
Relations
Functions and cardinality
Graph theory
Sequences
Fibonacci numbers and Pascal's triangle
Combinatorial geometry in the plane
Continued fractions
Answers or hints for selected exercises
Bibliography