Overview
- Emphasizes fundamentals of deductive logic to prepare students for a coherent collection of core topics in discrete mathematics
- Introduces the reading and writing of proofs by using a natural deduction approach to mathematical logic
- Engages students through a wide selection of interesting and novel exercises
- Highlights historical developments and connections between topics throughout
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (8 chapters)
Keywords
About this book
This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades.
Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include:
- Mathematical and structural induction
- Set theory
- Combinatorics
- Functions, relations, and ordered sets
- Boolean algebra and Boolean functions
- Graph theory
Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics.
Reviews
“The unique style of using the deductive perspective on mathematical logic will definitely help the students get a more balanced view of the methodology in mathematics. … the book gives a good introduction to logic and proof, using various topics in discrete mathematics. The exercises are well thought out and give additional material to think about. The choice of topics is balanced and the overall style is easy to read.” (Manjil Saikia, MAA Reviews, June 21, 2021)
Authors and Affiliations
About the author
Calvin Jongsma is Emeritus Professor of Mathematics at Dordt University in Sioux Center, Iowa. His research interests include logic and proof, the history and philosophy of mathematics, foundations of mathematics, and mathematics education.
Bibliographic Information
Book Title: Introduction to Discrete Mathematics via Logic and Proof
Authors: Calvin Jongsma
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-25358-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Hardcover ISBN: 978-3-030-25357-8Published: 12 December 2019
Softcover ISBN: 978-3-030-25360-8Published: 11 December 2020
eBook ISBN: 978-3-030-25358-5Published: 08 November 2019
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XX, 482
Number of Illustrations: 849 b/w illustrations, 5 illustrations in colour
Topics: Discrete Mathematics, Mathematical Logic and Foundations