Introduction to Discrete Mathematics via Logic and Proof
Authors: Jongsma, Calvin
Free Preview 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
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 About this Textbook

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.
 About the authors

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.
 Table of contents (8 chapters)


Propositional Logic
Pages 199

FirstOrder Logic
Pages 101147

Mathematical Induction and Arithmetic
Pages 149204

Basic Set Theory and Combinatorics
Pages 205253

Set Theory and Infinity
Pages 255296

Table of contents (8 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to Discrete Mathematics via Logic and Proof
 Authors

 Calvin Jongsma
 Series Title
 Undergraduate Texts in Mathematics
 Copyright
 2019
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030253585
 DOI
 10.1007/9783030253585
 Hardcover ISBN
 9783030253578
 Series ISSN
 01726056
 Edition Number
 1
 Number of Pages
 XX, 482
 Number of Illustrations
 849 b/w illustrations, 5 illustrations in colour
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