Introduction to Discrete Mathematics via L...

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Preface.- List of Notations.- 1. Propositional Logic.- 2. First-Order Logic.- 3. Mathematical Induction and Arithmetic.- 4. Basic Set Theory and Combinatorics.- 5. Set Theory and Infinity.- 6. Functions and Equivalence Relations.- 7. Posets, Lattices, and Boolean Algebra.- 8. Topics in Graph Theory.- A. Inference Rules for PL and FOL.- Index.

Details

Erscheinungsjahr:	2019
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xx 482 S. 849 s/w Illustr. 5 farbige Illustr. 482 p. 854 illus. 5 illus. in color.
ISBN-13:	9783030253578
ISBN-10:	3030253570
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Jongsma, Calvin
Auflage:	1st ed. 2019
Hersteller:	Springer International Publishing Undergraduate Texts in Mathematics
Maße:	241 x 160 x 31 mm
Von/Mit:	Calvin Jongsma
Erscheinungsdatum:	12.12.2019
Gewicht:	1,008 kg

Artikel-ID: 116806748