Introduction to Discrete Mathematics with ISETL

William E. Fenton, Ed Dubinsky (Autoren)

Buch | Hardcover

196 Seiten

1996
Springer-Verlag New York Inc.
978-0-387-94782-2 (ISBN)

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Intended for first- or second-year undergraduates, this introduction to discrete mathematics covers the usual topics of such a course, but applies constructivist principles that promote - indeed, require - active participation by the student. Working with the programming language ISETL, whose syntax is close to that of standard mathematical language, the student constructs the concepts in her or his mind as a result of constructing them on the computer in the syntax of ISETL. This dramatically different approach allows students to attempt to discover concepts in a "Socratic" dialog with the computer. The discussion avoids the formal "definition-theorem" approach and promotes active involvement by the reader by its questioning style. An instructor using this text can expect a lively class whose students develop a deep conceptual understanding rather than simply manipulative skills. Topics covered in this book include: the propositional calculus, operations on sets, basic counting methods, predicate calculus, relations, graphs, functions, and mathematical induction.

1 Numbers and Programs.- 1.1 The Basics of ISETL.- 1.2 Divisibility.- Overview of Chapter 1.- 2 Propositional Calculus.- 2.1 Boolean Expressions.- 2.2 Implication and Proof.- Overview of Chapter 2.- 3 Sets and Tuples.- 3.1 Defining Sets and Tuples.- 3.2 Operations on Sets.- 3.3 Counting Methods.- Overview of Chapter 3.- 4 Predicate Calculus.- 4.1 Quantified Expressions.- 4.2 Multi-Level Quantification.- Overview of Chapter 4.- 5 Relations and Graphs.- 5.1 Relations and their Graphs.- 5.2 Equivalence Relations and Graph Theory.- Overview of Chapter 5.- 6 Functions.- 6.1 Representing Functions.- 6.2 Properties of Functions.- Overview of Chapter 6.- 7 Mathematical Induction.- 7.1 Understanding the Method.- 7.2 Using Mathematical Induction.- Overview of Chapter 7.- 8 Partial Orders.- Activities.- Discussion.- Exercises.- Overview of Chapter 8.- 9 Infinite Sets.- Discussion.- Exercises.- Appendix 1: Getting Started With Isetl.- A. Working in the Execution Window.- B. Working with Files.- C. Using Directives.- D. Graphing in ISETL.- Appendix 2: Some Special Code.- Index of Frequently Used Sets and Functions.

Zusatzinfo	XVI, 196 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Programmiersprachen / -werkzeuge
	Informatik ► Theorie / Studium ► Compilerbau
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-94782-5 / 0387947825
ISBN-13	978-0-387-94782-2 / 9780387947822
Zustand	Neuware