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Resources for teaching discrete mathematics : classroom projects, history modules, and articles

Author: Brian Hopkins
Publisher: Washington Mathematical Association of America 2009
Edition/Format:   Computer file : English
Database:WorldCat
Summary:
A resource for discrete mathematics teachers at all levels. Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic  Read more...
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Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Brian Hopkins
ISBN: 9780883859742 0883859742 9780883851845 0883851849
OCLC Number: 967689311
Notes: Title from publisher's bibliographic system (viewed on 02 Oct 2015).
Description: 1 online resource (xiv, 323 pages)
Contents: Pt. 1. Classroom-tested projects. The game of "Take Away" / Mark MacLean --
Pile splitting problem: introducing strong induction / Bill Marion --
Generalizing Pascal: the Euler Triangles / Sandy Norman and Betty Travis --
Coloring and counting rectangles on the board / Michael A. Jones and Mika Munakata --
Fun and games with squares and planes / Maureen T. Carroll and Steven T. Dougherty --
Exploring recursion with the Josephus Problem: (or how to play "One Potato, Two Potato" for keeps) / Douglas E. Ensley and James E. Hamblin --
Using trains to model recurrence relations / Benjamin Sinwell --
Codon classes / Brian Hopkins --
How to change coins, M et M's, or chicken nuggets: the linear Diophantine problem of Frobenius / Matthias Beck --
Calculator activities for a discrete mathematics course / Jean M. Horn and Toni T. Robertson --
Bulgarian solitaire / Suzanne Dorée --
Can you make the geodesic dome? / Andrew Felt and Linda Lesniak --
. Exploring polyhedra and discovering Euler's Formula / Leah Wrenn Berman and Gordon Williams --
Further explorations with the Towers of Hanoi / John Stadler --
The two color theorem / David Hunter --
Counting perfect matchings and benzenoids / Fred J. Rispoli --
Exploring data compression via binary trees / Mark Daniel Ward --
A problem in typography / Larry E. Thomas --
Graph complexity / Michael Orrison --
pt. 2. Historical projects in discrete mathematics and computer science. Introduction / Janet Barnett [and others] --
Binary arithmetic: from Leibniz to von Neumann / Jerry M. Lodder --
Arithmetic backwards from Shannon to the Chinese abacus / Jerry M. Lodder --
Pascal's treatise on the arithmetical triangle: mathematical induction, combinations, the binomial theorem and Fermat's theorem / David Pengelley --
Early writings on graph theory: Euler circuits and the Königsberg bridge problem / Janet Heine Barnett --
Counting triangulations of a convex polygon / Desh Ranjan --
. Early writings on graph theory: Hamiltonian circuits and the Icosian Game / Janet Heine Barnett --
Are all infinities created equal? / Guram Bezhanishvili --
Early writings on graph theory: topological connections / Janet Heine Barnett --
A study of logic and programming via Turing machines / Jerry M. Lodder --
Church's thesis / Guram Bezhanishvili --
Two-way deterministic finite automata / Hing Leung --
pt. 3. Articles extending discrete mathematics content. A rabbi, three sums, and three problems / Shai Simonson --
Storing graphs in computer memory / Larry E. Thomas --
Inclusion-exclusion and the topology of partially ordered sets / Eric Gottlieb --
pt. 4. Articles on discrete mathematics pedagogy. Guided group discovery in a discrete mathematics course for mathematics majors / Mary E. Flahive --
The use of logic in teaching proof / Susanna S. Epp.
Responsibility: edited by Brian Hopkins.

Abstract:

A resource for discrete mathematics teachers at all levels. Resources for Teaching Discrete Mathematics presents nineteen classroom tested projects complete with student handouts, solutions, and notes to the instructor. Topics range from a first day activity that motivates proofs to applications of discrete mathematics to chemistry, biology, and data storage. Other projects provide: supplementary material on classic topics such as the towers of Hanoi and the Josephus problem, how to use a calculator to explore various course topics, how to employ Cuisenaire rods to examine the Fibonacci numbers and other sequences, and how you can use plastic pipes to create a geodesic dome. The book contains eleven history modules that allow students to explore topics in their original context. Sources range from eleventh century Chinese figures that prompted Leibniz to write on binary arithmetic, to a 1959 article on automata theory. Excerpts include: Pascal's 'Treatise on the Arithmetical Triangle,' Hamilton's 'Account of the Icosian Game,' and Cantor's (translated) 'Contributions to the Founding of the Theory of Transfinite Numbers.' Five articles complete the book. Three address extensions of standard discrete mathematics content: an exploration of historical counting problems with attention to discovering formulas, a discussion of how computers store graphs, and a survey connecting the principle of inclusion-exclusion to Möbius inversion. Finally, there are two articles on pedagogy specifically related to discrete mathematics courses: a summary of adapting a group discovery method to larger classes, and a discussion of using logic in encouraging students to construct proofs.

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