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Resources for Teaching Discrete Mathematics. [Pehme köide]

  • Formaat: Paperback / softback, 323 pages, illustrations
  • Ilmumisaeg: 13-Oct-2009
  • Kirjastus: Mathematical Association of America (MAA)
  • ISBN-10: 0883851849
  • ISBN-13: 9780883851845
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  • Formaat: Paperback / softback, 323 pages, illustrations
  • Ilmumisaeg: 13-Oct-2009
  • Kirjastus: Mathematical Association of America (MAA)
  • ISBN-10: 0883851849
  • ISBN-13: 9780883851845
Teised raamatud teemal:
Hopkins (Saint Peters College) collects the work of 35 instructors who share their innovations and insights about teaching discrete mathematics at the high school and college level. The book's 9 classroom-tested projects, including building a geodesic dome, come with student handouts, solutions, and notes for the instructor. The 11 history modules presented draw on original sources, such as Pascal's "Treatise on the Arithmetical Triangle," allowing students to explore topics in their original contexts. Three articles address extensions of standard discrete mathematics content. Two other articles explore pedagogy specifically related to discrete mathematics courses: adapting a group discovery method to larger classes, and using logic in encouraging students to construct proofs. There is no subject index. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)



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.
Introduction vii
I Classroom-tested Projects
The Game of ``Take Away''
3(4)
Mark MacLean
Pile Splitting Problem: Introducing Strong Induction
7(4)
Bill Marion
Generalizing Pascal: The Euler Triangles
11(8)
Sandy Norman
Betty Travis
Coloring and Counting Rectangles on the Board
19(12)
Michael A. Jones
Mika Munakata
Fun and Games with Squares and Planes
31(14)
Maureen T. Carroll
Steven T. Dougherty
Exploring Recursion with the Josephus Problem: (Or how to play ``One Potato, Two potato'' for Keeps)
45(10)
Douglas E. Ensley
James E. Hamblin
Using Trains to Model Recurrence Relations
55(6)
Benjamin Sinwell
Codon Classes
61(4)
Brian Hopkins
How to change coins, M&M's, or chicken nuggets: The linear Diophantine problem of Frobenius
65(10)
Matthias Beck
Calculator Activities for a Discrete Mathematics Course
75(8)
Jean M. Horn
Toni T. Robertson
Bulgarian Solitaire
83(10)
Suzanne Doree
Can you make the geodesic dome?
93(4)
Andrew Felt
Linda Lesniak
Exploring Polyhedra and Discovering Euler's Formula
97(20)
Leah Wrenn Berman
Gordon Williams
Further Explorations with the Towers of Hanoi
117(8)
Jon Stadler
The Two Color Theorem
125(6)
David Hunter
Counting Perfect Matchings and Benzenoids
131(12)
Fred J. Rispoli
Exploring Data Compression via Binary Trees
143(8)
Mark Daniel Ward
A Problem in Typography
151(8)
Larry E. Thomas
Graph Complexity
159(10)
Michael Orrison
Introduction 165(4)
Janet Barnett
Guram Bezhanishvili
Hing Leung
Jerry Lodder
David Pengelley
Desh Ranjan
II Historical Projects in Discrete Mathematics and Computer Science
Binary Arithmetic: From Leibniz to von Neumann
169(10)
Jerry M. Lodder
Arithmetic Backwards from Shannon to the Chinese Abacus
179(6)
Jerry M. Lodder
Pascal's Treatise on the Arithmetical Triangle: Mathematical Induction, Combinations, the Binomial Theorem and Fermat's Theore
185(12)
David Pengelley
Early Writings on Graph Theory: Euler Circuits and the Konigsberg Bridge Problem
197(12)
Janet Heine Barnett
Counting Triangulations of a Convex Polygon
209(8)
Desh Ranjan
Early Writings on Graph Theory: Hamiltonian Circuits and the Icosian Game
217(8)
Janet Heine Barnett
Are All Infinities Created Equal?
225(6)
Guram Bezhanishvili
Early Writings on Graph Theory: Topological Connections
231(10)
Janet Heine Barnett
A Study of Logic and Programming via Turing Machines
241(12)
Jerry M. Lodder
Church's Thesis
253(14)
Guram Bezhanishavili
Two-Way Deterministic Finite Automata
267(10)
Hing Leung
III Articles Extending Discrete Mathematics Content
A Rabbi, Three Sums, and Three Problems
277(10)
Shai Simonson
Storing Graphs in Computer Memory
287(1)
Larry E. Thomas
Storing Graphs in Computer Memory
287(6)
Larry E. Thomas
Inclusion-Exclusion and the Topology of Partially Ordered Sets
293(12)
Eric Gottlieb
IV Articles on Discrete Mathematics Pedagogy
Guided Group Discovery in a Discrete Mathematics Course for Mathematics Majors
305(8)
Mary E. Flahive
The Use of Logic in Teaching Proof
313(10)
Susanna S. Epp
About the Editor 323