# Resources for Teaching Discrete Mathematics

## Brian Hopkins, Editor

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.

Electronic ISBN: 9780883859742

Table of Content
Introduction - Part I
Introduction - Part II
 PDF Price POD Price Resources for Teaching Discrete Mathematics $37.00 Price per Chapter Price per Chapter Chapter 1: The Game of ‘‘Take Away’’$7.00 $8.50 Chapter 2: Pile Splitting Problem: Introducing Strong Induction$7.00 $8.50 Chapter 3: Generalizing Pascal: The Euler Triangles$7.00 $8.50 Chapter 4: Coloring and Counting Rectangles on the Board$7.00 $8.50 Chapter 5: Fun and Games with Squares and Planes$7.00 $8.50 Chapter 6: Exploring Recursion with the Josephus Problem$7.00 $8.50 Chapter 7: Using Trains to Model Recurrence Relations$7.00 $8.50 Chapter 8: Codon Classes$7.00 $8.50 Chapter 9: How to change coins, M&M’s, or chicken nuggets$7.00 $8.50 Chapter 10: Calculator Activities for a Discrete Mathematics Course$7.00 $8.50 Chapter 11: Bulgarian Solitaire$7.00 $8.50 Chapter 12: Can you make the geodesic dome?$7.00 $8.50 Chapter 13: Exploring Polyhedra and Discovering Euler’s Formula$7.00 $8.50 Chapter 14: Further Explorations with the Towers of Hanoi$7.00 $8.50 Chapter 15: The Two Color Theorem$7.00 $8.50 Chapter 16: Counting Perfect Matchings and Benzenoids$7.00 $8.50 Chapter 17: Exploring Data Compression via Binary Trees$7.00 $8.50 Chapter 18: A Problem in Typography$7.00 $8.50 Chapter 19: Graph Complexity$7.00 $8.50 Chapter 20: Binary Arithmetic: From Leibniz to von Neumann$7.00 $8.50 Chapter 21: Arithmetic Backwards from Shannon to the Chinese Abacus$7.00 $8.50 Chapter 22: Pascal’s Treatise on the Arithmetical Triangle$7.00 $8.50 Chapter 23: Early Writings on Graph Theory$7.00 $8.50 Chapter 24: Counting Triangulations of a Convex Polygon$7.00 $8.50 Chapter 25: Hamiltonian Circuits and The Icosian Game$7.00 $8.50 Chapter 26: Are All Infinities Created Equal?$7.00 $8.50 Chapter 27: Early Writings on Graph Theory: Topological Connections$7.00 $8.50 Chapter 28: A Study of Logic and Programming via Turing Machines$7.00 $8.50 Chapter 29: Church’s Thesis$7.00 $8.50 Chapter 30: Two-Way Deterministic Finite Automata$7.00 $8.50 Chapter 31: A Rabbi, Three Sums, and Three Problems$7.00 $8.50 Chapter 32: Storing Graphs in Computer Memory$7.00 $8.50 Chapter 33: Inclusion-Exclusion and the Topology of Partially Ordered Sets$7.00 $8.50 Chapter 34: Guided Group Discovery in a Discrete Math Course for Math Majors$7.00 $8.50 Chapter 35: The Use of Logic in Teaching Proof$7.00 \$8.50

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