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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.

A paperbound version of this book can be purchased in the MAA Store.

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

 

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