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Discrete mathematics [digital videodisc] / Professor Arthur T. Benjamin, Harvey Mudd College.

Chantilly, VA : The Teaching Company, [2009]

Combinatorial analysis.

Binomial coefficients.

Fibonacci numbers.

Fermat's last theorem.

Numbers, Prime.

Groups of divisibility.

Public key cryptography.

Markov processes.

Trees (Graph theory)

Computer science -- Mathematics.

Great courses (DVD). Science & mathematics.

4 videodiscs (720 min.) : sound, color ; 4 3/4 in. + 1 course guidebook (vi, 148 pages ; 19 cm).

Part 1: Disc 1. Lecture 1. What is discrete mathematics? ; Lecture 2. Basic concepts of combinatorics ; Lecture 3. The 12-fold way of combinatorics ; Lecture 4. Pascal's triangle and the binomial theorem ; Lecture 5. Advanced combinatorics: Multichoosing ; Lecture 6. The principle of inclusion-exclusion -- Disc 2. Lecture 7. Proofs: Inductive, geometric, combinatorial ; Lecture 8. Linear recurrences and Fibonacci Numbers ; Lecture 9. Gateway to number theory: Divisibility ; Lecture 10. The structure of numbers ; Lecture 11. Two principles: Pigeonholes and parity ; 12. Modular arithmetic: The math of remainders.

Part 2: Disc 3. Lecture 13. Enormous exponents and card shuffling ; Lecture 14. Fermat's "little" theorem and prime testing ; Lecture 15. Open secrets: Public key cryptography ; Lecture 16. The birth of graph theory ; Lecture 17. Ways to walk: Matrices and Markov chains ; Lecture 18. Social networks and stable marriages -- Disc 4. Lecture 19. Tournaments and King Chickens ; Lecture 20. Weighted graphs and minimum spanning trees ; Lecture 21. Planarity: When can a graph be untangled? ; Lecture 22. Coloring graphs and maps ; Lecture 23. Shortest paths and algorithm complexity ; Lecture 24. The magic of discrete mathematics.

Discrete mathematics is a subject that--while off the beaten track--has vital applications in computer science, cryptography, engineering, and problem solving of all types. Discrete mathematics deals with quantities that can be broken into neat little pieces, like pixels on a computer screen, the letters or numbers in a password, or directions on how to drive from one place to another. Like a digital watch, discrete mathematics is that in which numbers proceed one at a time, resulting in fascinating mathematical results using relatively simple means, such as counting. This course delves into three of Discrete Mathematics most important fields: Combinatorics (the mathematics of counting), Number theory (the study of the whole numbers), and Graph theory (the relationship between objects in the most abstract sense). Professor Benjamin presents a generous selection of problems, proofs, and applications for the wide range of subjects and foci that are Discrete Mathematics.

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