mathematics, computer science 

The Great Courses 

While continuous mathematics resembles an old-fashioned analog clock, whose second hand sweeps continuously across a dial, discrete mathematics is like a digital watch, whose numbers proceed one second at a time. As a result, discrete mathematics achieves fascinating mathematical results using relatively simple means, such as counting. Explore this modern realm in these 24 mind-expanding lectures that are mathematically rigorous and yet entertaining and accessible to anyone with a basic knowledge of high school algebra. Discrete mathematics covers a wide range of subjects, and you'll delve into three of its most important fields, presenting a generous selection of problems, proofs, and applications in three main areas. First is combinatorics, or the mathematics of counting. Central to many problems in combinatorics, you'll learn, is Pascal's triangle, whose numbers contain some amazingly beautiful patterns. Then you'll move on to number theory, which leads to come intriguing puzzles: Can every number be factored into prime numbers in exactly one way? Why do the digits of a multiple of 9 always sum to a multiple of 9? Finally, you'll examine graph theory, which focuses on the relationship between objects in the most abstract sense. By simply connecting dots with lines, graph theorists create networks that model everything from how computers store information to potential marriage partners. Professor Benjamin describes discrete mathematics as "relevant and elegant" - qualities that are evident in the practical power - from Amazon 

vi, 148 p. ; 19 cm. ; 2 videodiscs (ca. 360 min.) : sd., col. ; 4 3/4 in 

What is Discrete Mathematics? -- Basic Concepts of Combinatorics -- The 12-Fold Way of Combinatorics -- Pascal's Triangle and the Binomial Theorem -- Advanced Combinatorics- Multichoosing -- The Principle of Inclusion-Exclusion -- Proofs- Inductive, Geometric, Combinatorial -- Linear Recurrences and Fibonacci Numbers -- Gateway to Number Theory- Divisibility -- The Structure of Numbers -- Two Principles- Pigeonholes and Parity -- Modular Arithmetic- The Math of Remainders -- Enormous Exponents and Card Shuffling -- Fermat's "Little" Theorem and Prime Testing -- Open Secrets- Public Key Cryptography -- The Birth of Graph Theory -- Ways to Walk- Matrices and Markov Chains -- Social Networks and Stable Marriages -- Tournaments and King Chickens -- Weighted Graphs and Minimum Spanning Trees -- Planarity- When Can a Graph be Untangled? -- Coloring Graphs and Maps -- Shortest Paths and Algorithm Complexity -- The Magic of Discrete Mathematics