Discrete mathematics
By: the Teaching Company
Contributors: Teaching Company
Series: Science & mathematics; Great courses (DVD)
Publisher: The Teaching Company
Published: 2009
Place of publication: Chantilly, VA
Language: eng
Format: [videorecording] /
Number of pages: 720
ISBN-13: 9781598035735
Subjects: Prime Numbers; Public key cryptography; Trees (Graph theory); Fermat's last theorem; Groups of divisibility; Markov processes; Binomial coefficients; Computer science; Combinatorial analysis; Mathematics; Factorials; Matrices; Ramsey theory; Fibonacci numbers
Description: 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.
Notes: Course workbook includes professor biography, acknowledgments, statement of course scope, lecture outline with suggested readings and questions to consider, timeline, glossary, biographical notes, and bibliography.

Producer, Matt Costanza ; academic content supervisor, Jay Tate ; editors, Dan Shine, Zach Rhodes.

Twenty-four thirty minute lectures by Dr. Arthur T. Benjamin, Professor of Mathematics at Harvey Mudd College.

DVD.
Table of contents: title: Part 1: Disc 1. Lecture 1.; title: What is discrete mathematics? ; -- Lecture 2.; title: Basic concepts of combinatorics ; -- Lecture 3.; title: The 12-fold way of combinatorics ; -- Lecture 4.; title: Pascal's triangle and the binomial theorem ; -- Lecture 5.; title: Advanced combinatorics: Multichoosing ; -- Lecture 6.; title: The principle of inclusion-exclusion -- -- Disc 2. Lecture 7.; title: Proofs: Inductive, geometric, combinatorial ; -- Lecture 8.; title: Linear recurrences and Fibonacci Numbers ; -- Lecture 9.; title: Gateway to number theory: Divisibility ; -- Lecture 10.; title: The structure of numbers ; -- Lecture 11.; title: Two principles: Pigeonholes and parity ; -- 12.; title: Modular arithmetic: The math of remainders.; title: Part 2: Disc 3. Lecture 13.; title: Enormous exponents and card shuffling ; -- Lecture 14.; title: Fermat's "little" theorem and prime testing ; -- Lecture 15.; title: Open secrets: Public key cryptography ; -- Lecture 16.; title: The birth of graph theory ; -- Lecture 17.; title: Ways to walk: Matrices and Markov chains ; -- Lecture 18.; title: Social networks and stable marriages -- -- Disc 4. Lecture 19.; title: Tournaments and King Chickens ; -- Lecture 20.; title: Weighted graphs and minimum spanning trees ; -- Lecture 21.; title: Planarity: When can a graph be untangled? ; -- Lecture 22.; title: Coloring graphs and maps ; -- Lecture 23.; title: Shortest paths and algorithm complexity ; -- Lecture 24.; title: The magic of discrete mathematics.