Welcome to Discrete Mathematics, a subject that is off the beaten track that most of us followed in school but that has vital applications in computer science, cryptography, engineering, and problem solving of all types. Most of the mathematics taught after elementary school is aimed at preparing students for one subject—calculus, which is the mathematics of how things grow and change continuously, like waves in the water or clouds in the sky. Discrete mathematics, on the other hand, 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. 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 of digital math in Discrete Mathematics, 24 mind-expanding lectures by veteran Teaching Company Professor Arthur T. Benjamin, an award-winning educator and mathemagician who has designed a course that is 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 Professor Benjamin delves into three of its most important fields, presenting a generous selection of problems, proofs, and applications in the following areas:
- Combinatorics: How many ways are there to rearrange the letters of Mississippi? What is the probability of being dealt a full house in poker? Central to these and many other problems in combinatorics (the mathematics of counting) is Pascal's triangle, whose numbers contain some amazingly beautiful patterns.
- Number theory: The study of the whole numbers (0, 1, 2, 3, ...) leads to some 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? Moreover, how do such questions produce a host of useful applications, such as strategies for keeping a password secret?
- Graph theory: Dealing with more diverse graphs than those that plot data on x and y axes, graph theory 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 and communicate information to transportation grids to even potential marriage partners.
With these rich and rewarding lectures, Professor Benjamin equips you with logical thinking skills that will serve you well in your daily life—as well as in any future math courses you may take.
