Discrete mathematics is the study of mathematical structures that are fundamentally discrete. In mathematics, they are useful in geometry and certain parts of topology, e.g. Biggs (2002-12-19).

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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. Problems, Proofs, and Applications 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?