In Simple Words

A lot of students who sign up for math and computer science courses, see a strange and unrecognizable course title — “Discrete Mathematics”.

Is that “discrete” like … “adults only”? PG-13?

No, but saying exactly what discrete math IS … well …

The Most Boring Answer

If you just want an un-snarky, straight answer, discrete math is an introduction to mathematical topics which are kind of “blocky” and “jumpy”. The part of math that considers numbers from 0 to 1 to 2, but none of the numbers in-between. This includes

• Modular arithmetic - The study of integer divisibility and related topics.

• Graph theory - The study of nodes connected by edges, like computer networks and flow diagrams.

• Algorithms - The study of instructions that we give to a computer to make it solve problems, and how to minimize them.

• Logic - The study of inferring one proposition (usually but not always mathematical) from another.

• Set theory - The study of putting elements together in a set. (It turns out this is in a way the foundation of all of mathematics.)

• Group theory - The study of systems of combining and permuting elements.

Discrete math isn’t any one of these things or any one thing, it is a hodge-podge of all of them, usually introduced at an introductory level and never going extremely deep into any one topic. Often a discrete math course is hard, not because of the depth of the study, but because of just how many very new ideas it covers in a short amount of time.

The Most Real Answer

Discrete math isn’t anything! Nobody researches “discrete math”. There is no object or property that discrete math studies, the way that group theory studies groups or calculus studies limits.

It was invented to give students a taste of “the other side of mathematics”, especially because these topics are so relevant to computer science. Most students learn algebra and maybe calculus in high school, and walk away with the idea that math studies mostly “smooth” things like function curves. Occasionally their smoothness is interrupted by something like a discontinuity, and this is at most a little hiccup to be resolved through one strategy or another.

Discrete math is basically a whirl-wind tour through all the parts of math that this fails to reveal. Mathematicians research graph theory and its subfields. Mathematicians research modular arithmetic, or more often some field of p-adic arithmetic or groups and rings, or some related topic. But discrete math is a loose, sometimes “to the taste of any particular professor”, collection of non-calculus topics.