Let’s start with the word discrete:
dis·crete /disˈkrēt/
Adjective: Individually separate and distinct.
Synonyms: separate – detached – distinct – abstract
Defining discrete mathematics is tricky—because defining mathematics itself is tricky. Is math the study of numbers? Partly, yes. But it also includes functions, lines, triangles, parallelepipeds, vectors, and much more. Or maybe you'd say mathematics is a toolbox for solving problems—especially those involving patterns, structure, and logic.
So what makes mathematics discrete?
Try applying the dictionary definition of “discrete” to mathematics: individually separate and distinct. Some areas of math deal with continuous things, like the real numbers. In calculus, when you talk about numbers between 0 and 1, you can always find another number in between—like 0.5. And between 0 and 0.5? Sure—0.25. This can go on forever. There’s no smallest possible gap.
But discrete math is different.
Suppose you're working with natural numbers \(\{1, 2, 3, ...\}\). Take the numbers 4 and 5. Can you find a natural number between them? No—you’re stuck. Discrete math deals with things that come in individual chunks: integers, graphs, logic statements, sets, algorithms.
The best way to understand discrete math is to jump in and start doing it.
This course is often required in most computer science departments. It is usually considered a prerequisite for higher-level computer science courses, as it provides the mathematical background needed for courses like Data Structures, Computability, and Algorithms.
That said: this is a mathematics course. In some mathematics departments, there is a “bridge” course which connects the gap between calculus-based courses and upper-level, abstract mathematics courses. This course does not serve that explicit purpose, but much of the material found in those “bridge” courses will be covered here—material on logic, set theory, cardinality, induction, proof writing, etc.
You are strongly encouraged to form study groups. This course will be challenging at times, and it will be useful for you to check in with each other and see if others are struggling with the same things. I expect you to work on course materials about 8 hours a week altogether.
An old saying is worth repeating: Mathematics is not a spectator sport. No one can learn calculus just by listening to the lectures and reading the book. Your engagement and participation are essential. Read the book actively with a pencil and paper. Ask questions if you don't get the material. Seek help early in the process. Work as many exercises as possible. Nothing will boost your learning more than actually working through the exercises.