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Discrete Mathematics

Free Discrete Mathematics study guide: 9 units with summaries, key ideas, flashcards and 187 practice questions with step-by-step solutions.

Lines up with: GRE Mathematics Subject Test (additional topics).

Units

1. UNIT 01

   Logic & propositional calculus

   Logic is the grammar of mathematics. It defines exactly what "and," "or," "if…then" and "for all" mean.
2. UNIT 02

   Proof techniques

   A proof is a logical argument that a statement is always true. Different statements call for different proof strategies.
3. UNIT 03

   Sets, functions & relations

   Sets, functions and relations are the basic objects of discrete math. They describe collections and how elements connect.
4. UNIT 04

   Counting

   Counting answers "how many ways?" without listing them. Decide whether order matters and whether repetition is allowed.
5. UNIT 05

   Discrete probability

   Discrete probability counts favorable outcomes over total outcomes, using the counting tools from the previous unit.
6. UNIT 06

   Recurrence relations

   A recurrence defines each term from earlier ones. Solving it gives a closed formula.
7. UNIT 07

   Number theory

   Number theory studies integers: divisibility, primes and modular arithmetic. It's the math behind cryptography.
8. UNIT 08

   Graph theory

   Graphs model connections: networks, maps, schedules. Vertices are the objects and edges are the links.
9. UNIT 09

   Algorithms & complexity (intro)

   Big-O notation describes how an algorithm's running time grows as input size grows, ignoring constants.