Math 200
Discrete Mathematics I


Math 200 is an introductory course in Discrete Mathematics. It is the first of a two-quarter sequence, followed by Math 201 (Discrete Mathematics II). It will offer a foundation for further study in a variety of majors such as mathematics, computer science, statistics, biology, chemistry, engineering, social sciences, and many others.

Discrete Mathematics is the study of countable, discrete strutures as opposed to those that vary continuously. For example, the set of integers is discrete, while the set of real numbers is continuous. It encompasses topics such as logic, set theory, graph theory, combinatorics, number theory, probability, and more. Many important phenomena in our modern world can be modeled using discrete mathematics. For example:

  • Graph theory is the study of graphs, or networks. The human brain can be thought of as a graph in which neurons are connected by their functional interactions. Information travels across communication graphs such as the internet or social media platforms. Machine learning often relies on neural networks which are graphs.
  • Combinatorics allows us to understand all the different ways of arranging and choosing items: in how many ways can you complete your coursework to get a particular degree? Are some of these ways more efficient than others?
  • Probability explores the likelihood of events occurring. What is the chance that you will miss winning the lottery by one number?
Take Math 200 to learn how to approach such problems and to develop general mathematical thinking and problem-solving skills in discrete settings.

Who can take Math 200?

Math 200 has no prerequisites and is open to all students at the University of Washington.

How does Math 200 differ from Math 300?

Math 200 (followed by Math 201) is an introductory course in discrete math, designed to introduce students to basic notions and explorations in discrete mathematics. While Math 200 will introduce students to mathematical reasoning and the notion of proofs, this will not be done as formally as in Math 300.

On the other hand, Math 300 introduces students to formal mathematical reasoning and the techniques of proof-writing, essential skills for all upper division math classes. While discrete math is often used as a platform for teaching proof-writing techniques, it is not the focus of Math 300.

A tentative list of topics covered in Math 200

  • Foundations
    • Basic logic and set theory
    • Injective, surjective, bijective functions
  • Proof techniques
    • How to solve problems
    • Methods of proof (e.g. contradiction, induction, ...)
    • Parity/invariants
  • Graph theory
    • Definitions
    • Connectivity, trees
    • Planar graphs, Euler's formula
    • Graph coloring
  • Enumerative combinatorics
    • Addition and multiplication principles
    • Permutations and combinations
    • Binomial coefficients
    • Counting in two ways, combinatorial identities, bijections
    • Inclusion-exclusion
  • Probability
    • Basic discrete probability
    • Random variables, distributions
    • Conditional probability, independence
    • Expectation
  • Number theory
    • Modular arithmetic
    • Euclidean algorithm
    • Modular inverses