Course Overview

Welcome to Discrete Math!

Course Description

This course builds on Mathematical Thinking. Discrete mathematics has applications in computer science, as well as the natural and social sciences. The course focuses on core mathematical areas of logic, combinatorics and probability, set theory, graph theory, and elementary number theory. Each topic is covered with a focus on applications and real-world problem-solving. The unit on logic builds on previous knowledge, and has applications in real-world rhetoric as well as in mathematical proofs and in computing. Probability and combinatorics are foundational for statistical thinking and problem solving. In the course’s coverage of graph theory, students will explore numerous applications, such as data mining, clustering, and networking. The course also introduces number theory, beginning with fundamental results such as Euclid’s Algorithm and applications in cryptography.

Topics

  • Mathematical notation and LaTeX basics
  • Counting
  • Sequences
  • Induction, Recursion
  • Logic and proofs
  • Graphs
  • Number theory

How the course works

There are multiple ways you'll learn in this course:

  • Read and engage with the materials on this site
  • Attend live class and complete the activities in class
  • Answer practice exercises to try out the concepts
  • Complete assignments, exams, and projects to demonstrate what you have learned

Active engagement is necessary for success in the course!

You are encouraged to seek out additional practice problems outside of the practice problems included in the course. Problems in the textbook are mostly unused, and are a good starting place for extra practice.

Built-in Prompts

Many of the modules online will have built-in prompts. They come in three forms:

Check your understanding: These prompts are questions you should be able to answer with confidence if you've understood the material. If you're having trouble with these questions, try re-reading the section, both in the textbook and on the course webpage.

Think about it: These prompts require a deeper understanding of the material, and may be topics of discussion during the live class. If you can think of an answer, you're doing fantastic! However, it's not expected that you will be completely correct.

Think first: This prompt will be answered in the next line. You should stop and try to find your own answer first before proceding.

These prompts are meant to help you form an intuition when it comes to solving mathematical problems. Try to complete them as you're reading the material!

Learning Outcomes

By the end of the course, students will be able to:

  • Write clear mathematical statements using standard notation and terminology.
  • Perform operations on discrete structures such as sets, functions, relations or sequences.
  • Demonstrate mathematical reasoning by constructing proofs using a variety of techniques (direct proofs, contradiction, induction, etc.).
  • Solve problems using counting techniques and combinatorics.
  • Calculate probabilities of events and expectations of random variables.
  • Understand and perform modular arithmetic, including using the Euclidean Algorithm.
  • Identify real world problems that relate to graph theory, find basic features of a graph, and solve simple graph-related problems.
  • Name a number of real-life applications of discrete math related to the computer science discipline.

Instructor

Please contact on Discord first with questions about the course.

Live Class Time

Note: all times are shown in GMT.

Office Hours

Core Reading List

  • Levin, Oscar. (2019). Discrete Mathematics: An Open Introduction. (http://discrete.openmathbooks.org/dmoi3/dmoi.html)
  • https://open.umn.edu/opentextbooks/textbooks/21

Supplemental Reading List

  • Lovasz, L., Vesztergombi, K. (1999). Discrete Mathematics Lecture Notes. Yale University
  • Lehman, E., Leighton T., Meyer, A. (2015) Mathematics for Computer Science.
  • http://math.gordon.edu/ntic/ntic/ntic.html
  • https://crypto.stanford.edu/pbc/notes/numbertheory/book.pdf
  • https://web.mit.edu/rsi/www/pdfs/new-latex.pdf
  • https://web.mit.edu/rsi/www/pdfs/reference-latex.pdf
  • https://discretemath.org/ads/index-ads.html