Discrete Mathematics

This course introduces students to the basics of discrete mathematics, also known as finite or concrete mathematics. The students will study various concepts in logic, set theory, functions and relations, graphs, and modular arithmetic, among others. In addition to the theoretical concepts, the theory classes will cover some common mathematical notation and language, proof techniques, and problem-solving strategies. The tutorials will cover several examples in greater depth.

A good understanding of discrete mathematics is essential for grasping the underlying principles of computer engineering and data science. Starting from the very basics, this course will introduce the students to the wonderful world of formal mathematics. We will cover the basics of logic and proof techniques, sets and functions, study discrete structures such as graphs in detail, and wrap up the course with an introduction to abstract structures, including posets, lattices, and groups. The fundamental aim of this course is to introduce students to a formal way of studying discrete structures. By the end of the course, the students should be comfortable forming mathematical statements and writing formal proofs. The course also aims to develop the students’ ability to prove and write algorithms.

By the end of this course, each student will have the opportunity to:

• Learn the basic vocabulary of discrete mathematics | Know/Knowledge Outcome
• Understand mathematical proofs and algorithms | Comprehension Outcome
• Prove theorems and write algorithms for various problems | Application Outcome
• Choose an optimal way to solve a problem by breaking it into multiple smaller problems | Analysis Outcome
• Critique the efficacy and efficiency of various problem-solving techniques | Evaluation Outcome
• Design fresh solutions for existing as well as new problems in the real world | Create/synthesize outcomes

• Ralph P. Grimaldi, “Discrete and Combinatorial Mathematics: An Applied Introduction,” Pearson (2019, 5th ed.)
• Jiri Matousek & Jaroslav Nesetril, “Invitation to Discrete Mathematics,” Oxford University Press (2008, 2nd ed.)

• Gerard O'Regan, “Guide to Discrete Mathematics: An Accessible Introduction to the History, Theory, Logic, and Applications,” Springer (2021, 2nd ed.)
• Fred Roberts & Barry Tesman, “Applied Combinatorics,” CRC Press (2024, 3rd ed.)