Discrete Math
Why?
Discrete Mathematics provides the theoretical foundation for computer science and many aspects of data science. It develops logical thinking, problem-solving skills, and introduces the mathematical structures that underpin algorithms, data structures, and computational methods.
What?
This course introduces the fundamental concepts of discrete mathematics that are essential for computer science and data science. Topics include logic, proof techniques, set theory, relations, functions, counting principles, number theory, and cryptography basics. The course emphasizes rigorous mathematical thinking and provides the tools needed for more advanced computer science courses.
Curriculum:
The Foundation, Logic, and Proofs
Introduction to propositional and predicate logic, logical operators, truth tables, rules of inference, and various proof techniques including direct proof, contraposition, contradiction, and mathematical induction.
Basic Structures
Study of fundamental discrete structures including sets, functions, sequences, sums, matrices, counting techniques, and the principles of mathematical reasoning in discrete contexts.
Number Theory and Cryptography
Exploration of number theoretic concepts such as divisibility, modular arithmetic, prime numbers, greatest common divisors, and their applications in cryptographic systems like RSA and public key encryption.
Equivalence Relations
Analysis of relations and their properties, with a focus on equivalence relations, partial orderings, representation of relations, closures of relations, and applications to databases and algorithm design.
Notes
The logical reasoning and proof techniques in this course may seem different from math you've seen before. Drawing diagrams for concepts like set operations and relations, and writing out each step explicitly in proofs may make exercise easier.
