Master the essential mathematical foundations of computer science, covering logic, proofs, number theory, and graph theory to analyze algorithms and solve real-world problems.
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Foundations: Sets, Relations, Functions, and Logic
Unit 1: Introduction to Sets
Unit 2: Exploring Relations
Unit 3: Functions: The Building Blocks
Unit 4: Propositional Logic: The Basics
Unit 5: Building Arguments and Proofs
Proofs, Number Theory, and Modular Arithmetic
Unit 1: Predicate Logic and Quantifiers
Unit 2: Direct Proof and Contradiction
Counting, Combinatorics, and Probability
Unit 1: Basic Counting Principles
Unit 2: Permutations and Combinations
Unit 3: Binomial Theorem and Identities
Unit 4: Probability Basics
Unit 5: Expected Value and Applications
Graph Theory and Applications
Unit 1: Introduction to Graph Theory
Unit 2: Graph Traversal Algorithms
Unit 3: Applications of Graph Theory
Recurrence Relations, Finite State Machines, and Boolean Algebra