Overview
Computer Science Theory explores the formal mathematical foundations that govern computation, information, and algorithmic reasoning. This module covers discrete mathematical structures, combinatorial counting, graph theory, probabilistic analysis, recurrence relations, formal language models, finite automata, and the theoretical limits of what can be efficiently computed.
Core Book Modules
1. Discrete Structures
Foundational discrete mathematics covering counting principles, combinatorial identities, algorithmic asymptotic analysis, structural recursion, information encoding, graph topology, and discrete probability distributions.
2. Probability and Statistics for Computer Science
Probabilistic methods, random variables, expectation analysis, statistical inference, and stochastic models applied to computer science systems and randomized algorithms.
3. Theory of Computability
Formal language theory, grammar scopes, deterministic and non-deterministic finite state automata, regular expressions, non-regular language proofs, and fundamental computability models.