Mathematics provides the formal backbone for virtually every area of computer science. These notes cover the core mathematical topics a CS student encounters - from discrete structures and counting arguments to linear algebra and calculus - with an emphasis on how each area connects back to computation.
Discrete Math
The bread and butter of CS math: structures that are countable, finite, or combinatorial.
- Graph Theory - formal graph definitions, planarity, coloring, Euler and Hamilton paths
- Combinatorics - permutations, combinations, pigeonhole, inclusion-exclusion
Linear Algebra
Vectors, matrices, and transformations that power graphics, machine learning, and scientific computing.
- Linear Algebra Fundamentals - vectors, matrices, transformations, eigenvalues
Calculus
Continuous mathematics for analysis of algorithms, probability distributions, and optimization.
(Anchor notes coming soon.)
Number Theory
Divisibility, primes, and modular arithmetic - the engine behind cryptography.
(Anchor notes coming soon.)
Logic & Proofs
Formal reasoning techniques that underpin verification, type theory, and specification.
- Mathematical Induction - weak, strong, and structural induction
Combinatorics & Probability
Counting arguments and probabilistic reasoning for algorithm analysis and randomized methods.
- Combinatorics - permutations, combinations, pigeonhole, inclusion-exclusion
- Discrete Probability - sample spaces, Bayes’ theorem, expected value
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