Mathematics Codex

Mathematical reference covering college algebra through discrete math, with emphasis on concepts that directly apply to computing and security engineering.

Topics

Topic Description

Algebra

Equations, functions, exponents, logarithms, series

Calculus

Limits, derivatives, integrals — conceptual foundations

Linear Algebra

Vectors, matrices, determinants, eigenvalues

Logic

Propositional logic, predicate logic, Boolean algebra

Set Theory

Sets, operations, relations, cardinality

Discrete Math

Functions, induction, recurrences, modular arithmetic, growth

Combinatorics

Counting, permutations, combinations, pigeonhole principle

Probability

Conditional probability, Bayes' theorem, distributions

Statistics

Descriptive stats, percentiles, correlation, hypothesis testing

Number Theory

Primes, GCD, modular arithmetic, cryptographic foundations

Graph Theory

Graphs, traversal, shortest paths, centrality, the association engine

Proofs

Direct proof, contradiction, contrapositive, induction, counterexamples

Notation

Symbols, Greek letters, conventions for reading mathematical text

Why Math?

Domain Mathematical Foundation

Algorithms

Recurrences, asymptotic growth, combinatorics

Cryptography

Number theory, modular arithmetic, probability

Networking

Graph theory, probability, statistics (SLA)

Security

Probability (risk), statistics (anomaly detection), Boolean algebra

Machine Learning

Linear algebra, calculus, probability, statistics

Database Design

Set theory, relations, predicate logic