Contents
Part 0 — Start here
- How to use this guide · Role-based learning paths · Notation cheat sheet (every symbol, constant and unit) · How to read a formula
Part 1 — Beginner: the foundations everyone needs
- Number systems & bit-level math
- Modular arithmetic
- Boolean algebra & logic
- Sets, relations, and functions
- Exponents & logarithms
- Sequences, series & growth rates
- Geometry & trigonometry essentials
- Basic probability (axioms, conditional probability, expectation)
- Basic statistics (correlation, EWMA and TCP's retransmission timer)
Part 2 — Intermediate: core engineering mathematics 10. Linear algebra I — vectors & matrices (norms, neural layers, routing matrices, least squares) 11. Linear algebra II — eigenvalues, eigenvectors, determinants (PageRank, Markov chains, graph Laplacians) 12. Calculus I — limits, derivatives, integrals (Taylor, Newton's method, the Fundamental Theorem) 13. Calculus II — gradients, Jacobians, Hessians, the chain rule (backprop by hand, softmax gradient) 14. Probability distributions (CLT, LLN, concentration bounds, heavy tails, LLM sampling) 15. Combinatorics & counting 16. Bayes' theorem 17. Graph theory (Dijkstra's proof, max-flow/min-cut, spanning trees) 18. Complexity & asymptotic analysis 19. Number theory basics (extended Euclid, Fermat/Euler proofs, CRT, batch-GCD attacks)
Part 3 — Expert: domain-specific deep dives (senior level) 20. Linear algebra for AI/ML (SVD, PCA, tensors, attention) 21. Optimization & backpropagation (learning-rate limits, Adam, Lagrange and TCP fairness) 22. Statistics for ML & experimentation (MLE, z-tests, power analysis) 23. Information theory (entropy, min-entropy, Huffman coding, compression side channels) 24. Cryptographic mathematics (RSA proof, side channels, elliptic curves by hand, ECDSA nonce reuse, lattices) 25. Network & systems mathematics (M/M/1 derived, Erlang C, Kingman, AIMD fairness, buffer sizing) 26. Quantitative security (detection theory, cost-optimal thresholds, password hashing, differential privacy) 27. Signal processing basics (DFT by hand, convolution, decibels, QAM/OFDM, Wi-Fi rates) 28. Game theory & adversarial thinking (FGSM derived, security games, defender's dilemma) 29. Control theory basics (stability, dead time, steady-state error, the Kubernetes HPA)
Part 4 — Putting it together
- Role-based priority map · Formula cheat sheet · Theorem index · Practice labs