The math builders reach for when the problem pushes back.
Proof technique, combinatorics, linear algebra, probability, and game theory — the portable math that lets you reason clearly about systems, markets, and models. Worked problems, not watched lectures.
The math of strategic interaction, from Prisoner's Dilemma to mechanism design. Ten modules, a hundred worked problems, one capstone.
From sample spaces and random variables through the Central Limit Theorem, statistical inference, and Bayesian reasoning — the mathematical toolkit every quantitative builder needs.
From divisibility and modular arithmetic through primes, quadratic residues, elliptic curves, and computational algorithms — the number theory that powers RSA, DH, and modern cryptosystems.
From Caesar ciphers and Shannon entropy through symmetric encryption, public-key cryptography, digital signatures, zero-knowledge proofs, authenticated encryption, and a preview of homomorphic encryption.
Shor's algorithm, NIST post-quantum standards, lattice theory, LWE, CRYSTALS-Kyber, CRYSTALS-Dilithium, hash-based signatures, code-based cryptography, and isogeny-based cryptography.
The mathematical foundations of zero-knowledge proofs: interactive proof systems, Sigma protocols, Fiat-Shamir, polynomial commitments, R1CS, QAPs, Groth16, PLONK, and STARKs.
From Gentry's blueprint through Ring-LWE, BFV, BGV, CKKS, TFHE, bootstrapping, and practical FHE applications — the mathematics and engineering of computing on ciphertexts.