Notes

Objects, morphisms, and compositional structure across mathematical theories.

Continuity, spaces, and structure preserved by qualitative deformation.

Algebraic structures and the abstract patterns that organize mathematical operations.

Entropy, information, coding, and the mathematical language of communication and uncertainty.

Vectors, matrices, linear maps, and the algebraic structures used throughout computation.

Limits, derivatives, integrals, and the continuous mathematics needed for computation.

Probability, random variables, distributions, statistics, and stochastic ideas used in computation and machine learning.

Logic, Boolean algebra, number theory, relations, order, and the discrete structures behind computation.

Proofs, sets, functions, inequalities, complex numbers, and the basic structures used throughout computer science mathematics.

A bilingual series building reinforcement learning from the ground up in nine chapters: from what makes it a distinct learning problem, through the Markov ladder and the Bellman machinery, to a full derivation of policy gradient, the sample-reuse machinery of PPO, GRPO's removal of the critic, and DPO's direct formulation of preference learning as policy optimization.