Mathematics | Xingyu Yang · Research Notes

Reading guide

These notes develop the mathematical language used in computer science, modelling, and learning. Start with foundations for proof techniques, sets, and functions; continue into discrete mathematics for logic and finite structures, or calculus, linear algebra, and probability for continuous models. Computational mathematics connects these ideas to numerical algorithms.

Several chapters originated in Math for Computer Science and are being revised as standalone notes. The subjects below lead to their own reading paths; unfinished outlines are identified separately.

Reading path

Mathematical Foundations

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

14 notes

Discrete Mathematics

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

6 notes · 1 planned

Probability and Statistics

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

7 notes · 5 planned

Computational Mathematics

Numerical representation, approximation, algorithms, and computation with mathematical objects.

13 notes

Calculus

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

8 planned

Linear Algebra

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

14 notes

Information Theory

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

1 planned

Abstract Algebra

Algebraic structures and the abstract patterns that organize mathematical operations.

1 planned

Topology

Continuity, spaces, and structure preserved by qualitative deformation.

1 planned

Category Theory

Objects, morphisms, and compositional structure across mathematical theories.

1 planned