Mathematics

This trunk is a working mathematical toolkit. The goal is not to reproduce a textbook, but to preserve the definitions, intuitions, derivations, and computational patterns that support other branches.

Branches

Branch	Primary connection
Calculus	Change, gradients, optimization, and continuous models
Linear Algebra	Vectors, transformations, and machine learning — Eigenvalues and SVD
Information Theory & Entropy	Compression, uncertainty, and learning objectives — Channel capacity
Discrete Mathematics	Logic, combinatorics, and computer science — Counting and combinatorial proofs
Statistics & Probability	Inference, uncertainty, and data analysis — Hypothesis tests and multiple comparisons
Numerical Analysis	Reliable computation and approximation — Floating-point numbers and stability; Solving ODEs numerically
Convex Optimization	Structured optimization problems — Constrained optimality and duality

Suggested Paths

• For machine learning: Linear Algebra → Statistics & Probability → Calculus → Optimization
• For algorithms: Discrete Mathematics → Algorithms → Computer Science
• For quantitative modeling: Statistics & Probability → Numerical Analysis → Quantitative Finance

Use the branches together

Before calculating, specify the objects and assumptions: real numbers or discrete states, a deterministic function or a probability model, an exact identity or an approximation. For a linear prediction problem, linear algebra checks the shape of $Ax$ and whether coefficients are identifiable; probability describes observation noise and sampling; calculus differentiates the loss; numerical analysis asks whether the computed solution is reliable. A derivative, a fitted coefficient, and a confidence interval answer different questions.

The branch maps give a bounded starting reference and routes into deeper notes or courses. They are not prerequisites to read cover to cover: choose a question first, then fill in the definitions its solution uses.

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