Vol 10: Mathematics for Computing
Proving a loop correct, estimating a randomized algorithm's behavior, and fitting data call for different mathematics. This volume organizes the tools by problem: logic and discrete structures, counting and probability, linear algebra and calculus, plus error analysis for numerical computation. You can look up a formula; reading the conditions in the question is still your job.
Choose a module
Each module offers an entry point and lists the knowledge it assumes. Basic algebra and simple programming are enough to begin; add proofs, probability, or matrices as the problem requires.
Module 1
Module 2
Module 3
How the modules connect
Logic supplies precise statements and proof techniques. Counting turns finite choices into quantities and probability models. Calculus, linear algebra, and statistics then describe change, geometry, estimation, and noisy evidence.
Suggested order
For algorithms and formal reasoning, begin with Math A, then choose counting, graphs, or probability from Math B. For data science and machine learning, add Math B's probability and Math C's linear algebra and calculus. When computing with code, include floating-point arithmetic and numerical stability. You can return to your original problem before completing all three modules.