Mathematics Foundations

A free, self-paced math curriculum built on open-source textbooks. This track covers the mathematical foundations required for computer science, machine learning, and software engineering: from precalculus and single-variable calculus through probability and statistics, and on to the math an LLM system runs on (matrix calculus and autodiff, numerical methods and floating point, optimization, information theory). In the course, every math topic with code has a call site: the modules you build here are called by the system you build.

The primary math texts are free to read online. Access and reuse permissions differ; consult each source’s license. See the source register for checked references.

Prerequisite Graph

graph LR
    PC[00 Precalculus] --> C1
    C1[01 Calculus 1] --> C2[02 Calculus 2]
    C2 --> C3[04 Calculus 3]
    LA[03 Linear Algebra] --> C3
    D1[05 Discrete Math 1] --> D2[06 Discrete Math 2]
    C1 --> PS[07 Probability & Statistics]
    D1 --> PS
    C3 --> MC[08 Matrix Calculus & Autodiff]
    LA --> MC
    D2 --> MC
    C2 --> NM[09 Numerical Methods & Floating Point]
    PC --> NM
    C3 --> OPT[10 Optimization]
    LA --> OPT
    PS --> IT[11 Information Theory]
    LA --> IT
    LA --> SI[12 Signals & Images]
    PC --> SI
    NM --> SI

Topics

#	Topic	Textbook	Estimated Time
00	Precalculus	OpenStax Precalculus 2e	2-3 weeks
01	Calculus 1	OpenStax Calculus Vol 1	4 weeks
02	Calculus 2	OpenStax Calculus Vol 2	4 weeks
03	Linear Algebra	Hefferon, Linear Algebra	4 weeks
04	Calculus 3	OpenStax Calculus Vol 3	4 weeks
05	Discrete Math 1	Hammack, Book of Proof	4 weeks
06	Discrete Math 2	Levin, Discrete Mathematics	4 weeks
07	Probability & Statistics	Grinstead & Snell + OpenStax Stats	3-4 weeks
08	Matrix Calculus & Autodiff	Parr & Howard, Baydin et al. (free)	3 weeks
09	Numerical Methods & Floating Point	Goldberg (free), Higham	3-4 weeks
10	Optimization	Boyd & Vandenberghe (free)	3 weeks
11	Information Theory	Student’s Guide to Coding & Info Theory + MacKay (free)	3-4 weeks
12	Signals & Images	Oppenheim & Schafer; Smith (free)	2 weeks

Total: ~27-28 weeks for 01 to 07 as an intensive introductory pass, at 10-12 hours per week; 00 and 08 to 12 add about 17 weeks, or arrive just in time through the course passes. Full textbook coverage and degree-level mastery require additional problem sets and assessment.

Quick Start

1. Pick your entry point. Calculus 1, Linear Algebra, and Discrete Math 1 have no college-level prerequisites. Algebra and functions are assumed; calculus also requires trigonometry. Start with one subject unless your weekly time budget supports more.
2. Open the topic README. Each topic lists the free textbook, section-by-section study plan, key theorems, worked examples, and exercises.
3. Work problems with pencil and paper. Mathematics is learned by doing, not reading. Aim for 10-12 hours per week on each active topic.
4. Follow the prerequisite graph. Once you complete the entry-level topics, the graph above shows what unlocks next.
5. Connect to CS. Each topic README maps math concepts to their CS applications and links to the algorithms/systems tracks in this repo.

Recommended Parallel Schedules

Full-time (2 topics at once):

• Weeks 1-4: Calculus 1 + Discrete Math 1
• Weeks 5-8: Calculus 2 + Discrete Math 2
• Weeks 9-12: Linear Algebra + Probability & Statistics
• Weeks 13-16: Calculus 3

Part-time (1 topic at a time):

• Follow the numbering 01 through 07, respecting prerequisites.

Apply the mathematics

Use the CS curriculum math labs alongside these topics: prove a scheduler correct, implement least squares and PCA, check gradients, measure integration error, and simulate statistical inference. Each assignment requires a derivation, implementation, independent comparison, and failure analysis.

After the foundations, read Deisenroth, Faisal and Ong’s Mathematics for Machine Learning for the bridge to numerical optimization and data applications.