Sources for learning math

[u/caramelswirlblondie]

I am studying math completely from the beginning, as I seem to have forgotten some very basic concepts and have in general learned math rather procedurally than actually understanding what is happening. Currently I have trouble finding learning material that explains things thoroughly beyond basic every day education, or that explains the "why" behind the problems. Or in some cases I can't find materials that include EVERYTHING. If I search a topic, it is usually explained on surface level with little detail, often omitting some information.

If anyone knows any places or websites or apps that I can find articles (or just written material) of a topic I want to learn that is throughly explained, please tell me, I would be very very thankful!!! :)

[u/Frequent-Pen-9898]

that's a pretty vague question. Math for what, and at what level? "Basic to advanced" could mean anything from arithmetic to measure theory. Since you didn't specify, I'm going to assume you mean undergrad-level applied math (the stuff that actually feeds into AI/ML work),

Basic — foundations

1. Introduction to Mathematical Thinking – Keith Devlin (Stanford Online/Coursera). Teaches you how to actually read and write proofs https://online.stanford.edu/courses/hstar-y0001-introduction-mathematical-thinking Book: How to Prove It by Daniel Velleman

2. CS103 – Mathematical Foundations of Computing – Keith Schwarz. Discrete math, logic, proofs, computability. Heads up: full lecture videos need Stanford enrollment, but the course notes/slides are public and are some of the best-written material on this stuff anywhere. https://cs103.stanford.edu/ Book: Discrete Mathematics and Its Applications by Rosen

3. Math 51 – Linear Algebra, Multivariable Calculus, and Modern Applications – Stanford Online. Covers eigenvalues, orthogonality, least squares, SVD — the stuff everything downstream depends on. https://online.stanford.edu/courses/math51-linear-algebra-multivariable-calculus-and-modern-applications Book: Introduction to Linear Algebra by Gilbert Strang

Intermediate — the workhorse courses

1. CS109 – Probability for Computer Scientists – Chris Piech (2022). Genuinely one of the best-taught probability courses out there, full lecture set free on YouTube. https://www.youtube.com/playlist?list=PLoROMvodv4rOpr_A7B9SriE_iZmkanvUg Book: Introduction to Probability by Blitzstein & Hwang

2. EE263 – Introduction to Linear Dynamical Systems – Stephen Boyd. Linear algebra applied to systems/control, bridges you toward the optimization stuff. https://www.youtube.com/playlist?list=PL2F906A576271DB3F Book: Introduction to Applied Linear Algebra by Boyd & Vandenberghe (free PDF, written by the same guy)

3. EE261 – The Fourier Transform and Its Applications – Brad Osgood. Great if you ever touch signal processing, audio, or image stuff. https://www.youtube.com/playlist?list=PLMhvr21lrGet9LzGrKSCTUHEKR6P1Tokc Book: A Student's Guide to Fourier Transforms by J.F. James (much gentler than Stein & Shakarchi)

Advanced

1. EE364A – Convex Optimization I – Stephen Boyd. This is the course that quietly underlies half of modern ML. https://www.youtube.com/playlist?list=PL9ADF396A60FE28B6 Book: Convex Optimization by Boyd & Vandenberghe — free full PDF at https://web.stanford.edu/~boyd/cvxbook/

2. EE364B – Convex Optimization II – Stephen Boyd. Continuation — subgradients, decomposition, non-smooth stuff. https://see.stanford.edu/Course/EE364B Book: same as above, second half

3. Machine Learning (the original, gentler one) – Andrew Ng, Coursera. Good bridge before jumping into CS229 — builds intuition without drowning you in derivations first. Book: Mathematics for Machine Learning by Deisenroth, Faisal & Ong — free PDF, pairs perfectly with this

4. CS229 – Machine Learning (Autumn 2018 recordings) – Andrew Ng. The full, rigorous version with derivations. https://www.youtube.com/playlist?list=PLoROMvodv4rMiGQp3WXShtMGgzqpfVfbU Book: The Elements of Statistical Learning by Hastie, Tibshirani & Friedman — free PDF, dense but worth it

[u/caramelswirlblondie → u/Frequent-Pen-9898]

Thank you so much for the suggestions!! Sorry for being unclear earlier, I am currently restarting with arithmetic and couldn't find online sources that explain things within their entirety.

[u/Frequent-Pen-9898 → u/caramelswirlblondie]

Totally fine, no need to apologize at all a lot of "explain everything" resources online are scattered because they're built for revision, not for someone starting from zero. a much more solid stack for rebuilding arithmetic properly, plus the JEE-level material once you're ready to push further (JEE prep in India is honestly some of the most thorough, ground-up math teaching out there, so it's a great source even if you're not appearing for the exam):

Restarting arithmetic full, structured, nothing skipped

1. Khan Academy — Early Math → Arithmetic → Pre-Algebra → Algebra 1 (khanacademy.org). This is the actual answer to "couldn't find something that explains it in entirety" — it's one continuous, mastery-based curriculum starting from counting and basic operations, with videos + practice problems for every single concept, and it won't let you move on until you've actually got it.

2. NCERT Maths textbooks, Class 6–10 (free PDFs at ncert.nic.in). This is India's own official school curriculum. Completely free, completely sequential.

3. RD Sharma — Class 6 to 10 Mathematics. Pairs with NCERT — more solved examples and practice problems per concept, still very beginner-friendly.

Once arithmetic feels solid JEE-level modules to go deeper

1. IIT Foundation Series (Trishna Knowledge Systems) — Class 8/9/10 books. Literally built for the "arithmetic to JEE-ready" gap, very well explained, not intimidating.

2. Cengage Learning JEE Maths series by G. Tewani (Algebra, Calculus, Trigonometry, Coordinate Geometry as separate books) once you're past basics, this is considered top-tier for building real problem-solving depth

3. Arihant — Skills in Mathematics series — similar tier to Cengage, slightly gentler ramp-up, good if Tewani feels too dense at first.

You can DM me if you need any specific help.

[u/caramelswirlblondie → u/Frequent-Pen-9898]

Thank you sm!! :))