Self-Study Resources for Mathematics
Mathematics is best learned actively, with the right book and a good explainer at your side. Below is a curated path — the textbooks, lecture series, and online courses I'd point a motivated self-learner to, organized by topic and roughly ordered from high-school foundations toward more advanced material. Pick a tile to jump straight to a subject; every book links to a neutral catalogue page so you can track it down at a library or wherever you prefer.
Tip: press Ctrl/Cmd + F to find a specific book or topic.
General Mathematics
Problem-solving, proof, and the bridge into college math.
Books
The Art of Problem Solving — Richard Rusczyk
A comprehensive series of books that cover a wide range of mathematical topics, perfect for high school students and beyond.
DetailsPrecalculus — Michael Sullivan
A great book to bridge the gap between high school math and college-level calculus.
DetailsHow to Prove It: A Structured Approach — Daniel J. Velleman
An excellent introduction to mathematical proofs, providing a clear and structured approach to understanding and constructing proofs.
Details
Lectures & videos
- Khan AcademyA wide range of math tutorials, from basic arithmetic to advanced calculus and beyond.
- PatrickJMTCovers a variety of math topics, including calculus, algebra, and statistics.
Calculus
Limits, derivatives, integrals, and the language of change.
Books
Calculus for the Practical Man — J. E. Thompson
The book a teenage Richard Feynman famously used to teach himself calculus. A gentle, example-driven introduction written for self-learners rather than classroom courses.
DetailsCalculus — James Stewart
A widely used textbook for learning calculus, suitable for beginners and advanced students alike.
Details
Lectures & videos
- Essence of Calculus (3Blue1Brown)A visually intuitive series that explains the fundamental concepts of calculus.
- Khan AcademyComprehensive tutorials on calculus topics.
- Professor LeonardDetailed lectures on calculus and other math subjects.
Online courses
- Coursera: Calculus: Single Variable Part 1 - FunctionsAn introductory course on single-variable calculus, from the University of Pennsylvania.
- edX: Calculus I — From Functions to Differential EquationsA single-variable calculus course from TU Delft, from differentiation through to differential equations.
Linear Algebra
Vectors, matrices, and linear transformations.
Books
Linear Algebra Done Right — Sheldon Axler
An excellent introduction to linear algebra, focusing on understanding the concepts rather than just computational techniques.
Details
Lectures & videos
- Essence of Linear Algebra (3Blue1Brown)A visually intuitive series that explains the fundamental concepts of linear algebra.
- MIT OpenCourseWare: Linear AlgebraA complete lecture series on linear algebra by MIT.
Online courses
- Coursera: Mathematics for Machine Learning — Linear AlgebraAn applied introduction to linear algebra, from Imperial College London.
- edX: Linear Algebra - Foundations to FrontiersA course that covers the foundations of linear algebra, from UT Austin.
Differential Equations
Modeling change with equations for rates.
Lectures & videos
- Differential Equations (3Blue1Brown)A visually intuitive series that explains the fundamental concepts of differential equations.
Probability & Statistics
Reasoning about chance, data, and uncertainty.
Books
Introduction to Probability — Joseph K. Blitzstein & Jessica Hwang
A great resource for learning probability, with clear explanations and plenty of examples.
Details
Lectures & videos
- StatQuest with Josh StarmerClear and engaging explanations of statistics and probability concepts.
- Khan AcademyTutorials on probability and statistics topics.
Online courses
- Coursera: Introduction to Probability and Data with RAn introductory course on probability and data analysis, from Duke University.
- edX: Introduction to ProbabilityA course that covers the basics of probability, from Harvard University.
Tools & References
Calculators, lecture notes, and communities to lean on along the way.
Reference hubs
- Paul's Online Math NotesA comprehensive set of math notes and tutorials covering algebra, calculus, and differential equations.
- Wolfram AlphaA powerful computational engine that helps with solving math problems and visualizing concepts.
- Art of Problem SolvingA community and resource hub for students interested in math competitions and advanced problem-solving.
These should give you a solid foundation for learning mathematics, whatever your starting point. Happy learning!