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AoPS is a comprehensive mathematics learning community offering challenging problems, step-by-step solutions, and active forums, along with online courses and textbooks for competition math. It provides problem sets, tutorials, and classroom resources covering topics from fundamentals to advanced contest math.
More resources on Introduction to Mathematics
Wolfram Alpha
Computational knowledge engine that answers typed natural-language or symbolic queries by solving equations, factoring and simplifying expressions, and plotting functions. Students can check algebra work and inspect results, though full step-by-step solutions require a paid Pro subscription.
Pauls Online Math Notes
Complete lecture-note sets and worked practice problems from Paul Dawkins at Lamar University, spanning algebra, trigonometry, and calculus I through III plus differential equations. Useful for working problems step by step when a textbook explanation stalls.
Khan Academy Math
Free video lessons and adaptive exercise sets covering arithmetic through calculus, linear algebra and statistics, with mastery tracking that identifies gaps. Suited to rebuilding school mathematics systematically before attempting university-level courses.
Single Variable Calculus (MIT 18.01SC)
MIT's self-paced 18.01SC covers differentiation, applications of derivatives, integration, techniques of integration, and infinite series, with problem sets, recitation videos, and exams with solutions. Completing it gives the standard first-semester calculus foundation.
The Joy of x
The acclaimed mathematician and author Steven Strogatz interviews some of the world's leading scientists about their lives and work. You've learned from Quanta. Now we want to learn from you! Quanta is conducting a series of surveys to better serve our audience. Take our podcast listener survey and you will be entered to win a free Quanta book, t-shirt or tote bag: quantamag.typeform.com/podcast
My Favorite Theorem
Interview podcast in which mathematicians Kevin Knudson and Evelyn Lamb ask a guest mathematician to explain a favorite theorem and why it matters. Episodes span topology, number theory, analysis, and combinatorics, giving listeners an accessible sense of research mathematics and its culture.