▸ Sciences · Mathematics

Mathematics

From counting to ∫f(x)dx to ∇²ψ — the language the rest of science is written in. Built around proof, intuition, and worked problems.
4,000topics
12problem libraries
6exam tracks
+218trending this week

By topic

browse the canon · choose where to start
x²
Algebra
From quadratic equations to abstract structures — groups, rings, fields, modules.
240 topics
∫
Calculus & analysis
Limits, derivatives, integrals, series — and the rigor behind them. Real, complex, functional.
320 topicstrending
⟨,⟩
Linear algebra
Vectors, matrices, eigenvalues, inner-product spaces. The workhorse of every applied field.
180 topicstrending
∂
Differential equations
ODEs, PDEs, dynamical systems. From population growth to Laplace's equation.
160 topics
P(A)
Probability & statistics
Random variables, distributions, inference. Classical and Bayesian.
200 topics
△
Geometry & topology
Euclidean, projective, differential geometry. Topology — the shape of space.
220 topics
ℕ
Number theory
Primes, modular arithmetic, Diophantine equations. The crown jewel.
140 topics
∑
Combinatorics & discrete
Counting, graphs, generating functions. The math of CS and Olympiads.
160 topics

Problem libraries

canonical sources · solve, struggle, ask
Spivak · Calculus
The rigorous calculus textbook. Real-analysis-flavored, problems that teach.
★★★★★ · 540 problems · UG analysis
Apostol · Calculus I & II
Integration-first treatment, classical exposition. Vector calculus included.
★★★★★ · 720 problems · UG
Rudin · Principles of analysis
"Baby Rudin." The benchmark for real analysis at the undergrad/grad bridge.
★★★★★ · 380 problems · UG–grad
Strang · Linear algebra
MIT's flagship LA textbook. Geometric, computational, accessible.
★★★★★ · 520 problems · UG
Putnam archive
75+ years of the hardest undergrad math competition in the US.
★★★★★ · 900+ problems · UG-elite
IMO archive
All problems from every International Mathematical Olympiad since 1959.
★★★★★ · 360 problems · pre-college elite
Hatcher · Algebraic topology
The free standard text. Hard, beautiful, the road into topology.
★★★★☆ · 240 problems · grad
Dummit & Foote · Abstract algebra
Comprehensive grad text. Groups, rings, fields, Galois theory, modules.
★★★★★ · 600 problems · grad

Exam prep

where math matters most for testing
JEE Main · AdvIndia · undergrad-engAlgebra · calculus · coordinate geom · 3D · vectors. Heavy problems.
SAT & ACTUS · collegeAlgebra-heavy with geometry & basic stats.
GRE quantgrad schoolArithmetic, algebra, geometry, data interpretation.
GMAT quantbusiness schoolProblem solving + data sufficiency.
PutnamUS · elite UG12 brutal problems · 6 hours · top math undergrads.
IMOinternational · HSNumber theory · geometry · algebra · combinatorics.

By level

match your background · move up or down anytime
▸ entryPop mathCurious, no formula required. "Why is 0.999… exactly 1?" energy.~280 topics
▸ HSHigh schoolAlgebra · trig · calc-AB · stats. NCERT/AP/IB level.~720 topics
▸ UGUndergradCalc III · LA · ODEs · proof-based analysis · abstract algebra intro.~1,640 topics
▸ gradGraduateReal / complex analysis · functional · algebraic geom · topology · PDEs.~1,360 topics

Trending in math this week

▲ 1 · +218Why is e everywhere?curiosity · ~12 min
▲ 2 · +186Eigenvectors, intuitivelyUG · ~25 min
▲ 3 · +152Fundamental theorem of calculusHS-UG · ~30 min
▲ 4 · +124Bayes' theorem from scratchstats · ~25 min
▲ 5 · +98Why is 0.999… = 1?curiosity · ~10 min
▲ 6 · +84Galois theory, slowlygrad · ~1 hour
OmniTutor · Math · v0 ← all subjects physics → history → tutor runtime