Learn

Follow a course from its first idea to its main theorems. Each course lists its ideas in teaching order, so each idea comes after the ideas that it builds on. To explore one area of mathematics in depth, choose a subject.

Year 1

Logic and sets145 ideas · 144 writtenStarts with Proposition
Number systems103 ideas · 102 writtenStarts with Natural numbers
Discrete mathematics188 ideas · 186 writtenStarts with Combinatorics
Analysis and calculus of one variable330 ideas · 315 writtenStarts with Sequence
Linear algebra315 ideas · 312 writtenStarts with Linear equation
Geometry100 ideas · 98 writtenStarts with Euclidean plane
Elementary number theory178 ideasStarts with Divisibility
Probability178 ideas · 174 writtenStarts with Probability theory

Year 2

Group theory195 ideas · 194 writtenStarts with Binary operation
Rings and fields180 ideas · 179 writtenStarts with Ring
Multivariable calculus142 ideas · 138 writtenStarts with Function of several variables
Ordinary differential equations108 ideasStarts with Differential equation
Metric spaces and topology170 ideasStarts with Metric space
Complex analysis84 ideasStarts with Domain in the complex plane

All of mathematics

The subjects follow the Mathematics Subject Classification. Each subject has a map of its main ideas, sorted by area and in teaching order.