Advanced university

Level 8: Pure Mathematics Track

Analysis, algebra, topology, number theory

This level is part of a complete math learning path that spans from foundations to research topics. Start with the first skills and move forward when you feel confident.

Tap a skill to open focused practice.

Level 8: Pure Mathematics Track

Core skills in this level

Sequences and series (rigorous)

Continuity and compactness

Differentiation theory

Riemann integration

Metric spaces

Topology (introduction)

Group theory

Ring theory

Field theory

Galois theory

Module theory

Complex functions

Contour integration

Residue theorem

Conformal mapping

Analytic continuation

Point-set topology

Topological spaces

Continuity and homeomorphisms

Compactness and connectedness

Fundamental group

Divisibility and primes

Modular arithmetic

Diophantine equations

Quadratic reciprocity

Cryptography applications