Learning Path — Representation Theory & Lie Theory
Suggested preparation for Representation Theory & Lie Theory. Choose an entry point that fits your preparation.
Open any node directly. Marking a node familiar never locks, hides or removes links. No study progress is uploaded or stored.
Entry / bridge route · Additional preparation for research reading · All paths
Entry / bridge route
Proofs & Mathematical Writing
Read quantified statements; write direct, contrapositive, contradiction and induction arguments.
Book of Proof — Richard Hammack. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can explain the quantifiers in a statement and write these forms of proof without relying on a worked solution.
Linear Algebra
Work with vector spaces, bases, linear maps, kernels, rank and eigenvalues.
Linear Algebra — Jim Hefferon. Open online text / archive
Compare resources in this subject
Can skip if… / selective review
You can prove rank–nullity, change bases and distinguish diagonalizable maps from general linear maps.
Abstract Algebra & Galois Theory
Use groups, rings, ideals, quotient constructions and field extensions.
Abstract Algebra: Theory and Applications — Thomas W. Judson. Open online text / archive
Compare resources in this subject
Can skip if… / selective review
You can construct quotient groups and rings correctly and state the assumptions of the isomorphism theorems.
Representation Theory & Lie Theory
Study group actions on vector spaces and basic representation decompositions before Lie or tensor-categorical references.
Introduction to Representation Theory — Pavel Etingof et al.. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can construct representations, intertwining maps and basic decompositions; infinite-dimensional and Lie-theoretic preparation must be checked separately.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.
Category Theory
Understand functors, natural transformations, limits and adjunctions through examples.
Category Theory in Context — Emily Riehl. Direct open PDF
Compare resources in this subject
Can skip if… / selective review
You can express a universal property and verify a natural transformation or an adjunction in a concrete example.