Learning Path — Homological Algebra
Suggested preparation for Homological Algebra. Choose an entry point that fits your preparation.
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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
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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
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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
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You can construct quotient groups and rings correctly and state the assumptions of the isomorphism theorems.
Homological Algebra
Work with chain complexes, homology, exact sequences and resolutions.
Notes on Basic Homological Algebra — Andrew Baker. Direct open PDF
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You can compute elementary homology and explain kernels, cokernels and exactness; deeper derived-functor gaps may remain.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.