MATH 505

Fall 2014 All Classes

All Classes

Homological Algebra

Credit: 4 hours.

Topics include: 1. Snake lemma, homology, long exact sequence in homology; 2. Projective and injective modules and resolutions; 3. Categories, functors and derived functors. Tor and Ext, local cohomology; 4. Group cohomology, bar resolution; 5. Spectral sequences, techniques of computation, Serre spectral sequence. Grothendieck spectral sequence of composite functors; 6. Time permitting: Derived categories, Gysin sequence, Kunneth formula, universal coefficient theorm, Eilenberg-Moore sequence.

Prerequisite: MATH 501 or equivalent.

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MATH 505 class schedule data for fall 2014
	CRN	Type	Section	Time	Day	Location	Instructor	Section Details
	30818	Lecture-Discussion	G1	3:00PM -3:50PM	MWF	343 Altgeld Hall	Rezk, C	Part of Term: 1 Date Range: 08/25/14-12/10/14 Section Info: Undergraduate students may register with approval. For more information go to room 313 AH. Students from the following programs must contact the Director of Graduate Studies in Mathematics <Laugesen@illinois.edu> to request permission to register for the course: MS:Economics:Policy Econ -UIUC or MS: Financial Engineering. Restriction(s): Restricted to Graduate - Urbana-Champaign. Not intended for MS:Economics:Policy Econ -UIUC or MS: Financial Engineering.