MATH 571: Higher Algebra 2
Winter 2011
Course description
Instructor
Course information
Time:  Monday, Wednesday, Friday 9:35 AM  10:25 AM 
Location:  Burnside Hall 1234 
Dates:  Jan 04, 2011  Apr 08, 2011 
There will be a midterm and final exam, as well as weekly exercises.
The final grading will be based on the exercises (20 %), midterm exam (20 %) and
final exam (60 %).
Exercises
Exercises are usually to be handed in on Mondays.
Textbooks
Recommended:

Dommit, David S; Foote, Richard M.;
Abstract Algebra. Wiley; 3 edition (July 14, 2003), 944 pp., ISBN: 9780471433347
...on reserve in Schulich Library.
Other:
 Eisenbud, David; Commutative Algebra with a View Toward Algebraic Geometry
SpringerVerlag, New York, 1995, ISBN: 9780387942698
 Lang, Serge; Algebra. Revised third edition. Graduate Texts in Mathematics, 211. SpringerVerlag, New York, 2002. xvi+914 pp. ISBN: 038795385X
 Jacobson, Nathan; Basic algebra. II. Second edition. W. H. Freeman and Company, New York, 1989. xviii+686 pp. ISBN: 0716719339
 Atiyah, M. F.; Macdonald, I. G.; Introduction to commutative algebra. AddisonWesley Publishing Co., Reading, Mass.LondonDon Mills, Ont. 1969 ix+128 pp.
Syllabus
Rings, Part I.
 Integral extensions and the goingup and goingdown theorems.
 Noether's normalization lemma, and Hilbert's Nullstellensatz.
 Noetherian and Artinian rings.
 Hilbert's basis theorem.
Modules, Part II.
 Tensor products.
 Projektive modules.
 Injective modules.
 Flat modules.
Rings, Part II.
 The Jacobson radical.
 Nakayama's lemma.
 Semisimple rings and modules.
 Jacobson's density theorem and the ArtinWedderburn theorem.
Categories, Part III.
 Exact functors.
 Adjoint functors.
Groups, Part II.
 Linear representations of groups.
 Maschke's theorem.
 Characters. Orthogonality of characters. Frobenius Reciprocity.
 Representations of nilpotent groups.
 Representations of the symmetric group.
 Representations of GL_2(F), for F a finite field.
 if time is left  Homological algebra.
 The snake lemma and the 5 term lemma.
 Projective and injective resolutions and derived functors.
 The derived functors Tor and Ext.
 Homotopy and independence on the resolution.
Notice
McGill University values academic integrity. Therefore, all students
must understand the meaning and consequences of cheating, plagiarism and
other academic offenses under the Code of Student Conduct and
Disciplinary Procedures (see McGill web page on Academic Integrity for more information).