MATH 571: Higher Algebra 2
Winter 2013
Course Outline [PDF]

Instructor

Miljan Brakocevic
Office:Burnside Hall 1242
Office hours:Wednesday and Friday 1:30 - 2:30 PM
eMail: first name dot last name at mcgill dot ca
Web: http://www.math.mcgill.ca/brakocevic/

Course information

Time:Monday, Wednesday, Friday 10:35 AM - 11:25 AM
Location:Burnside Hall 1205
Dates:Jan 07, 2013 - Apr 16, 2013

There will be a take home final exam, as well as weekly homework. The final grading will be based on the homework (70 %) and final exam (30 %).

Exercises

Hand in onExercise
Mon, Jan 21 Assignment 1
Mon, Jan 28 Assignment 2
Mon, Feb 4 Assignment 3
Mon, Feb 11 Assignment 4   Hints
Mon, Feb 18 Assignment 5   Hints
Mon, Feb 25 Assignment 6
Mon, Mar 11 Assignment 7
Mon, Mar 18 Assignment 8
Mon, Mar 25 Assignment 9
  
  
  

Exercises are usually to be handed in on Mondays.

Textbooks

Recommended:

  1. Dummit, David S; Foote, Richard M.; Abstract Algebra. Wiley; 3 edition (July 14, 2003)
...on reserve in Schulich Library.

Other:

  1. Atiyah, M. F.; Macdonald, I. G.; Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969
  2. Lang, Serge; Algebra. Revised third edition. Graduate Texts in Mathematics, 211. Springer-Verlag, New York, 2002
  3. Jacobson, Nathan; Basic algebra. II. Second edition. W. H. Freeman and Company, New York, 1989

Syllabus

Rings, Part I.

  1. The spectrum of a ring.
  2. Integral extensions and the going-up and going-down theorems.
  3. Noether's normalization lemma, and Hilbert's Nullstellensatz.
  4. Noetherian and Artinian rings.
  5. Hilbert's basis theorem.

Modules, Part II.

  1. Tensor products.
  2. Projective modules.
  3. Injective modules.
  4. Flat modules.

Rings, Part II.

  1. The Jacobson radical.
  2. Nakayama's lemma.
  3. Semisimple rings and modules.
  4. Jacobson's density theorem and the Artin-Wedderburn theorem.

Linear representations of finite groups.

  1. Linear representations of groups.
  2. Maschke's theorem.
  3. Characters. Orthogonality of characters. Frobenius Reciprocity.
  4. Representations of nilpotent groups.
  5. Representations of the symmetric group.
  6. Representations of GL_2(F), for F a finite field.

Notice on Academic Integrity

  1. McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic o ences under the Code of Student Conduct and Disciplinary Procedures (see McGill web page on Academic Integrity for more information).
  2. In accord with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.