General Information

Place and time:TuTh 1:00pm-11:20pm, Math 4-130

Professor: Leon Takhtajan, Office: Math. Tower 5-111. Office hours: TBA.

Grader: Dingxin Zhang Office: Math. Tower 2-114. Office hours: TBA.

Course description (from the graduate bulletin):

• Vector spaces: Cayley-Hamilton Theorem, Jordan normal form, bilinear forms, signature, tensor products, symmetric and exterior algebras.
• Homological algebra: categories and functors, universal and free objects, exact sequences, extensions.
• Representation theory for finite groups: irreducible representations and Shur's Lemma, characters, orthogonality.
• Galois theory: splitting fields, finite fields, extension fields of various types, Galois polynomial and group, fundamental theorem of Galois theory, symmetric functions.

Textbook: David S. Dummitt and Richard M. Foote, Abstract algebra, 3rd ed. available at the University Bookstore @ Stony Brook or from amazon.com. A copy of the textbook will be on reserve in the Mathematics, Physics and Astronomy Library.

Please be aware that there is a number of misprints in the book; you can find the errata here.

Additional references:

• D. Cox, Galois Theory, Wiley-Interscience, 2004.
• M. Artin, Algebra, Prentice Hall, 1991.
• S. Lang, Algebra, 3rd ed., Springer-Verlag, 2002.
• Jacobson, Basic Algebra,, 2nd ed, W.H. Freeman, New York, 1985, 1989.
• S. Roman, Advanced Linear Algebra, 3rd ed., Springer-Verlag, 2007.
• B. L. van der Waerden, Algebra, Springer-Verlag, 1994.
• Blyth, Module Theory, Oxford University Press, 1990.
• J.-P. Serre, Linear Representations of Finite Groups, Prentice Hall, 1991.

Exams, homeworks, and grading. There will be weekly homeworks, two midterms, and the final exam. Your final grade will be determined by the following scheme:
Homeworks: 25%
Midterms: 20%
Final Exam: 35%

Information for students with disabilities
If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or http://studentaffairs.stonybrook.edu/dss/. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.sunysb.edu/ehs/fire/disabilities.shtml