General Information

Place and time:TuTh 9:45am-11:05am, Math 4-130

Professor: Leon Takhtajan, Office: Math. Tower 5-111. Office hours: TuTh 2pm-3pm in 5-111 and by appointment.

Grader: Mads Villadsen Office: Math. Tower 2-118. Office hours: M 11am-12pm by Zoom.

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 and there.

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%

Material covered in Algebra I, Fall 2022