SUNY at Stony Brook MAT 534: Algebra I
Fall 2015

General Information

Place and time:TuTh 10:00am-11:20am, Math 4-130

Professor: Leon Takhtajan, Office: Math. Tower 5-111. Office hours: Tuesday and Thursday, 2:30pm-3:30pm in 5-111.

Grader: Harrison Pugh Office: Math. Tower 2-107. Office hours: Tuesaday, 12:00pm-1:00pm in 2-107 and 1:00pm-2:00pm in MLC and Friday, 1:00am-11:00am in MLC.

Course description (from the graduate bulletin):

  • Groups: normal subgroups, quotient groups, Lagrange's theorem, class formula, finite p-groups and solvable groups, Sylow's theorems, finitely generated abelian groups.
  • Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID's, PID's, UFD's, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID.
  • Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and eigenvectors, inner products, spectral theorem for normal operators.

Textbook: David S. Dummitt and Richard M. Foote, Abstract algebra, 3rd ed. available at the University Bookstore @ Stony Brook or from 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:

  • A. Knapp, Basic Algebra, Birkhauser, 2006.
  • M. Artin, Algebra, Prentice Hall, 1991.
  • S. Lang, Algebra, 3rd ed., Addison-Wesley, 1993.
  • Jacobson, Basic Algebra, 2nd ed, W.H. Freeman, New York, 1985, 1989.
  • Rotman, Introduction to the Theory of Groups, Springer Verlag.

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 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: