Leon Takhtajan

Synopsis

The course will cover the basics of abstract algebra and is the first course in the 2-semester sequence (Algebra I, Algebra II). The lectures and homework assignments will be posted on the detailed weekly schedule. The homework problems will vary from routine to rather challenging. The use of online resources for solving the homework problems is prohibited. The schedule will be regularly updated and it is necessary to check it each week. The grades, solutions of selected homework problems and solutions to the midterm will be posted on the Brightspace. Students are expected to attend class regularly and complete the assigned readings in the course schedule before lecture. During lecture the instructor and the students will discuss the material in those readings, there will be exercises to practice the material, etc. For the lectures to be effective, you must complete the assigned reading from the syllabus before lecture.

Lectures

MW 11:00am-12:20pm, Physics P127

Instructor

Leon Takhtajan

Office hours: Monday, 2:00pm-3:00pm and Wednesday, 2:00pm-4:00pm in 5-111.

Grader

Zhulei Pan

Office: Math Tower 3-106

Office hours: Friday, 9:30am-11:30am in 3-106.

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 and from other sources. Be certain that you have the third edition. There is a number of misprints in the book; you can find the errata here.

Additional classic references include:

• 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. scheduled as follows:

• Midterm 1 - September 28, in class
  
• Midterm 2 - November 4, in class
  
• Final exam - December 9, 11:15am-1:45pm, in class.
  

Homework is assigned on a weekly basis via weekly schedule, and is due on Wednesdays. Homework is returned to the grader, either in person, or via a dedicated box/envelope in front of the grader’s office. Please write your solutions nicelely (preferrably in the latex if you can), and staple the sheets together. No late homework will be accepted; there are no exceptions to this rule.

Your final grade will be determined by the following scheme:

• Homeworks: 15%
  
• Midterms: 25% + 25%
  
• 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 Student Accessibility Support Center, Stony Brook Union, Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Arrangements should be made early in the semester (before the first exam) so that your needs can be accommodated. All information and documentation of disability 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.

Academic integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website.

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.