Place and time TuTh 9:30am-10:50am, Physics P-130

Professor Leon Takhtajan, Office: Math. Tower 5-111. Office hours: W 2pm-4pm in 5-111 and by appointment.

Grader Xuande Liu Office: Math. Tower 2-113. Office hours:TBA

Course description

• 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.There are free copies online, just check that you have a thrid edition.

There is a number of misprints in the book; you can find the errata here and there.

Lectures The lectures cannot, should not and will not attempt a line-by-line approach to the textbook. The emphasis will be on the important concepts, some key proofs, examples and discussions.Besides the textbook, other sources will be used. Topics of the lectures will be regularly announced on the BRIGHTSPACE.

Homework and exams There will be weekly homeworks, two midterms, and the final exam on May 19, 11:15am-1:45pm The homework will be assigned via Brighspace weekly, and due on Tuesdays in class. Homework is returned by the grader via a dedicated box/envelope in front of the grader’s office. Homework MUST be stapled, or it will not be collected. No late homework will be accepted.

Academic Integrity and homework There are online sources for the homework. If it is determined that the student used, even in part, these resources to hand in the homework, a grade of zero will be given for the first occurrence; for the second occurrence, this will be reported to the appropriate offices.

Attendance and class behavior Attendance is not required but is highly recommended. No texting/surfing during class; e-note takers, computers, ipads, etc. must be in silent mode and stored away; keep smartphones on the desk upside down in silent mode; no food or drinks

Grading The final grade will be determined by the following scheme:
Homeworks: 25%
Midterms: 20%
Final Exam: 35%

Material covered in Algebra I Fall 2024 course syllabus.

Student Accessibility Support Center Statement

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the 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. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities and search Fire Safety and Evacuation and Disabilities.

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 at http://www.stonybrook.edu/commcms/academic_integrity/index.html.

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 Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.