| Spring 2025 MAT 314/525: Abstract Algebra II | ||
| Schedule | TR 9:30-10:50am Physics P-117 | |
| Instructor | Robert Hough | |
| Office hours | M 3-5pm in Math Tower 4-118, Thurs 7-8pm in Math Learning Center | |
| Grader | ||
| Description | This course is a continuation of MAT 313, Abstract algebra. It covers modules over rings, including structure theorem for modules over PID, theory of fields and field extensions and introduction to Galois theory. It is intended for math majors, in particular math majors in advanced track program. | |
| Textbook | Artin's Algebra. Supplementary text Dummit and Foote's Abstract algebra. | |
| Homework | Weekly problem sets will be assigned, and collected in class according to the syllabus below. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class. | |
| Grading | Homework: 40%, Final: 60%. | |
Accommodations for students with hearing and communication impairments:
Some students with hearing and communication impairments may need their instructor to wear a
clear mask for lip and facial expression purposes. If the student has registered with the Student
Accessibility Support Center (SASC) and has requested an accommodation for clear masks, SASC
will reach out to the students instructors and provide a clear mask for them to wear while teaching
and/or interacting with the student. If you have questions, please email sasc@stonybrook.edu or
call (631) 632-6748.
Syllabus/schedule (subject to change)
| Tu 1/28 | 1. | The classical groups, SU2 and SO3 | 9.1-9.4 |
| Th 1/30 | 2. | One parameter groups, the Lie algebra | 9.5-9.7 |
| Tu 2/4 | 3. | Irreducible representations | 9.8, 10.1-10.2 HW 1 Due 2/6 Chapter 9 Problems 1.1, 3.4, 5.1, 5.5, 6.1, 6.11, 8.4, M.4 |
| Th 2/6 | 4. | Unitarization, characters | 10.3-10.5 |
| Tu 2/11 | 5. | Schur's lemma, orthogonality | 10.6-10.8 |
| Th 2/13 | 6. | Compact groups | 10.9, Topics from Serre's Linear representations of finite groups |
| Tu 2/18 | 7. | Rings and ideals | 11.1-11.3 HW 2 Due 2/20 Chapter 10 Problems 1.1, 3.1, 3.5, 4.10, 5.5, 7.1, 7.5, M.7 |
| Th 2/20 | 8. | Quotient rings | 11.4-11.5 |
| Tu 2/25 | 9. | Fractions | 11.6-11.7 |
| Th 2/27 | 10. | Maximal ideals | 11.8-11.9 |
| Tu 3/4 | 11. | Prime ideals | HW 3 Due 3/6 Chapter 11 Problems 1.2, 1.8, 2.1, 3.5, 3.12, 5.7, 6.8, 7.4 |
| Th 3/6 | 12. | Unique factorization domains | 12.1-12.2 |
| Tu 3/11 | 13. | Gauss's lemma, factoring integer polynomials | 12.3-12.5 |
| Th 3/13 | 14. | Algebraic integers | 13.1-13.3 HW 4 Due 3/25 Chapter 12 Problems 1.2, 2.1, 2.5, 2.10, 3.2, 4.13, 5.3, M.6 |
| Tu 3/18 | Spring break | ||
| Th 3/20 | Spring break | ||
| Tu 3/25 | 15. | Factoring ideals | 13.4-13.6 |
| Th 3/27 | 16. | Ideal classes and the ideal class group, relationship to binary quadratic forms | 13.7-13.8 |
| Tu 4/1 | 17. | Real quadratic fields, lattices, primes in arithmetic progression | 13.9-13.10 HW 5 Due 4/3 Chapter 13 Problems 3.1, 3.3, 4.1, 5.1, 6.1, 6.3, 9.1, 10.2 |
| Th 4/3 | 18. | Modules, identities | 14.1-14.3 |
| Tu 4/8 | 19. | Diagonalizing integer matrices, generators and relations | 14.4-14.5 |
| Th 4/10 | 20. | Noetherian rings, structure of abelian groups | 14.6-14.7 |
| Tu 4/15 | 21. | Linear operators, rational and Jordan forms | 14.8-14.9 HW 6 Due 4/17 Chapter 14 Problems 1.2, 2.1, 3.3, 4.6, 4.7, 7.4, 8.2, M.6 |
| Th 4/17 | 22. | Alegraic and transcendental extensions of fields | 15.1-15.3 |
| Tu 4/22 | 23. | Irreducible polynomials | 15.4-15.6 |
| Th 4/24 | 24. | Finite fields | 15.7-15.10 HW 7 Due 4/29 Chapter 15 Problems 1.1, 2.2, 3.1, 3.10, 7.13, 8.1, 10.1, M.1 |
| Tu 4/29 | 25. | Symmetric functions, splitting fields | 16.1-16.3 |
| Th 5/1 | 26. | Fixed fields, Galois extensions | 16.4-16.6 |
| Tu 5/6 | 27. | The main theorem of Galois theory | 16.7-16.9 HW 8 Due 5/8 Chapter 16 Problems 1.1, 3.1, 3.2, 6.1, 7.2, 7.10, 10.3, M.5 |
| Th 5/8 | 28. | Kummer extensions, quintic extensions | 16.10-16.12 |
Disability Support Services: If you have a physical, psychological, medical, or learning disability that may affect your course work, please contact Disability Support Services (DSS) office: ECC (Educational Communications Center) Building, room 128, telephone (631) 632-6748/TDD. DSS will determine with you what accommodations are necessary and appropriate. 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 requiring emergency evacuation are encouraged to discuss their needs with their professors and DSS. For procedures and information, go to the following web site http://www.ehs.stonybrook.edu 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 are required to report any suspected instance of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/.
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 Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, and/or inhibits students' ability to learn.