| Fall 2025 MAT 311: Number theory | ||
| Schedule | MW 2-3:20pm Physics P-130 | |
| Instructor | Robert Hough | |
| Office hours | F 9-11am in Math Tower 4-107, Thurs 7-8pm in Math Learning Center | |
| Grader | Yichen Cheng | |
| Description | Congruences, quadratic residues, quadratic forms, continued fractions, Diophantine equations, number- theoretical functions, and properties of prime numbers. | |
| Textbook | Niven, Zuckerman and Montgomery. Introduction to the theory of numbers. John Wiley and Sons (1991). | |
| Homework | Weekly problem sets will be assigned, and collected in class on Monday. 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: 30%, Midterm: 30%, Final: 40%. | |
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)
| Mon 8/25 | 1. | Divisibility, primes, the binomial theorem | 1.1-1.4 |
| Wed 8/27 | 2. | Congruences, Chinese remainder theorem | 2.1-2.3 |
| Mon 9/1 | No class - Labor day | ||
| Wed 9/3 | 3. | Cryptography | 2.4-2.7 |
| Mon 9/6 | 4. | Primitive roots, groups, rings and fields | 2.8-2.11 |
| Wed 9/10 | 5. | Quadratic reciprocity | 3.1-3.3 |
| Mon 9/15 | 6. | Binary quadratic forms, reduction theory | 3.4-3.7 |
| Wed 9/17 | 7. | Arithmetic functions, Mobius inversion | 4.1-4.3 |
| Mon 9/22 | 8. | Recurrence sequences, combinatorial number theory | 4.4-4.5 A4 |
| Wed 9/24 | 9. | Solutions of integer linear systems | 5.1-5.3 |
| Mon 9/29 | 10. | Ternary quadratic forms | 5.4-5.6 |
| Wed 10/1 | 11. | Elliptic curves | 5.7-5.9 |
| Mon 10/6 | 12. | Farey fractions, rational approximation | 6.1-6.2 |
| Wed 10/8 | Midterm | ||
| Mon 10/13 | No class - Fall Break | ||
| Wed 10/15 | 13. | Geometry of numbers | 6.3-6.4 |
| Mon 10/20 | 14. | Continued fractions | 7.1-7.3 |
| Wed 10/22 | 15. | Best approximation of irrational numbers | 7.4-7.6 |
| Mon 10/27 | 16. | Pell's equation | 7.7-7.9 |
| Wed 10/29 | 17. | Dirichlet series | 8.1-8.2, A3 |
| Mon 11/3 | 18. | Primes in arithmetic progression | 8.3-8.4 |
| Wed 11/5 | 19. | Algebraic numbers | 9.1-9.3, A1 |
| Mon 11/10 | 20. | Algebraic integers | 9.4-9.6 |
| Wed 11/12 | 21. | Factorization into primes | 9.7-9.8 |
| Mon 11/17 | 22. | Cubic case of Fermat's last theorem | 9.9-9.10 |
| Wed 11/19 | 23. | Partitions, formal power series | 10.1-10.3, A2 |
| Mon 11/24 | 24. | Euler and Jacobi formulas | 10.4-10.6 |
| Wed 11/26 | No class - Thanksgiving | ||
| Mon 12/1 | 25. | The Riemann zeta function | |
| Wed 12/3 | 26. | The explicit formula and zero free region | |
| Mon 12/8 | 27. | The Prime Number Theorem |
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.