| Fall 2020 MAT 311: Number theory | ||
| Schedule | MW 2:40-4:00pm Physics P-113 | |
| Instructor | Robert Hough | |
| Office hours | F 9-11am in Math Tower 4-118, W 6-7pm in Math Learning Center | |
| Grader | Ajmain Yamin | |
| Description | Congruences, quadratic residues, quadratic forms, continued fractions, Diophantine equations, number- theoretical functions, and properties of prime numbers. | |
| Prerequisites | C or higher in MAT 312 or 313 or 318; C or higher in MAT 200 or permission of instructor | |
| 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: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%. | |
Face mask policy:
If a student does not wear a face mask, please follow these steps:
Students should be aware that a face mask is required while in the classroom. If a student does
not comply, the student will be asked to leave the classroom.
If the student does not comply or leave the classroom, we will end the class and the students
will be reported to the Office of Student Conduct and Community Standards at communitystandards@stonybrook.edu.
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.
Face mask accommodations, modifications or exemptions: The Student Accessibility Support Center (SASC) works with students who may require academic accommodations. If a student is unable to wear a mask for health reasons, the student should contact SASC at sasc@stonybrook.edu. SASC will work with the student to help identify arrangements to complete in-person courses in an alternate format. If, however, there is an in-person class that cannot be accommodated in an alternate format, a student may be approved by the Medical Director of Student Health Services to wear a modified face mask or no face covering. In this situation, SASC will communicate this information to the faculty member. Approved students will also be provided with a written exemption from the Medical Director of Student Health Services that indicates any modifications or exceptions, which they must carry with them to show faculty if requested. Please note that medical exemptions are rare and are based solely on medical necessity. If a student is exempt from the face mask policy, please consider how to seat students to ensure proper social distancing within a given instructional setting. If you have questions regarding accommodations, please email sasc@stonybrook.edu. For health related concerns in the classroom, please contact Dr. Rachel Bergeson, Medical Director, at rachel.bergeson@stonybrook.edu.
Syllabus/schedule (subject to change)
| Mon 8/24 | 1. | Divisibility, primes, the binomial theorem | 1.1-1.4, 2.1-2.3 |
| Wed 8/26 | 2. | Congruences, Chinese remainder theorem, Slides | HW Due 8/31: p.17 #2, 7, 46, p.29 #5, 37, p.40 #1, 3, 10, p.56 #15, 18, 47, 57, p.62 #5, p.71 #3, 19, 21 |
| Mon 8/31 | 3. | Cryptography, Slides | 2.4-2.11 |
| Wed 9/2 | 4. | Primitive roots, groups, rings and field, Boards | HW Due 9/9: p.82 #4, 13, p.91 #3, 9, p.96 #1, 4, p.106 #1, 22, 32, p.114 #2, 3, p.119 #2, p.126 #20, 22, 23 |
| Mon 9/7 | No class - Labor day | 3.1-3.3 | |
| Wed 9/9 | 5. | Quadratic reciprocity, Boards | HW Due 9/14: p.135 #8, 11, 24, p.140 #1, 7, 24, p.147 #1, 5, 17 |
| Mon 9/14 | 6. | Binary quadratic forms, reduction theory, Boards | 3.4-3.7, 4.1-4.3 |
| Wed 9/16 | 7. | Unique factorization in the Gaussian integers, Boards | HW Due 9/21: p.154 #4, 5, p.162 #2, 13, 15, 16, p.169 #2, 12, p.176 #1, 4 |
| Mon 9/21 | 8. | The class number formula, Boards | 4.4-4.5 |
| Wed 9/23 | Midterm 1 Practice Midterm, Solutions | Midterm 1 solutions | |
| Mon 9/28 | 9. | Arithmetic functions, Mobius inversion, Boards | 5.1-5.6 |
| Wed 9/30 | 10. | Linear Diophantine equations, Ternary quadratic forms, Boards | HW Due 10/5: p.184 #15, 20, p.191 #20, p.195 #7, 19, 24, 28, p.204 #3, 6, 7, 15, 25, p.210 #2, 4, 9, 10, 14 |
| Mon 10/5 | 11. | Diophantine Equations, Boards | 5.7-5.9, 6.1-6.2 |
| Wed 10/7 | 12. | Elliptic curves, Boards | HW Due 10/12: p.218 #2, 5, p.229 #1, 6, 10, p.233 #10, 14, p.239 #14, 15, p.248 #1, 3, p.260 #1, 7, 14 |
| Mon 10/12 | 13. | Farey fractions, rational approximation Boards | HW Due 10/12: 6.3-6.4, 7.1-7.3 |
| Wed 10/14 | 14. | Geometry of numbers Boards | HW Due 10/19: p.278 #3, 10, p.287 #3, 6, p.300 #1, 4, 5, 9, p.307 #1, 2, 5 |
| Mon 10/19 | 15. | Euclidean algorithm, continued fractions, Boards | 7.4-7.9 |
| Wed 10/21 | 16. | Irrational numbers, best approximation, Boards | HW Due 10/28: p.311 #3, 8, 9, p.319 #7, 12, 13, 14, p.327 #1, p.329 #1, p.333 #3 |
| Mon 10/26 | 17. | Pell's equation, Boards | 8.1-8.2 |
| Wed 10/28 | Midterm 2 Practice Midterm 2, Solutions, Midterm 2 solutions | HW Due 11/2: p.336 #1, 2, p.340 #3, 4, p.344 #4, 5, p.351 #1, p.356 #1, 2, 6 | |
| Mon 11/2 | 18. | Prime number theory Boards | 8.3-8.4, 9.1-9.3 |
| Wed 11/4 | 19. | Dirichlet series Boards | HW Due 11/9: p.373 #1, 2, 6, 19, 20, p.387 #4, 6, 7, 23, 24 |
| Mon 11/9 | 20. | Primes in arithmetic progression, Slides | 9.4-9.8 |
| Wed 11/11 | 21. | Algebraic numbers Boards | HW Due 11/16: p.398 #3, 5, 16, p.405 #5, 6, p.414 #5, 7, 9, p.419 #1, 2, 3, p.423 #2, 3 |
| Mon 11/16 | 22. | Factorization into prime ideals Boards | 9.9-9.10, 10.1-10.3 |
| Wed 11/18 | 23. | Cubic case of Fermat's last theorem Boards | HW Due 11/30: p.425 #2, 3, p.427 #1, 2, 3, 4, 5, p.429 #1, p.431 #2, 3, 5, p.432 #1, 4 |
| Mon 11/23 | No class - Thanksgiving | ||
| Wed 11/25 | No class - Thanksgiving | ||
| Mon 11/30 | 24. | Partitions, formal power series | 10.4-10.6, 11.1-11.2 |
| Wed 12/2 | 25. | Euler's formula, bounds on the partition number | HW Due 12/7 (optional): p.440 #1, 2, 6, p.445 #1, p.447 #1, p.450 #1, 2, p.457 #1, 2, 3 |
| Mon 12/7 | 26. | Asymptotic density |
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.
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