Fall 2020 MAT 311: Number theory
ScheduleMW 2:40-4:00pm Physics P-113
InstructorRobert Hough
Office hoursF 9-11am in Math Tower 4-118, W 6-7pm in Math Learning Center
GraderAjmain 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
TextbookNiven, 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.
GradingHomework: 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 8/241. Divisibility, primes, the binomial theorem 1.1-1.4, 2.1-2.3
Wed 8/262. Congruences, Chinese remainder theorem, SlidesHW 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 8/313. Cryptography, Slides 2.4-2.11
Wed 9/24. 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 9/95. Quadratic reciprocity, Boards HW Due 9/14: p.135 #8, 11, 24, p.140 #1, 7, 24, p.147 #1, 5, 17
Mon 9/146. Binary quadratic forms, reduction theory, Boards3.4-3.7, 4.1-4.3
Wed 9/167. Unique factorization in the Gaussian integers, BoardsHW Due 9/21: p.154 #4, 5, p.162 #2, 13, 15, 16, p.169 #2, 12, p.176 #1, 4
Mon 9/218. The class number formula, Boards4.4-4.5
Wed 9/23 Midterm 1 Practice Midterm, Solutions Midterm 1 solutions
Mon 9/289. Arithmetic functions, Mobius inversion, Boards5.1-5.6
Wed 9/3010. Linear Diophantine equations, Ternary quadratic forms, BoardsHW 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 10/511. Diophantine Equations, Boards 5.7-5.9, 6.1-6.2
Wed 10/712. Elliptic curves, BoardsHW 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 10/1213. Farey fractions, rational approximation BoardsHW Due 10/12: 6.3-6.4, 7.1-7.3
Wed 10/1414. Geometry of numbers BoardsHW Due 10/19: p.278 #3, 10, p.287 #3, 6, p.300 #1, 4, 5, 9, p.307 #1, 2, 5
Mon 10/1915.Euclidean algorithm, continued fractions, Boards7.4-7.9
Wed 10/2116. Irrational numbers, best approximation, BoardsHW Due 10/28: p.311 #3, 8, 9, p.319 #7, 12, 13, 14, p.327 #1, p.329 #1, p.333 #3
Mon 10/2617. Pell's equation, Boards8.1-8.2
Wed 10/28 Midterm 2 Practice Midterm 2, Solutions, Midterm 2 solutionsHW Due 11/2: p.336 #1, 2, p.340 #3, 4, p.344 #4, 5, p.351 #1, p.356 #1, 2, 6
Mon 11/218. Prime number theory Boards8.3-8.4, 9.1-9.3
Wed 11/419. Dirichlet series BoardsHW Due 11/9: p.373 #1, 2, 6, 19, 20, p.387 #4, 6, 7, 23, 24
Mon 11/920. Primes in arithmetic progression, Slides9.4-9.8
Wed 11/1121. Algebraic numbers BoardsHW 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 11/1622. Factorization into prime ideals Boards9.9-9.10, 10.1-10.3
Wed 11/1823. Cubic case of Fermat's last theorem BoardsHW 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 11/3024. Partitions, formal power series10.4-10.6, 11.1-11.2
Wed 12/225. Euler's formula, bounds on the partition numberHW 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 12/726. Asymptotic density
Final Exam: Due Wednesday December 9, by Midnight. Files should be submitted on Blackboard. The exam.

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