2022 Fall Course Syllabus - Mathematics 3003.001

Course: Mathematics 3003.001.

Course Title: Theory of Numbers.

Credits: 3.

How this course will be taught: In person (hopefully).

Time: Monday-Wed-Friday, 2-2:50pm.

Place: Wachman 408.

Instructor: Vasily Dolgushev.

Instructor Office: Wachman 530.

Instructor Email: vasily.dolgushev@temple.edu

Instructor Phone: 215-204-7287.

Office Hours: Wednesdays 3-4:30pm, Fridays, 10:30am-12pm and by appointment.

Prerequisites: Math 2111 (Basic Concepts of Math) with a grade of C or higher. You need to be comfortable with writing simple proofs.

Course Materials: Elementary Number Theory and its applications (6th Edition), by Kenneth H. Rosen.

Course Goals: To master key concepts of elementary number theory and work with some of its applications.

Topics Covered: Topics of the course include divisibility properties of integers, the fundamental theorem of arithmetic, distribution of primes, special congruences, multiplicative functions, primitive roots, quadratic residues, quadratic reciprocity, simple Diophantine equations and applications to cryptography. If time will permit, we will talk about continued fractions, the Gaussian integers and p-adic numbers.

Course Grading: Quizzes: 30%, Midterm: 30%, Presentations 10%, Comprehensive Final Exam: 30%.

Exam Dates: Midterm: October 12, Wednesday, time/place TBD, Final Exam: Monday, December 12, 1-3pm in Wachman 408.

Attendance Policy: I am going to monitor the attendance.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Canvas page: I will use the Canvas page of this course to post homework assignments, announcements and additional materials.

Homework: Homework assignments (with the due dates) will be posted on the Canvas page of this course. I will ask you to scan your homework and upload it to Canvas. If an assignment contains programming exercises, you may also need to upload to Canvas your Magma script together with a "print-out" of your Magma session. Feedback about your solutions of selected homework exercises (as well as your work with Magma) will be given.

Quizzes: Typically, on Fridays, during the last 25 minutes of the meeting, we will have a quiz. There will be occasional "surprise Fridays" without quizzes. I do not plan to announce "surprise Fridays" in advance. So please be prepared for a quiz every time we have a meeting on Friday. When calculating the total quiz grade, the quiz with the lowest score will be dropped.

Presentations: Each student should prepare a 20 minute presentation on a topic of her/his choice. We will try to have your presentations during the last 4 meetings of the course. (You need to be ready to answer questions after your presentation.) Possible topics for presentations include: continued fractions, nonlinear Diophantine equations, the Gaussian integers, p-adic numbers, elliptic curve cryptography. If you like, you may choose a topic of exploratory nature. For example, you may want to explore a nonabelian version of the Diffie-Hellman key exchange and present the results of your exploration together with the background. Another possible topic may involve exploration of open questions of number theory using Magma. Of course, you may also try to turn any of the above topics into a topic of exploratory nature. Please talk to me about a possible topic of your presentation around mid-October. Several students may choose the same topic for a presentation. In this case, I encourage a collaboration and a coordination of your presentations on this topic. Regardless of the nature of your topic, please start working on the material of your topic on November 1 or earlier. The grade for your presentation will depend on the clarity of the presentation and the level at which you mastered the relevant material.

Programming Exercises/Magma: For our programming exercises, we will use the computer algebra system Magma http://magma.maths.usyd.edu.au/magma/handbook/. For Temple students, Magma is available through the high performance computing (HPC) server "compute". If you do not yet have an account at this server, please request one at https://www.hpc.temple.edu/ For working on your Magma scripts on the server "compute", you may need the openly available client FileZilla https://filezilla-project.org/.

Additional Comments: Please justify your steps in the work on your homework assignments, quizzes and tests. Also please write legibly! Your score will be reduced for not writing legibly and for not justifying your steps.

Letter Grades: 93-100 A, 90-92 A-, 87-89 B+, 83-86 B, 80-82 B-, 77-79 C+, 73-76 C, 70-72 C-, 50-69 D, 0-49 F.

Make Up Policy: No make ups for missed tests or exams will be given except in cases of documented emergencies. If such an emergency occurs, students must contact their instructor as soon as possible. No make ups will be given after graded tests are returned. There will be no make ups for missed quizzes. You are already insured by the policy of dropping the lowest quiz score.

Exam Security Policy: Under no circumstances is the use of personal electronic devices such as phones, computers, smart watches, etc., allowed during exams. All such items must be stowed away and out of sight for the duration of the exam. Any student found with such a device during an exam will not be allowed to complete the test, will receive a score of ZERO for the test, and will be reported to the Student Code of Conduct Board. In addition, under no circumstances, will students be allowed to bring in any kind of papers for use during the exam. Should a student need extra paper during a test, the proctor will provide it. Any student found using papers that they themselves brought into the exam will not be allowed to complete the test, will receive a score of ZERO for the test, and will be reported to the Student Code of Conduct Board.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.