2018 Fall Course Syllabus - Mathematics 4096.001
Course: Mathematics 4096.001.
Course Title: Senior Problem Solving.
Time: TuTh 3:30-4:50.
Place: Wachman Hall 206.
Instructor: Matthew Stover.
Instructor Office: Wachman Hall 1024.
Instructor Email: mstover@temple.edu
Instructor Phone: (215) 204-6433.
Office Hours: TBD.
Prerequisites: Minimum grade of C- in Math 3096 or Math 3098. Minimum grade of C- or concurrent registration in Math 3138, Math 3142, or Math 3044.
Textbook: Rational Points on Elliptic Curves, second edition, by Joseph Silverman and John Tate. This is available as a free ebook download from the Temple Library website. The book will also be the source of several of the homework exercises.
Course Goals: The majority of classroom time will be inquiry-based learning. This course has no textbook, and there are virtually no lectures. The goal is to learn mathematics by doing mathematics rather than listening to a lecture with the pre-packaged correct answer. More specifically, the point is not only to know what is true, but to discover why. Students will learn the material the way a research mathematician solves a problem: through experimentation, trial and error, discussion with their peers, and a lot of hard work. Consequently, each student will essentially write their own textbook on elliptic curve cryptography over the course of the semester. Major goals of the course include developing written and oral communication skills, sharpening the students' mathematical reasoning, and honing their problem-solving skills. Specifically, students will spend class time working together in groups of 3 or 4 on a worksheet based upon a mathematical or cryptological idea. Worksheets will include definitions, exercises, and mathematical statements (Lemmas and Theorems). As students solve each problem and come to understand why each mathematical statement is true, they will present their solutions to the class in a style similar to that of a mathematical research seminar; the final answer is rarely as important as the process used to discover that solution. Students are forbidden from working on the current worksheet outside of class! This defeats much of the purpose of inquiry-based learning. There will also be a handful of classes spent in the computer lab working in groups on experimentation.
Topics Covered: This course will study the arithmetic of elliptic curves, with the ultimate goal of understanding elliptic curve public key cryptography. As motivation for studying elliptic curve cryptography, we will also discuss RSA and ElGamal encryption.
Course Grading: Final textbook: 40% Homework: 15% Class participation: 30% Presentation: 15%.
Exam Dates: There are no exams in this course.
Attendance Policy: Participation is fundamental in this course, hence attendance is mandatory. Every two unexcused absences reduces the final grade one letter grade. That is, the second unexcused absence reduces an A- to a B-, five will change a B+ to a D+, etc. Absences will only be excused by documentation from a doctor or other health professional, Student Health Services, other University office, etc.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
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.
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar 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)
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)