Math 4351 Number Theory & Cryptography Spring 2022

Timings

• Lecture: 2pm-3pm MWF, Cupples II L015

• Office hours: 3-4pm MF, Zoom on M (see Canvas for link) & Cupples II L015 on F

Resources

We'll generally follow these notes from Prof. Matt Kerr. Lecture notes will also be posted online after each class.

Here is a nice discussion (for a different class) of some methods and philosophy for how to approach proofs.

Here is an online calculator for addition and integral scalar multiplication on elliptic curves in characteristic zero and p.

Assessment

• Homework - roughly every two weeks due at 11:59pm CT on Sundays (30%)

• Self-reflections - roughly every two weeks due at 11:59pm CT on Sundays (10%)

• Midterm - take-home exam 8am 3/8- 8am 3/9; see resurrection final below (30%)

• Final - take-home exam 9am 5/9 - 9am 5/10; see resurrection final below (30%)

Piazza bonus points: Each time you post a (mathematical!) question or answer on Piazza, you will receive 1 bonus point. These count as 1 point towards your overall homework score up to a maximum of 10 points. For example, if you dropped 15 points on homework throughout the semester and asked 5 questions on Piazza, your score for homework would be as if you only dropped 10 points. The deadline for Piazza points is 11:59pm the day before the final.

Dropped scores: I will drop the lowest homework score and allow for two missed self-reflections. Because of this and the Piazza bonus points I don't allow for makeups under any circumstances.

Resurrection final: We will use a resurrection final in this course. This means that we will calculate two grades: G1 = grade calculated as above, and G2 = grade calculated with midterm counting 0% and final exam counting 60%. Your final grade will be max(G1, G2). Because of this I don't allow for makeups under any circumstances.

Virtual testing: I will offer a virtual option for the final in circumstances such as quarantine due to sickness or potential exposure to covid-19.

Grading scale: I will use a 'European' grading scale throughout the course, where 70% is an A, 60% is a B+, 50% is a B, 40% is a C. There are no 'minus' grades in this course, and I will award an A+ for scores exceeding 90%. The consequence of this is that exams will require more creative thought and that many students might not have time to answer all questions.

Integrity

• Attempting to cheat in this course is unacceptable and will be strongly penalised. A first offense will be penalised with a zero grade on the relevant piece of assessment. A second offense will be penalised with an immediate fail grade.

• Collaboration is permitted (actually encouraged!) on homework assignments, however each student must write up solutions in their own words. Please write the names of any other students you have collaborated with at the top of each assignment. Significant similarities between submissions from different students that fail to mention any collaboration counts as an act of cheating and will be penalised as such.

Syllabus