Announcement: Homework #6 is due on Wednesday, December 3 at 3 PM. You can give your solutions to the staff in the mathematics office (MATH 121) for them to put in my mailbox, if you can't find me in person.
Announcement: For the "final exam" component of the course, students will prepare a 40-minute presentation on a topic related to what we have learned in the course. This presentation will be evaluated primarily by its content, though you should strive to make it as accessible as possible. Students should come talk to me about their proposed topics, as I would like each student to learn something new for their presentation.
All talks will be given in the Math Annex, room MATX 1118. The schedule is:
Description: The first few weeks will be spent quickly covering the foundations of elementary number theory: divisibility, congruences, prime numbers, and so on, some of which might already
be familiar to you. Once we have this foundation, many different subjects will be open to us. Topics I intend to cover include: finding roots of polynomial
congruences; the Quadratic Reciprocity Theorem; running times of number-theoretic algorithms; RSA cryptography; writing numbers as sums of
squares; Farey fractions and continued
fractions; arithmetic functions and Dirichlet series; prime number estimates (the last couple if time permits). I will also indicate the connections
between these topics and other advanced areas of number theory (algebraic
number theory, analytic number theory, diophantine approximation, etc.).
This course will not require any particular background in number theory. What is required is “mathematical sophistication”, which certainly includes being able to understand and write proofs. I anticipate that the course will proceed at a fairly rapid pace.
Evaluation: The course mark will be based on six homework assignments (60% of the final mark) and a final presentation (40% of the final mark). The homework assignments will be due every other Friday beginning September 19. Students are allowed to consult one another concerning the homework problems, but your submitted solutions must be written by you in your own words.