AcademicsNumber Theory

Instructor: Matt Ollis, Sci 218, matt@marlboro.edu

Timetable: MTh 1.30 - 2.50pm Sci 217

Course Outline: Number theory is primarily concerned with the properties of and relationships between whole numbers. Topics we will study:

1. Prime numbers

2. Modular arithmetic

3. Sums of squares

4. Pythagorean triples

5. Fermat's Last Theorem

6. Magic squares

7. Continued fractions

8. Approximation of reals by rationals

We will also spend a couple of weeks studying cryptography. In particular, we will look at how the RSA system works. This relies heavily on some of the number theory we will have learnt and is behind almost all modern cryptographic systems.

You will need two books for the course: "A Pathway Into Number Theory" by R.P. Burn and "An Introduction To Number Theory" by H. Stark. Burn's book will lead us to discover and prove for ourselves some of the main results of number theory. Stark's book is more traditional.

Grades: Class participation and attendence 10%. Homework 50%. In-class quizzes 10%. Final exam 30%

Office hours: TBA

Course material:

Template for proof by induction