Mathematics 128S, Spring 2012

Number Theory

Instructor: Lenny Ng
Meeting time: Tuesdays, Thursdays 1:15-2:30
Location: Physics 227
Office hours: Tuesdays 2:30-3:30, Wednesdays 1-2, and by appointment

Course Syllabus

Material for this course will be posted on Sakai.

Course synopsis:

This course is an introduction to some of the main questions and ideas of classical number theory, with a focus on individual exploration and personal discovery. We'll begin by investigating the question "What is a number?", and see how this question led to some brilliant and celebrated breakthroughs by mathematicians such as Euler, Fermat, and Gauss. This will culminate in an examination of modern-day cryptography: how number theory allows transactions over the internet, and many more things, to be made secretly and securely.

You are not assumed to have any technical mathematical knowledge beyond the basic operations of arithmetic, only a desire to understand for yourself the surprisingly mysterious properties of the natural numbers (1, 2, 3, ...). Some previous familiarity with making precise mathematical statements and working with proofs will be very helpful, but is not absolutely necessary.

The course is roughly divided into two parts. The in-class "seminar" part is a series of lectures where we explore properties of the natural numbers. This will cover the foundations of number theory as well as modern applications to cryptography. The other part is your personal exploration of some topic in number theory that branches off from the lectures, and culminates in a mathematical paper where you explain the topic in detail, as well as a 30-minute presentation to your colleagues. You'll have ample help along the way.

Public service announcement:

If you would like to take this course and have not previously taken Math 104, please see me so that I can make sure you're ready for the course.


No required textbook. Elementary Number Theory and Its Applications, 6th edition, by Kenneth H. Rosen is highly recommended. I encourage you to get this book; it will serve as a useful reference to complement the lectures.