This course will be a gentle introduction to the basic concepts of number theory: prime numbers, factorization, and congruences.  Using these concepts we will be able to investigate such diverse topics as 2,000-year-old word problems, "casting out nines" to check arithmetical calculations, perpetual calendars, and the Pythagorean Theorem.  A highlight of the course will be a thorough discussion of the RSA (public key) cryptography system, which is still widely used by government and industry.  By the end of the course, students will be able to understand what the RSA system is, how it works, and why it is so difficult to crack.

Use of the Web

Every enrolled student will be given an account on the Mathematics department undergraduate computer lab located in the MSRC building.  The computer lab is open 24 hours a day.  As part of your account, you will have a quota of 100 pages of free printouts.  You may also access the course web page on any public terminal at UBC, or via your own internet connection.

All documents will be posted in PDF format and can be read with the free Acrobat reader.  This software is already installed on the computers in the Math lab.  You may also download the free Acrobat reader at no cost.

Evaluation

• Final exam : 50 percent
• Midterm exams (in class) : October 5th, November 9th : 40 percent
• Homework: 10 percent

Homework will be assigned on Fridays and due the following Friday in class. Late homework will not be accepted. Students are allowed to consult one another concerning the homework problems, but your submitted solutions must be written by you in your own words. If two students submit virtually identical answers to a question, both can be found guilty of plagiarism. The lowest assignment grade will be dropped.

Course syllabus