Number Theory and Cryptography
Mathematics V3020: Fall 2001

Professor: Rachel Pries, MW 10:35-11:50, 520 Mathematics.

Detailed information on homework, exams, and final projects

Text: A Friendly Introduction to Number Theory (Second Edition), Joseph Silverman  Publisher Prentice Hall. Please buy the book at Labyrinth Bookstore which is located at 536 West 112th St or use the copies on reserve in the library. Also on reserve is a book by Kumanduri/Romero which has more information on cryptography.

Course Description: The main topic of this class is the beautiful and accessible subject of Number Theory. We will investigate questions and discover patterns about integers which have fascinated people for centuries. We will learn about the applications of Number Theory to cryptography. Some topics are: divisibility; history of cryptography; units; primes; public key ciphers; primitive roots; and quadratic reciprocity.

Course Philosophy: One goal for this course is for everyone to be actively involved and to explore material through experimentation. Another is to develop skill at writing proofs. The class has no formal prerequisites but is geared towards people with some college math experience who are willing to work hard on the material.

Examinations: There will be a midterm given in class on Monday, October 22nd.
There will be a three-hour final examination given Monday, Dec. 17th, 9 am- 12 noon.
There are no makeups for missed exams, regardless of the reason for absence. You must take the final examination at this time scheduled by the university; no final exams will be given earlier. If you have two final examinations scheduled at the same time, it is the responsibility of the other department to provide an alternate exam. Examinations will not be rescheduled because of travel arrangements. It is your responsibility to schedule travel appropriately.

Grading: The course grades will be computed as follows.
40% Homework and Class Participation; 25% Midterm; 35% Final.

Homework: Homework is the most important part of this class. It should demonstrate your knowledge of the material, your investigation of open ended questions, and your skill at writing proofs. Homework is due every Wednesday at 10:30. Homework must be neat, legible, and stapled in order to receive credit. You may hand in the homework either in class or into my mailbox. Late homework will be given a score of no more than 50%. The lowest homework score will be dropped. Both independent and group work is encouraged.

Help: Help is available if you have trouble with homework or lecture material. If you are unable to attend my office hours, go to the Mathematics Help Room  (406 Mathematics). This room is always staffed by at least one mathematics professor or graduate student Monday through Friday during business hours. You may drop by whenever the Help Room is open; no appointment is necessary.

Method of Study: Your work on every topic should include the following:
  1. Reading the book.   2. Contributing to class.   3. Searching for data.   4. Discussing material with others.   5. Creating conjectures.   6. Proving statements.   7. Asking new questions.

Detailed information on homework, exams, and final projects