MTH382 Number Theory

### University of Rhode Island

Instructor: Lubos Thoma
Office: Tyler Hall 214
Tel: 874.4451
Email: thoma@math.uri.edu

Class Schedule: TuTh 9.30am--10.45am, Bliss Hall 206
Office hours: M 2.00--3.30pm, TuTh 11.00am - 12.30pm, and by appointment

Class log    contains worksheets, handouts, homework, detailed guide to the portfolio, ....

Maple worksheet containing programs and examples for the Pollard's Rho factorization method:     pollard-rho.mw

Suggested problems                                 Printable syllabus:   postscript     pdf

Important dates:
Exam 1:     Tuesday February 28, in class.
Exam 2:     Thursday April 13, in class.
Portfolio due:     Tuesday April 25.
Final Exam:     Thurs May 4, 8:00 am - 11:00 am       Spring 2006 final exam schedule

Description:   The sections to be covered are listed on the class schedule. We will cover roughly one section per lecture. However, some sections will require more time.
Topics to be covered include introductory number theory: divisibility, congruences, prime numbers, multiplicative functions, primitive roots. Number theory has a wide variety of applications. We will go over some of htem in the class: factoring integers, cryptography, random number generators.
There are a couple of goals of this class: to introduce you to numebr theory, to expose you and to make you more familiar with proofs.

Textbook:   K.H. Rosen, Elementary Number Theory, 5th edition, Addison Wesley.

Exams:   Exams will draw from material covered in class, that is, any theorems, proofs, example, or homework problem that we cover in class is a possible material for the tests. So, the best way to prepare for the exams will be to start with your class notes. There will be two in-class exams and a comprehensive final. Dates see above.

Homework:   You learn more by doing, than by watching others give demonstrations. Therefore, homework is very important. When you sit down to do your homework is when you realize whether or not you understood the material from class. You also learn by practice, so do as many of the examples assigned as possible. I will assign homework on a regular basis. Your solutions should be written up with your best effort at explanation and should be neat. These problems will challenge your problem solving abilities. You may work in groups provided you follow the following guidelines: each person must write up each problem in their own words, no copying. Whenever you would like to discuss the class material, have any questions or are stuck on the homework, please visit me in my office either during my office hours or by appointment.

Portfolio:   The purpose of the project is that you learn to present your solutions. The portfolio will be distributed in class and it is due Tuesday April 24, 2006. However, feel free to show me a draft version earlier for comments.