MTH382 Number Theory

Spring 2006

University of Rhode Island

Instructor: Lubos Thoma
Office: Tyler Hall 214
Tel: 874.4451

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:

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.

Grading:   Your grade will be based on your exam scores, final exam score, portfolio, and homework grades.
  homework 20%
  in-class exams 20% each
  portfolio 15%
  final 25%

  1.   Read the book carefully. I chose this book because I believe it gives nice explanations. It is helpful to read sections before we talk about them in class.
  2.   Do all of the homework assigned. If you don't gain experience in doing the problems yourself, it will be hard to remember how to do them on a test. It is helpful to start study groups and work together on homework. I do believe that how well you do in this course will depend on how well you study.
  3.   Attend class to keep current, ask questions, and learn knew topics. Also, attending class allows you to see what is emphasized. Remember the material for the tests will come from what was emphasized.
  4.   Be sure to keep current of all topics. You will need to study a little almost everyday. If you don't understand something, don't let it wait too long because the concepts in this class build, one upon the next. You don't want the ``snowball effect'' to take over.
  5.   You may not understand an idea at first. Give it time to sink in. Sometimes you must go over it several times before it begins to make sense. It is not unusual for someone to be stuck on a particular kind of problem and not understand it in class. You may need to have it explained again, later. Please feel free to ask me to do so outside of class.