MTH 382 Number Theory Spring 2008

Department of Mathematics, University of Rhode Island


Instructor Orlando Merino,, 874-4442, Tyler Hall 222
Meets MWF 11:00 a.m., Tyler Hall room 106
Text Elementary Number Theory and its applications, by Kenneth H. Rosen, 5th Edition, Pearson/Addison Wesley, ISBN 0-321-23707-2
Prerequisites MTH 307 or permission of the instructor.
Topics We will study selected sections from the following chapters: 1. The Integers (1.3, 1.5) 3. Primes and GCDs (3.1-3.7) 4. Congruences (4.1-4.6) 5. Applications of Congruences (5.1-5.5) 6. Some Special Congruences (6.1,6.3) 7. Multiplicative Functions (7.1,7.3) 8. Cryptology (8.1,8.3,8.4)
Evaluation Final Exam (30%), Midterm Exam (25%), Portfolio (20%), Assignments (25%)
About the Course The course gives an introduction to elementary number theory, which is the study of properties of the integers that can be proved using only elementary techniques. You will do problem solving including proofs and also numerical exploration using Maple. Written communication of mathematics is an important part of this course and will be evaluated with a portfolio.
About the Portfolio The portfolio consists of solutions to a list of problems which are selected by the instructor from the list of problems assigned as homework. The purpose of the portfolio is to give the student an opportunity to practice formal written communication in mathematics. It should demonstrate a student's ability to solve problems, communicate mathematics, and write mathematics. The portfolio should:
  • Be typed in a word processor.
  • Have a title page containing the text "Number Theory MTH 322 Portfolio", date, name of instructor, name of student, and an abstract (which is a paragraph describing what is to be found in the document).
  • Have a paragraph that proceeds each mathematical proof or solution and that contains some information about the result, such as an explanation on how it fits in the chapter or topic, a historical reference, or any other comment you may deem appropriate.
  • Have correct solutions or proofs, complete and without unnecessary details.
  • Have correct English.
  • Have only one author. No collaborative work is allowed.
Links (Links in web site of the text)
Additional Number Theory Links 1
Additional Number Theory Links 2
On assignments Assignments will be announced in class. Students may work individually or in group, but each student must submit his or her own solution.