Math 627 (Section 600) -- Fall 2006

Theory of Numbers

MWF 3:00-3:50
ZACH 104D

http://www.math.tamu.edu/~map/courses/627-fa06/


Homework


Course Description:


This course will be an introduction to Number Theory from an advanced standpoint. We will study in depth the arithmetic properties of integers, starting with prime factorizations and then investigating implications and generalizations. We will cover the following topics as time permits:
  • unique factorization
  • congruences, Fermat's Little Theorem, and Euler's Theorem
  • primitive roots
  • quadratic residues and quadratic reciprocity
  • Gauss and Jacobi sums
  • cubic and biquadratic reciprocity
  • polynomial equations over finite fields and congruence zeta functions
  • Pell's equation
  • sums of squares

Course Information:


Instructor: Dr. Matthew Papanikolas


Office Hours: Mon. & Wed. 11-12





Office: 321 Milner


Office Phone: 845-1615


E-mail: map@math.tamu.edu





Textbook: A Classical Introduction to Modern Number Theory, 2nd ed., by Kenneth Ireland and Michael Rosen, Springer-Verlag, 1990, ISBN 0-387-97329-X.





Prerequisites: Math 415 (groups, rings, fields, vector spaces); or equivalents





Course Webpage: http://www.math.tamu.edu/~map/courses/627-fa06/





Course Work and Exams: There will be regular homework assignments, as well as a midterm exam and a final exam. Schedules and grading policies are outlined below.

Exam Schedule:


There will be a midterm exam during the semester as well as a cumulative final exam. The dates and times are listed below.


Midterm Exam

Final Exam

Date/Time

Oct. 13 (Fri)
3:00-3:50

Dec. 12 (Tue)
10:30-12:30

Location

ZACH 104D

ZACH 104D

Grading:


Your final grade will be determined by the total number of points obtained on exams and homework. Out of 300 total points, each component contributes to your grade as follows:

Component

Points

Homework

100

Midterm

100

Final

100

Grades will be distributed along the following basis: A 90%-100%, B 80%-89.9%, C 70%-79.9%, D 60%-69.9%, F 0%-59.9%.




Page maintained by Matt Papanikolas, Dept. of Mathematics, Texas A&M University.