Math 575: Introduction to Number Theory

Fall 2007, Section 1

Time:

MWF 2:00 p.m- 3:00 pm.

Place:

East Hall 2866

Instructor:

Jeffrey Lagarias, 3086 East Hall, 763-1186, lagarias@umich.edu

Office hours:

Monday/Friday at 11am-noon; Friday 3pm-4pm in office, 3086 East Hall
(Or by appointment: call or email me)

Course homepage: http://www.math.lsa.umich.edu/~lagarias/ Public/html/m575fa07.html

Text (required): I. Niven, H. S. Zuckerman and H. L. Montgomery,
An Introduction to the Theory of Numbers, 5th edition, John Wiley & Sons, 1991. [Consider purchasing at half.com]
Supplements and Errata to textbook

Prerequisites: Basic understanding of groups, rings, fields (level of Math 412); ability to write a proof (Math 451).

From departmental course description: Number theory has long been admired for its beauty and elegance,
and for its rich legacy of fundamental unsolved problems in mathematics.
It has recently turned out to have many applications in coding theory and cryptography.

This is a first course in number theory. Topics covered include divisibility and prime numbers, congruences,
quadratic reciprocity, quadratic forms, arithmetic functions and Diophantine equations.

Students should have some experience writing proofs (at the level of Math 451). Proofs are emphasized, but they are often pleasantly short.

Grades: These will be based on problem sets, two midterm exams, and a final exam. The first midterm is in class, closed book. Weighting of scores: Homework 60%; Midterms 10% each; Final exam 20%.
Your lowest homework set score will be dropped.

Homework: There will be approximately 9 problem sets. The first problem set will be due on Friday, Sept. 14.

Collaboration on the homework is permitted, but each person is responsible for writing up her/his own solutions.

Exams: are closed book, closed notebook.

The two midterm exams will be held in class. No makeup exams will be given.

The final exam will be take-home (handed out Wed. Dec. 5, due in class Mon. Dec. 10.)

Schedule:

Here is a current

  • Syllabus

    • Homework Assignments:

      Homework 1 (due Friday, Sept. 14 )

      Homework 2 (due Monday, Sept. 24 )

      Homework 2 (bonus) (due Monday, Sept. 24 )

      Homework 3 (due Friday October 5 )

      Homework 4 (due Friday October 19 )

      Homework 5 (due Wednesday October 31 )

      Homework 6 (due Wednesday November 9 )

      Homework 7 (due Wednesday November 28 )

      Homework 8 (due Wednesday December 5 )