Syllabus for Theory of Numbers (Math 453, M13). Spring, 2007.

Professor: Scott Ahlgren
Email: ahlgren@math.uiuc.edu
Phone: 244-1738
Office: 302 Altgeld Hall

Number Theory is known as the ``Queen of Mathematics,'' as it is one of the most beautiful areas in all of mathematics. The subject is famous for vast numbers of elegant problems which are simple to state. Some of these have simple solutions which have been known for thousands of years, while others have frustrated the attempts of the best thinkers for generations. Very recently, there have been important practical applications of Number Theory (for example, in cryptography).

Text. Elementary Number Theory, by James Strayer. The text will be substantially supplemented with class notes.

Webpage. This syllabus and other course material can be found on the course webpage: http://www.math.uiuc.edu/~ahlgren/math453/math453.html

Classes. Tuesday, Thursday, 9-10:20 am, 341 Altgeld Hall. You should be present at each class meeting.

Grading. Your course grade will be computed using the following system.

Two midterm exams in class. Each exam is 1/6 of final grade.
Final Exam: 1/3 of final grade.
Homework (and other work): 1/3 of final grade.

Exams. The two midterm exams will be held during the normal class hour. The dates will be announced at least two weeks in advance of each exam.
The final exam will be held in the normal classroom from 8:00-11:00 AM on Wednesday, May 9.

Written Homework. Written homework problems will be assigned weekly, and will be collected at the start of class each Thursday. You are welcome to discuss homework problems with other students in the class. However, you must write up your solutions on your own. Your solutions should be written legibly, in complete mathematical sentences, and should be stapled. Problems will be graded and returned promptly. The homework category may include other types of work as the semester progresses.

Office hours. For the first two weeks, my regular office hours will be:

Tuesday: 2-4
Wednesday: 2-3

These will be changed during the semester to fit the needs of the students. I am always available by appointment (talk to me during class or email me). Or, if you are nearby, you can stop by and I'll talk with you then or tell you when I can.

Books on reserve. There are three books on reserve in the math library.

Montgomery, Niven and Zuckerman, Introduction to the theory of numbers. A standard undergraduate text.
Hardy and Wright, Introduction to the theory of numbers. A classic reference; written at a somewhat higher level.
Guy, Unsolved problems in number theory. As the name suggests, a long list of unsolved problems.

Final note. I am always open to productive suggestions about the course. Please feel free to contact me with any suggestions or concerns.

Best wishes for a productive and enjoyable semester!