Professor: Scott Ahlgren
Email: ahlgren@math.uiuc.edu
Phone: 244-1738
Office: 302 Altgeld Hall
Course Description:
The natural numbers 1, 2, 3, 4, 5, ....... have
fascinated humankind since the beginning of recorded history.
Number Theory is the study of the profound and subtle relationships
between these numbers. 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 very simple to state
(for example, how many prime numbers are there?) Some of these have simple
solutions which have been known for thousands of years,
while others have frustrated the attempts of the most
brilliant thinkers for generations. Very recently,
there have been very important practical applications of Number Theory
(for example, in cryptography).
This course will provide a hands-on introduction to this subject.
There will be short lectures to introduce important
concepts, and students will spend much of class time actively engaged in
mathematics (this includes experimenting, formulating hypotheses, and
proving these hypotheses). Emphasis will be placed on thinking in a way
which is simultaneously creative, clear, elegant, and logical.
This course is suitable for anyone with an interest in mathematics.
There is no formal mathematical prerequisite.
There are two prerequisites. The first is an intellectual interest
in math and a willingness to engage new ideas. The second is NOT
currently taking Math 347, and not having completed any math course at
the 300 level.
Text.
A friendly introduction to number theory, by Joseph Silverman.
Webpage. This syllabus and other course material and announcements, can be found on the course webpage: http://www.math.uiuc.edu/~ahlgren/math199sp09/math199.html
Classes. Monday, Wednesday, Friday, 11-11:50 am.
243 Altgeld Hall.
Grading. Your course grade will be computed as follows:
Attendance and participation. You will be doing a lot of work during class. Therefore everyone should be at the class meetings. The first three meetings which you miss will not affect your grade. After the first three, each unexcused absence will reduce your score in this category by 5 points.
Problems. You will spend a lot of time thinking about problems, both in and out of class, both alone and with others. The 50 points in this category will be awarded based on your performance and effort on these problems.
Project. Each of you will work on a semester project, perhaps in a small group. I will suggest a number of topics related to the course material. You will prepare a written version and will also give a presentation to the class (these will take place at the end of the semester and perhaps during the final exam period).
Note on expectations. The students in this class have different mathematical backgrounds, and come with different mathematical skill sets. Obviously, this can make grading somewhat tricky. My approach is the following: I expect students to expand their skill set, and to put their skills to good use. Trust me--this will work out fine if everyone has a good attitude about it.
Office hours. By appointment. Email me or talk with me after class to set up a time to talk.
Other books. There are many books in the mathematics library on elementary number theory. There are also many books from the popular press about the topics and the people introduced in this class. You are encouraged to explore these--let me know if you want suggestions, or if you find a book which is especially interesting or helpful.
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!