Introduction
Number theory is one of the oldest and most beautiful branches of
mathematics. Apparently simple questions, such as whether a given
number can be written as a sum of squares, are answered by deep and powerful
theory.
This course provides an introduction to number theory. Our focus will
be on integral and rational solutions to equations, on the
algebraic structures which explain the shape of those solution sets,
and on the distribution of those solutions.
Prerequisites
You should have taken (and understood!) MATH 360 or 366.
Logistics
-
Textbook: Elements of Number Theory, John Stillwell,
Springer-Verlag 2003.
The last part of the semester will draw on different online resources,
such as
- MWF 11:00AM -- 11:50AM, ENGRG E205.
- Professor Jeff Achter
j.achter@colostate.edu
Weber 216, 491-6716
Requirements and other expectations
As in any other 400-level class, you will need to work both diligently
and creatively.
- Homework -- 30% Homework will be
assigned weekly, and is due at the beginning of class on
Fridays. No late homework will ever be accepted. Your work must be
neat, and the pages stapled, in order to be graded.
- Exams -- 50%
There will be two in-class exams, on Friday, March 7 and Friday, April 18. No makeup exam will be
given; you must take each exam as scheduled.
- Final project -- 20%
You will be asked to write a final project and give an oral
presentation in class. Presentations will be given during the last
week of classes (May 5, May 7, May 9) and during the scheduled final
period Thursday, May 15, 11:20-1:20. Your attendance at these presentations is mandatory.
Help
This is challenging material; it's fully expected
that sometimes you'll need a little help. Unless specifically
noted, you're encouraged to work with other students in the class.
(Please observe that the work you actually turn in must be your own.)
Questions directed to j.achter@colostate.edu
will be answered swiftly.
However, some questions are best answered in person. You
can come by office hours or schedule an appointment.
This page is available at http://www.math.colostate.edu/~achter/405