Math 4550: Introduction to Number Theory
Spring 2008
Instructor: Bryan Shader
Office: Ross Hall 204
Phone: 766-6826
Office Hours: Monday 11-12, Tuesday 10-11, Thursday 2-3, and by appointment.
e-mail: bshader at uwyo dot edu
Recommended text: A Friendly Introduction to Number Theory}, 3rd edition, by J. Silverman.
Objectives
- To explore some of the fascinating, beautiful properties of numbers.
- To develop algebraic, geometric and analytic tools to study numbers.
- To develop the ability to think abstractly, and to clearly explain difficult ideas and thoughts.
- To enhance proof development and writing skills.
- To have fun doing and learning mathematics.
Expectations
- Work hard and regularly. This will be a difficult class. Re-write your notes.
- Memorize definitions and main results.
- Strive to truly understand the proofs.
- Work through the proofs again and again until you completely understand them. The arguments given in the proofs presented in class are the prototypes for the type of arguments that you'll need for the homework.
- Be willing to seek help. There will be times in this course that you will be frustrated. This is natural. This is not an easy course. Anytime you are learning a difficult new task, you encounter frustration. Don't let the frustration get you down. Come in and talk with me!
- Make numbers your friends by playing with them.
- Start your homework assignments early. In order to have acceptable solutions you will have to go through many revisions.
- Enjoy! You will be exploring an exciting new world, and will be challenging your mind. What a wonderful opportunity!
Grading
Quizzes
8%
Homework 20%
Two midterm exams 24% each
Final exam 24%
Quizzes
There will be a weekly, 5-minute pop quiz, in which you will be asked
to state definitions or theorems. Definitions and theorems that
you are expected to know will be indicated in class as they are
presented. You will need to spend time daily learning these. I
encourage you to make "flash-cards" to aid in your study. Missed
quizzes can only be made-up if they are related to an university
excused absence.
Homework
Approximately every week you will be assigned a set of homework
problems. You will be given a week to complete these. Many
of the
problems will be asking you to prove a result or explain a mathematical
phenomenon. Your explanations should be (a) logically
and mathematically correct, (b) clear and to the point, and (c) in
complete mathematical sentences. You should plan on writing,
re-writing, re-writing, and
re-writing your explanations before they are in acceptable form.
This will require that you start work on the homework as soon as it is
assigned. I don't mind you discussing the problems with other
students. However, the proofs that you write down should consist
of your ideas expressed in your own words. Late assignments will
not be accepted.
Exams
There will be 3 exams (2 midterms and the final). The final will not
(technically) be a cumulative exam, and will only cover the material
presented in the last third of the course.
All information in this syllabus is tentative. If the instructor finds that changes are necessary, they will be announced.