Math 310: Introduction to Number Theory Fall Semester 2009 Bradley University

General information

Instructor: Dr. Alberto L. Delgado
Office: BR 466
Office Hours: MWF 1:15-2:00, 3:00 -- 4:00, and by appointment
Office Phone: 677-2504
Email: delgado@bradley.edu
Webpage: hilltop.bradley.edu/~delgado/index.html

The Course

At its most basic, Number Theory refers to the properties of the integers, especially the natural numbers.  The great mathematician Carl Friederich Gauss called this subject arithmetic and said of it, Mathematics is the queen of the sciences and arithmetic the queen of mathematics.  While you might think of arithmetic as one of the simplest subjects in mathematics, it's a surprisingly deep subject with many unsolved problems.  While you (probably) won't solve any unsolved problems this semester, you'll learn to use the basic tools needed to do so.  

We'll start the course with an introduction into mathematical foundations, proof techniques, and induction.  After that, we'll dive straight into the integers and study divisibility, congruences, Pythagorean triples, some famous number theoretic functions, primes and their distribution.  Our goal for the semester is to prove the Chebychev form of the Prime Number Theorem,

Let π(x) denote the number of primes no greater than x, then  ,

and we'll discuss, without proof, the full statement of the Prime Number Theorem:

Course Materials

The nominal text for the course is Elementary Number Theory by David M. Burton.  Most of  the material we will cover is in the text, although I won't always follow the text in either order or style.  It is therefore not required for the course;  it is nevertheless available at the bookstore.  We will cover material from chapters1- 7, 11 and 12.  I strongly recommend that you use some textbook as a source.  I'll provide you with a list of suitable texts available in our library as well as on the internet.  In addition, I'll make course materials available to you from time to time.

Updated course materials are available on my webpage. In addition to this syllabus, you'll find information on homework, textbooks, readings, assignments, exam dates, and miscellaneous thoughts.

Grading

The class will meet Monday, Wednesday, and Friday at 2:00.  Your attendance is expected.  Your grade in the class will be based on your performance on two hour-exams, a final exam, and homework.  The exams will be worth 100 points each, the final exam and the homework will count for 200 points each. Your final grade in the class will be based on these 600 points.  I'll announce the dates of the hour-exams about two weeks before the exams are given. The final exam is scheduled for

It's important that you be present for all examinations. There are no make-up examinations! If you expect to miss an hour-exam and have a reasonable excuse (for example, a documented illness or scheduled University business) notify me in advance as soon as possible. If you are excused from that examination your grade will be based on your other work in the class. In the unlikely case that you should be excused from more than one hour-exam or from the final exam, you will receive a grade of "Incomplete" for the course; we will then make arrangements for you to complete the course on an individual basis.

I will assign homework in class.  It will normally be due one week after it is assigned.  Homework is very important; if you have any trouble with it (and only the rarest of student doesn't), ask questions in class or come to my office. No late homework will be accepted  for any reason! At the end of the semester, I'll arrange for there to be a few more than 200 points available from homework, so missing an assignment, though never a good idea, will not necessarily hurt you.

A Final Word

On the course evaluation form at the end of the semester, we always ask the students: What one piece of advice would you give to someone taking this course next year?  Every time the answer is overwhelmingly the same:  Do your homework; do it early; and ask questions about it when you don't understand.  If you're not going to listen to me (and, trust me, I'm used to that by now!) take the advice of your fellow students.  Attend all your classes; read your book; take notes in class; ask lots of questions.  And one last thing: Do the homework.