We will be using the text An Introduction to the Theory of Numbers (5th edition) by Niven, Zuckerman and Montgomery. The material covered will be approximately the first seven chapters. The student is expected to acquire an understanding of the elementary theory of numbers. There will be some discussion of the computational aspects of these topics, but the main thrust of the course will be theoretical. You will be expected not only to follow the proofs presented in class and in the text, but also to learn to construct new proofs. Proofs must be logically correct and care must be taken to write precisely and in grammatically correct English.
The prerequisite for this course is MATH 420. We will also use some linear algebra in places (but not much).
There are a plethora of books dealing with elementary number theory. Some more popular ones include (besides our text) those by Apostol, Burton, Davenport and Hardy & Wright. Check out the QA241 section in the library. Warning/inside joke: A. Weil's Basic Number Theory is not particularly well-titled ("No knowledge of number theory is presupposed in this book . . ." though "Already in Chapter 1, and throughout the book, essential use is made of the basic properties of locally compact commutative groups, including the existence and unicity of the Haar measure . . .").
The last day for undergraduates to withdraw from the course without penalty is Friday, October 18. Graduate students can figure out the last drop day on their own (after all, you are graduate students).
Grades for section 1 will be based on homework, a midterm exam and the final exam. The weights for these are 50%, 20% and 30%, respectively.
Homework will be collected once a week on Fridays. It will be turned in at the beginning of class. You are free to work with other students on the homework; in fact, this is encouraged. Sloppy and/or illegible work will be returned back with no credit! Your homework is something of which you should be proud (notice how I didn't end with a preposition there). Expect to spend lots of time on it. All of the homework problems will be checked to see that each has been done, and certain of the problems will be graded in detail, but just which problems from each assignment will be graded will not be announced in advance. The specific assignment for each week will be available on this webpage (hopefully no later than) that Monday (see below).
The midterm exam will be during class on a date yet to be determined. I try to schedule it so that you know your midterm grade before the drop deadline. The final exam is Wednesday, December 11 from 10:00 to 11:50 in the morning.
Last update: November 26, 2019