Course: Math 540, Number Theory
Time and Place: MWF 2:00 - 2:50, Snow Hall 152
Instructor: Professor D. Katz
Office: Snow Hall 405
Office Hours: Snow 405, MWF 1:00 - 2:00pm, and by appointment. You may also send an e-mail with questions about what is going on in class or with questions concerning a particular homework problem you might be having trouble with.
E-mail: dlk53 AT ku dot edu
Description: This is an introductory course on number theory. Topics to be covered include: basic (abstract) properties of the integers - including the division algorithm and unique factorization, distribution of primes, integers modulo n, quadratic recoprocity, continued fractions, and other topics as time permits.
Text: We will use the texts Elementary Number Theory: Primes, Congruences, and Secrets, by William Stein and Elementary Number Theory by W. Edwin Clark. Both of these books are available for free online: Stein and Clark. Two notes regarding these texts. Stein's book is available at Amazon at a very reasonable price, for those wanting a hard copy. Regarding Clark's book, please note that it is protected by copyleft, meaning we are free to copy the book and use it for our course, but may not make copies for commerical distribution. Any copies should contain the relevant copyleft caveat as it appears in the original online version located here and at Clark's webpage.
Course Grading: We will have two in-class midterm exams, each worth 25 percent of your grade. There will be regular (almost daily) homework assignments. Your HW score together with weekly quizzes will be 25 percent of your grade and the final exam will be worth 25 percent of your final grade. grade. The weekly quizzes will be very short quizzes (5-10 minutes long) where you will be asked to state some basic defintions or facts covered recently in class.
In-class Exam Dates: Friday, February 17 and Friday, April 7.
Final Exam Date: Wednesday, May 10, 1:30pm - 4:00pm.
Homework Assignments: You may discuss homework problems with your fellow classmates. However, I would like to ask that each person in the class write up the final version of each assignment, on their own, not in the presence of any other classmate. Homework assignments are posted here: Homework
Study Guide for Exam I
Practice Problems for Exam I, Solutions
Solutions to Exam I
Study Guide for Exam 2
Gauss and Quadratic reciprocity
The Prime Number Theorem
The Pursuit of Beauty
Euler's φ or "totient" function
Students with disability
The KU Office of Disability Resources (DR) coordinates accommodations and services for all eligible students with disabilities. If you have a disability and wish to request accommodations and have not contacted DR, please do so as soon as possible. Their office is located in 22 Strong Hall; their phone number is 785-864-2620 (V/TTY). Information about their services can be found at www.disability.ku.edu. Please also contact me privately in regard to your needs in this course.
Policy on religious observances
Any student who has a conflict between the course schedule and a religous holiday
should contact the instructor as soon as possible.