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Course: Math 540, Elementary Number Theory
Time and Place: TuTh 1:00 - 2:15pm, Snow Hall 454.
Instructor: Professor D. Katz
Office: Snow Hall 501
Office Hours: Snow 501, TuTh 11:00am - 12:15pm, and by appointment via Zoom. You are welcome to 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
Course Description: This is a proof based introductory course on elementary number theory. Note that elementary does not mean easy, but rather that sophisticated techniques from abstract algebra and analysis are not used. Topics to be covered include: basic properties of the integers including the division algorithm and unique factorization; distribution of primes; integers modulo n; quadratic equations modulo a prime; quadratic reciprocity; Euler's sums of squares theorem; Lagrange's sums of squares theorem; and other topics as time permits.
Textbooks: While our lectures will not be following any particular text, we will use as references, and sources for homework, the following texts, which are freely available online: Number Theory: In Context and Interactive, by Karl-Dieter Crisman, Crisman. The online version of the text has lots of interesting interactive examples using Sage. I strongly encourage you to experiment with the examples in the online version of the text. You can also download a pdf copy of this text or purchase a hard copy.
We will also refer to 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 commercial distribution. Any copies should contain the relevant copyleft caveat as it appears in the original online version located here and at Clark's webpage.
Daily Update: After each class, a synopsis of what was covered will appear here Daily Update.
Homework: Homework will be assigned after each class, but is not to be turned in. Even though homework is not to be turned in, you are strongly encouraged to work as many problems as possible. 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 the assignment, on their own, not in the presence of any other classmate. Homework assignments are posted here: Homework
Weekly Quizzes: We will have a 10-15 minute each Tuesday, except those Tuesdays following a midterm exam, beginning January 28. The quiz questions will test you over definitions and statements of theorem, propositions, etc, covered in the previous week. Randomly selected homework problems will also appear on the quizzes.
Quiz 1 solutions, Quiz 2 solutions, Quiz 3 solutions, Quiz 4 solutions, Quiz 5 solutions, Quiz 6 solutions
In-class Exams: We will have two in-class midterm exams. The dates for these exams are: February 27 and Friday, April 17.
Solutions to practice problems for Exam 1, Solutions to Exam 1
Final Exam Date: The final exam will be held in our classroom on Monday May 12, 1:30pm - 4:00pm.
Course Grading: Each midterm exam and the final exam will count 25 percent of your grade. Your homework and quizzes combined will account for the remaining 25 percent. Bonus problems will be assigned throughout the semester. You may use your final exam score to replace your lowest midterm grade, if doing so improves your final average in the course.
Grading Scale: Your final course grades will be determined as follows: A = 90-100 percent; B = 80-89 percent; C = 60-79 percent; D = 55-59 percent; F = 0-54 percent.
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.
Additional resources and policy information
Students are encouraged to familiarize themselves with University Policies and Student Resources. Relevant information may be found here:
Resources and policies