Number Theory

Monday and Wednesdays from 10:25am to 11:40am
Room: Lechase Room 181
Office hours: Wednesdays 17:30pm to 18:45pm

Instructor: Dr. Andrés Chirre

Office 1005 Hylan Building
Phone: (585) 273-2329
E-mail: cchirrec at math period rochester period edu
Personal webpage: https://sites.google.com/view/andreschirre

Course description

This course is an introduction to number theory. We will cover divisibility, primes, congruences, quadratic residues, quadratic reciprocity, and primitive roots. Depending of the students, the last topics we will focus in the theory of the Riemann zeta-function or RSA and elliptic curves.

Textbook

J. H. Silverman, A Friendly Introduction to Number Theory, 4th Ed., ISBN 978-0321816191.

The author has made the first six chapters of the text available on his personal webpage. This should be helpful if you are still waiting for your book to arrive or if you are still deciding whether to take the course.

Grading

Exams

Both exams will take place in class. Mastery of topics from early in the course is essential for success late in the course.

Exam 1: Thursday, October 26
Exam 2: TBA

Please let me know as soon as possible if you will have an excused absence (academic conference, athletic competition, etc.) on one the exam dates.

Homework

We will have problem sets throughout the course. These problem sets will include exercises from the Silverman text, as well as from other sources, or will be written by me. Students must solve these sets of problems and give me in a given time.

Students may work together on both the daily homework and weekly problem sets, but solutions must be written on your own without reviewing others’ work. The use of online solution guides, paid resources (e.g. Chegg), and forums (e.g. Math Stack Exchange) is prohibited. If you are struggling with a problem, please consult your classmates, send me an email or come to office hours.

Disability support

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. You can reach the Office of Disability Resources at (585) 275-3424 or visit Disability Resources.

Please note that to be granted alternate testing accommodations, you (the student) must fill out forms with Disability Resources at least seven days before each and every exam. These forms are not sent automatically. Instructors are not responsible for requesting alternative testing accommodations at CETL or making accommodations on their own.

Academic integrity

All assignments and activities associated with this course must be performed in accordance with the University of Rochester’s Academic Honesty Policy. More information is available at www.rochester.edu/college/honesty.

Math Department policy on unauthorized online resources: Any usage whatsoever of online solution sets or paid online resources (chegg.com or similar) is considered an academic honesty violation and will be reported to the Board on Academic Honesty. In particular, any assignment found to contain content which originated from such sources is subject to a minimum penalty of zero on the assignment and a full letter grade reduction at the end of the semester (e.g. a B would be reduced to a C). Depending on the circumstances, this may apply even if the unauthorized content was obtained through indirect means (through a friend for instance) and/or the student is seemingly unaware that the content originated from such sources. If you have any questions about whether resources are acceptable, please check with your instructor.