Methods of Applied Mathematics: Introduction to Fourier Analysis

Mondays and Wednesdays from 9:00am to 10:15am
Room: Hylan Building Room 306
Office hours: Mondays 3:00pm to 4:00pm

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 semester Math 285 will focus on Fourier Analysis. If you are interested in learning many things related to the Fourier series and Fourier Transform, it will be a good opportunity to take this course and I encourage you to enroll in it. Some applications to number theory will be presented, as the analytic extension of the famous Riemann zeta-function. Depending on the people, the last part will cover topics like interpolation formulas or Fourier transform in R^n.

A background is necessary: sequences, limits, series, continuity, differentiation, integrals, vector space, inner product, and how to do proofs. If you have taken a course like Real analysis or Complex analysis is sufficient. If you have taken at least Math171 in the sequence of Honors Calculus is also ok.

There are some parts of the course where we will need something of Complex analysis. I will take a few classes to review the topics we need.

Textbook

Fourier Analysis: An Introduction, by Elias M. Stein and Rami Shakarchi. Princeton Lectures in Analysis I

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.