Fourier Analysis, Math 103

Instructor Info: Larry Guth, E17-314, lguth@math.mit.edu

Class times: MWF 2-3, E17-129

Office hours: Mon 3-4 and Tues 3-4.

Announcements:
Office hours in the first two weeks. I will have office hours on Friday Sep. 11 after class (3 pm). I'll have office hours on Monday Sep. 14 at the usual time, but I won't have office hours on Tues. Sep. 15.
Midterm: The midterm will be Tuesday Oct. 27, 7:30 - 9:30 pm, in our usual classroom, E17-129.

Course description: In Fourier analysis, we study how to decompose a complicated function as a sum of many simple pieces. In particular, we will prove that an arbitrary function can be written as a linear combination of sine waves. This decomposition has a remarkable range of applications, including partial differential equations, number theory, geometry, and some topics in applied math. We will rigorously study this decomposition, and we will look at many applications. Here is a description of the things we will study: Course description. Here is a course syllabus with exam dates and basic logistical information: Course syllabus.

Textbooks: We will use two textbooks from the Princeton Lectures in Analysis sequence, written by Stein and Shakarchi: Fourier Analysis: An Introduction, and Real Analysis: Measure theory, Integration, and Hilbert Spaces.
I think that these are really good books, and that you'll enjoy owning both of them. We will cover Chapters 1 - 7 of Fourier Analysis and most of Chapters 1 and 2 of Real Analysis.

Course work: We will have weekly problem sets. There will be a midterm halfway through the semester and a final exam.

References:
Formula list . This is a list of formulas from our class that you will be able to use during the midterm.
Practice Midterm. You can work on these problems to study for the midterm. This practice test also shows the format of the actual midterm.
Solutions to the practice midterm.
Practice Final. This was last year's final exam. You can work on these problems to study for the final. This practice test also shows the format of the actual exam.
Solutions to the practice final. .

Problem Sets:
Problem Set 1, due Wednesday Sep. 16 in class.
Problem Set 2, due Wednesday Sep. 23 in class.
Problem Set 3, due Wednesday Sep. 30 in class.
Problem Set 4, due Wednesday Oct. 7 in class.
Problem Set 5, due Wednesday Oct. 14 in class.
Problem Set 6, due Wednesday Oct. 21 in class.
Problem Set 7, due Monday Nov. 9 in class.
Problem Set 8, due Wednesday Nov. 18 in class.
Problem Set 9, due Friday Dec. 4 in class.

Optional Open-Ended Projects
:
Fourier analysis and probability .