Summer School

Here you can find details about the activities of Math SPIE 2021. This year, the program will be entirely online, via video conferencing.

Expected Background

The only background that will be assumed is abstract algebra (group theory), elementary linear algebra (over the real numbers), and a first course in analysis. In fact, this program is explicitly targeted to students who might have taken few math courses as undergrads. Please do not hesitate to contact us if you have any concerns about your preparedness, because this program is probably for you!

Structure of the Summer School

The times listed on this website are all US-Eastern.

10:30 – 11:00 Morning Greetings and Coffee
11:00 – 11:50 Mini-Course A
12:00 – 1:00 Grad School Life Topics
1:00 – 2:00 Lunch (free time)
2:00 – 2:50 Guest Lecture
3:00 – 3:30 Coffee Break
3:30 – 4:20 Mini-Course B
4:30 – 5:30 Do Math Together
6:00 – 7:00 Problem Sessions with TA

A tentative plan for the two mini-courses that will run during the summer school is as follows. Both courses are meant to be “crash courses” and the emphasis will be on motivation and becoming familiar with concepts and theorems, and plenty of illustrative examples that the students can draw from when they study the topics in earnest during their first year in grad school.

Mini-course A: “Topology” by Christelle Vincent (University of Vermont). In this course we will cover the basics of topological and metric spaces, continuous maps, induced topologies, separation axioms, compactness and connectedness.

Mini-course B: “Abstract Linear Algebra” by Álvaro Lozano-Robledo (University of Connecticut). This crash course may cover the following topics: vector spaces, subspace and quotient space, basis, dimension, linear transformations (including matrix representation using a basis). Dual spaces, dual of linear map, double duality. Determinant and trace, characteristic polynomial, eigenvalues and eigenvectors. Inner product spaces, orthogonal and orthonormal bases, adjoint of linear map, spectral theorem for self-adjoint operators (over R).

Grad School Life Topics. During these sessions, we will discuss components of graduate student life, such as: being a TA, first steps in teaching, strategies to pass preliminary/qualifying exams, narrowing down a topic of concentration, first steps in research, finding an advisor, choosing an advisor, picking a thesis topic, navigating funding options, attending seminars and conferences, applying for funding and fellowships, etc. We will also offer sessions on LaTeX and Beamer skills.

Guest Lectures. On some days of the week we will have guests come to talk to the students in the program, either about research topics in mathematics, or other topics that our guests think are valuable for the target audience. The list of guests will include:

Do Math Together and Problem Sessions with TA. These are times for students to collaborate on understanding the material and on homework problems. A grad student will be available in the later hour to help!