Linear Algebra Bootcamp

Why?

The Department of Computational Mathematics, Science and Engineering at MSU prides itself on being interdisciplinary in research, and as a result, the caliber and background of graduate students in the program varies drastically cohort to cohort, and within individual cohorts themselves. Accordingly, incoming doctoral students frequently don't have the math background that is considered to be prerequisite for the core courses.

Even if they do, they may not have taken the relevant courses in years due to being in the workforce between undergraduate and graduate school, or just taking the relevant courses early in undergrad.

One of the core courses for the first semester as a doctoral student in CMSE is Numerical Linear Algebra I.

What?

With coordination of the faculty instructor for the course, I created content that covered the main takeaways of Introduction to Linear Algebra courses. The plan wasn't for the students to learn all of the relevant material if they haven't seen it before, but to "dust off the cobwebs" if they have taken relevant courses before and/or highlight areas and concepts in which they need to improve quickly.

The concepts covered were:

• Matrices and their Definition

• Matrix Arithmetic and the Determinant

• Row Operations

• Calculating the Inverse of a Matrix

• Linearity

• Diagonalization and the Eigen Problem

• Orthogonalization and Orthonormalization

• The Big Theorem

When?

Offer letters to graduate students instruct them to be on campus at the technical beginning of the fall term. However, classes don't start until a couple weeks later and professors frequently don't realize that and/or don't have work for first year students that early beyond go to class. Accordingly, incoming graduate students have a lot of time on their hands for a few weeks and all they have to do is to go two orientations.

This, combined with the fact that you need to know this material before classes start, creates a nice window to lead the bootcamp.
This turned into an afternoon of bootcamps, as I was able to convince a friend to do a similar bootcamp for the other core course in the fall.

The first iteration of the Linear Algebra Bootcamp went quite well  in 2024 with the plan of officers in the Graduate Student Organization to continue hosting it off the created content in subsequent years. Additionally, the material was linked to the Graduate Student Resources document as well as the First Year Survival Guide.

Results

I conducted pre- and post-surveys regarding the students' comfort level on a scale from 1 (not comfortable at all) to 10 (Extremely comfortable and confident) on several concepts listed below, and the students self-reported an increase in comfortability and confidence!