YouTube Channel & supplemental materials

I maintain an educational YouTube channel, Professor Macauley, that has over 22K subscribers and 2 million views, as of May 2023. On this page, I will link to the playlists, summarize them, and provide direct links to revelant course webpages. When possible, I post my course materials there for anyone interested in using them for self-study.

Want to get in touch? My contact info is on my webpage, or you can follow me @VisualAlgebra on Twitter.

With 156.5 hours of content---nearly an enitre week, there will be mistakes! In some cases, I have put them in the video description, and in other cases, viewers have pointed them out in the comments.

Differential Equations

I made these videos when I first taught Differential Equations (Math 2080) online in Summer 2016. At that point, I had already taught it ten times in person, and my course had converged to something that I really liked then, and still do now. It's doesn't follow any book that I am aware of, though texts that "shaped" it include Polking/Boggs/Arnold, and Brannan/Boyce.

This course has a particular focus on the structure of linear differential equations (rather than just being a cookbook of "how to solve" them), and their utility in modeling in science and engineering. It covers a number of topics that are often not done in an ODEs course, such as PDEs, Fourier series, power series solutions, and nonlinear systems. Topics that aren't covered include higher-order linear systems (I only do 2x2) and exact equations. In terms of content, I think there are very few ODE courses that cover more than this one.

Advanced Engineering Mathematics

I made these videos when I first taught Advanced Engineering Mathematics (Math 2080) online in Summer 2017. I had taught this during the semester once before, but much of the content is an "expanded version" of what I already do in Differential equations (Math 2080), which I had taught a dozen times. I can be thought of as a follow-up to that course. Though there is some overlap, I dive in deeper into that material in this course. It covers more topics than most courses with this title (including what we normally teach at Clemson), except that I don't do any numerical methods. Instead, I have include Sturm-Liouville theory, generalized Fourier series, PDEs on unbounded domains, in higher-dimensions, and in other coordinates.

This course doesn't really follow any textbook---I mostly developed it from scratch, although I used Logan's Applied PDEs book as a guide for a few topics (especially PDEs on unbounded domains). Some courses on PDEs and Fourier series are basically formula-driven Engineering classes, of little use to math majors. Others are theoretical applied analysis classes, of little use to engineers. My goal with this class was to strike a balance between these extremes, and lean heavily into the linear algebra theory behind the scenes, but not the mathematical analysis required for ideas like convergence. All of the linear algebra needed is self-contained. Overall, I'm really happy with how it turned out.

Visual Group Theory

In 2010, I taught Abstract Algebra (Math 4120), roughly following Visual Group Theory (VGT), by Nathan Carter. VGT has 300 color illustrations, and focuses on the intuition behind the difficult concepts in group theory. However, it is, by design, a "general audience book," and so I needed to greatly supplement it to meet the needs of undergraduate math majors.

After a few iterations of the course, it had converged to something that I thought would never change, and I recorded these videos when I taught it online in Summer 2016. Three years later, after my students and I were equally frusterated at the lack of a textbook for the material I was teaching, I bit the bullet and decided to write Visual Algebra. Several years and 700 pages later, I have so much more content than I ever thought would exist, including hundreds of new visuals. I now look back at this YouTube playlist with slight disappointment, and cannot wait until I get to re-record a brand new series of videos that follows Visual Algebra!

Advanced Linear Algebra

I recorded these videos when I taught Graudate Linear Algebra (Math 8530) three semester in a row during the COVID pandemic. Some advanced linear algebra classes, especially those geared to engineers and often called "matrix analysis," focus on computations involving matrices and under-emphasize the theory of vector spaces. Yet many other treatments take the opposite approach by presenting the theory of modules, which is too far detached from most applications that an applied mathematician, statistician, or optimizer will need. My goal was to take a "Goldilocks" approach, and emphasize the theory of vector spaces (not modules), while being grounded in applications.

I loosely followed Peter Lax's Linear Algebra textbook, but that is quite dense and "Rudinesque," and so I do a lot of things differently. My approach to determinants is closer to Halmos' old Finite Dimensional Vector Spaces text, and I borrow a few ideas from Strang. Other topics were patched together as needed. My target audience is a graduate student in applied math, statistician, or optimization.

Discrete mathematical structures

I made these videos when I first taught this course online in Summer 2019. Our Math 4190 course is required for several engineering majors for accredidation purposes, and the majority of students are engineers. Math majors are encouraged to take our combinatorics (Math 4110) class instead. I don't even remember what I used to write these course lecture notes, though I assigned the free open textbook by Levasseur/Doerr, and most HW used WeBWork.

Calculus 2

My first foray into recording videos was in Summer 2014, when I taught Calculus 2 (Math 1080) online. I made a series of 23 videos covering the main topics. At this point, our classes were part lecture, and part "recitation" for working on "Learning activities," answering questions, etc. Later, in the Zoom era, when I was teaching this in a "long summer session", I recored another 32 videos where I lectured on more specialized problems and material that my original videos did not cover, as well as my own commentary about solving HW and worksheets problems.

What this means is that this playlist is as blend of two styles of videos, which mirrors the structure of may calculus claseses: polished lectures, followed by recitation/work/review sessions.