Back to school: teaching an old dog new tricks

I've determined that my early sixties is as good a time as any to begin an intensive self-study of mathematics! I haven't decided on a specific area of focus yet (what's the rush!), but I'm leaning toward data science, machine learning and artificial intelligence. I think a more specific focus will become clear as I progress.

I asked five different LLMs for a mathematical roadmap, and then I asked Claude (on xhigh effort) to review the five roadmaps, and produce a new one, which I'm tentatively following. I had a fairly full math load in undergrad, and a year of graduate school, but enough time has passed to warrant a pretty thorough review, so I'm beginning with a review of the following in parallel:

  • Single variable calculus
  • Linear algebra

For the single variable calculus review, I've really been enjoying Khan Academy AP®︎/College Calculus BC, and in case I want to spend more time drilling problems, I picked up "The Humongous Book of Calculus Problems", which has 1,000 calculus problems with solutions.

For the linear algebra review, I have "Introduction to Linear Algebra 5th ed." by Gilbert Strang, and the accompanying MIT 18.06SC OpenCourseWare

Another handy book is "Mathematical Notation: A Guide for Engineers and Scientists". In addition to providing a refresher on notation, it shows how to produce symbols in LaTeX. I had Claude tweak my Material for MKDocs setup to be able to properly render LaTeX. For example:

\[ \frac{d}{dx}f(g(x)) = f'(g(x))\,g'(x) \]

or

\[ A\mathbf{x}=\mathbf{b}, \qquad A= \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9 \end{bmatrix}, \qquad \mathbf{x}= \begin{bmatrix} x_1\\ x_2\\ x_3 \end{bmatrix}, \qquad \mathbf{b}= \begin{bmatrix} b_1\\ b_2\\ b_3 \end{bmatrix}. \]

I'm planning on posting about my studies regularly as a mild form of personal accountability. My goals are much more pragmatic than theoretical. As interesting as pure mathematics may be, I'm mainly interested in acquiring new tools that will allow me to build things I would otherwise be unable to build.

I may have to get through a fair amount of mathematical review and introductory material before I can post anything of much practical value, but until then, I'll just post about some of the topics I'm covering along the way.

As of today, I've covered the chain rule of differentiation and vectors & linear combinations.