Susan Rigetti

I'm a fellow programmer who has been self-learning physics for the past few months. My opinion is that a programming background will neither help nor hurt the "learning physics" part. It might help depending on what you want to do with the physics after you learn it, if that involves writing simulations or something like that. But really learning physics mostly involves reading and solving problems.

Read textbooks. Solve lots of problems. Calculus, differential equations, and linear algebra are really important. Don't skip the core physics subjects (it's tempting to jump into the "cool" modern physics topics like quantum mechanics and general relativity before you have the necessary background).

If you haven't taken any physics at the university level, you probably want to start with one of the standard calculus-based intro physics books like Young's University Physics. People speak highly of the Feynman Lectures, but I've also heard some physicists (e.g. Sean Carroll) say that they believe the Feynman Lectures are only good when you already know the subject matter.

The core subjects in undergraduate physics are classical mechanics, electrodynamics, special relativity, quantum mechanics, and statistical mechanics/thermodynamics. You will encounter these subjects in your intro book, then take a second pass on each subject at a deeper level with more mathematical sophistication. General relativity and quantum field theory are usually taught at the graduate level or as…

I was a Physics guy, a significant portion of my personality was centered around Physics.

When I started my Physics major, I had to complete two advanced Maths courses titled- Mathematical Methods I, II.

My love for Math took off from there. If you ask for books, then I would mention the MP book by Arfken, Weber, Harris. So minimal, yet straight to the point. Consistent and edifying.

I read a different Maths book in HS than what everyone else read. It was a local book, but very well written by prominent Mathematical intellectuals- the kind that write Math columns or act as mentors of syllabus advisory committee. This made a huge difference.

I liked Statistical Mechanics in college. I read Blundell and Blundell for it along with an unusual book as a reference- https://www.amazon.com/Thermal-Physics-Thermodynamics-Statistical-mechanics/dp/1259097617/ .

How Math explains the physical world so prominently blew my mind. I loved it.

I also watched Calculus video from MIT-OCW when in HS.

I switched to Deep Learning after college. How I could actually use Math to build something extremely practical made me love Math even more. This was the true turning point.

I now want to spend three years- part-time, studying higher math by myself. I think it is worth it, and I want to do original, basic research in the Deep Learning space.

While I keep my eye out for resources, I follow these lists-

* https://www.susanrigetti.com/math

*…

As always, this is written by someone who admits to never having learned to reason abstractly about algebraic objects, because it is hard.

Quoting from the OP:

> The traditional arithmetic I learned in the early grades made sense to me because I could relate it back to real-world things. Later, when I was learning how to design, finding the area of a circle proved essential to practical tasks such as sizing hydraulic and pneumatic cylinders. I could do trigonometry by visualizing, for example, the cables on a suspension bridge. But algebra: no.

For a different perspective, I recommend reading instead Susan Rigetti (nee Fowler)'s posts about overcoming challenges to learn Math and Physics. She says she had to solve what felt like "millions of exercises" to become familiar with many abstract concepts, until they finally clicked for her and she was able to reason about them. In her words: "Solving problems is the only way to understand mathematics. There's no way around it."

https://www.susanrigetti.com/math

https://www.susanrigetti.com/physics

https://www.susanjfowler.com/blog/2016/8/26/from-the-fledgling-physicist-archives-if-susan-can-learn-physics-so-can-you

Practice.

Don't just read, binge YouTube, or click through banal tutorials with a misplaced hope of learning through osmosis. You learn math by doing math. Most likely without a computer. It's unpleasant as you will be quite bad at it, but that's a good thing as it means you can get better.

I'm a bit younger but also with kids and have been using the fracture in life that brings to fill in similar gaps in education. UoL have some courses as part of an online degree. I don't recommend it, but the references are good for fundamentals. I've been collecting them and some study notes here: https://simple.industries/notes/uol-comp-sci.html.

The Susan Rigetti guide (https://www.susanrigetti.com/math) already posted is also an incredible reference.

Also, learn with your kid(s)! There a whole set of publications around the math circles movement. I'm currently working through this with my 3yo: https://www.goodreads.com/en/book/show/12689040.

Susan Rigetti has a nice overview [0]

In this Susan recommends https://www.khanacademy.org/, which is good for most things learned in primary or secondary school.

There is an open source curriculum equivalent for an undergrad compromised of MOOC and similar resources [1]

Similar to the above is a markdown [2], with a scope directed towards people coming from a CS background.

After this perhaps focus more on statistics & data science for metric interpretation. R for Data Science [3] is an option.

[0] https://www.susanrigetti.com/math

[1] https://github.com/ossu/math

[2] https://github.com/NavigoLearn/RoadmapsMarkdown/blob/master/math/math for computer science/full-roadmap.md

[3] https://r4ds.hadley.nz/

Came here to recommend this. I completed my bachelors in mathematics back in 2003. However, recently I am thinking of going back to school to study graduate level mathematics or higher, and possibly do a PhD in a related field. My tentative plan over the next couple of years is as follows

1) Art of Problem Solving - all of the books to review mathematics at middle/high school level
2) Roughly follow the plan mentioned in https://www.susanrigetti.com/math to redo an undergraduate degree
3) Also complete the books here - https://foundations-of-applied-mathematics.github.io/
4) Move on to more advanced graduate level mathematics