The absolute best teaching of the Fourier transform I've ever encountered is the extremely bizarre book "Who is Fourier?"

https://www.amazon.com/Who-Fourier-Mathematical-Transnationa...

Try this remarkable book:

Who Is Fourier?: A Mathematical Adventure

https://www.amazon.com/Who-Fourier-Mathematical-Transnationa...

It started off as a bunch of non-math literate folks teaching themselves math from scratch, including trigonometry, calculus etc, and ending in Fourier series. It is a very approachable and fun book.

I would second the recommendation for Who is Fourier? A Mathematical Adventure. It's an unusual and engaging introduction to waves, Fourier coefficients, and transforms. The slope is gentle but not dumbed down. https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n....

My recommendation below is not the equivalent of a Feynman's series for math, but one that is pegged much lower, for someone interested in basic remedial math.

It is called "Who is Fourier: A Mathematical Adventure".

I was tremendously surprised by this unusual gem of a book. It covers the range from basic arithmetic to logarithms, trigonometry, calculus to fourier series.

https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...

I suggest the following approach;

Start with some school textbooks for grades 8-12 i.e. Secondary Education. This is more for a refresher course in the absolute basics.

The above can be supplemented with the following books to develop intuition;

1) Who is Fourier - https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...

2) Functions and Graphs - https://www.amazon.com/Functions-Graphs-Dover-Books-Mathemat...

After this is when you enter undergraduate studies and you have to fight the dragon of "Modern Maths" which is more abstract and conceptual. In addition to standard textbooks; i suggest the following;

1) Concepts of Modern Mathematics - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

2) Mathematics: Its Content, Methods and Meaning - https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Boo...

3) Mathematical Techniques (i am linking this so you can see the reviews but get the latest edition) - https://www.amazon.com/Mathematical-Techniques-Dominic-Jorda...

Finally, if you would like to learn about all the new-fangled mathematics your best bets are;

a) The Princeton Companion to Mathematics - https://www.amazon.com/Princeton-Companion-Mathematics-Timot...

b) The Princeton Companion to Applied Mathematics - https://www.amazon.com/Princeton-Companion-Applied-Mathemati...

One important piece of advice that i have is to become comfortable with the Symbols, Notation and Formalism used in Mathematics. Most students are intimidated by the Formalism (which is nothing more than a precise form of shorthand to express abstract concepts) and give up on studying Mathematics altogether. This is a shame since it is merely the Form and not the Function of Mathematics.

Fellow Marine Engineer (KP) here, and just wrapping up my Master's in CS Data Science. If you're like me, ou got rushed through a number of higher level match (between bar crawls), passing tests, but not digesting.

So, the feer of a math intensive grad program (and admission had me worried). My CS program offered some math refresher, but I ended up just jumpting in without it. If the program is decent, you will be guided along at a digestable pace. As a responsible adult with a hunger to learn, and you will enjoy and digest more. In a curriculum, you'll also have peers/teachers to help you when absolutely stumped - which will happen.

For books - I just have one that I saw referenced here on HN, which is a little odd, but highly recommend for understanding Fourier transforms [1].

1. Who Is Fourier? A Mathematical Adventure 2nd Edition... Amazon link: https://www.amazon.com/dp/0964350432/ref=cm_sw_r_other_apa_i...