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....

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...

This book isn't a text book, and doesn't want to be, but for Fourier Analysis, "Who is Fourier? A Mathematical Adventure" provides an introduction to the subject that, IMO, few books can match: https://www.amazon.com/Who-Fourier-Mathematical-Adventure-2n...

There's an interesting book about Fourier and his series and transform written for a general audience: "Who Is Fourier? A Mathematical Adventure" [1], by an organization called the Transnational College of LEX (which seems to have some sort of connection with Hippo Family Club[2]).

The only math assumed going in is basic high school algebra.

They also have a book on quantum mechanics ("What is Quantum Mechanics? A Physics Adventure" [3]) and biology ("What is DNA? A Biology Adventure"[4]).

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....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.

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...

The only math assumed going in is basic high school algebra.

They also have a book on quantum mechanics ("What is Quantum Mechanics? A Physics Adventure" [3]) and biology ("What is DNA? A Biology Adventure"[4]).

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

[2] https://www.amazon.com/What-Quantum-Mechanics-Physics-Advent...

[4] https://www.amazon.com/What-Biology-Adventure-Transnational-...