You may find this resource useful. It was written by Susan Rigetti (née Fowler) [1]:

So You Want to Study Mathematics https://www.susanrigetti.com/math

She also wrote:

So You Want to Learn Physics https://www.susanrigetti.com/physics

[1] https://en.wikipedia.org/wiki/Susan_Fowler

Woah, from a quick look that seems perfect. I'll jump right into the math one.

This looks great. Thanks a lot!

It depends. What math are you trying to learn? The correct approach will depend on what material you are looking to review and what you are trying to learn anew.

For review of anything up to and including calculus, I would recommend Khan Academy. It wouldn't be great on its own for learning a subject from scratch in my opinion but it's good as a refresher because the videos and exercises come in well-organized bite-sized chunks.

If you strongly prefer books, for review I'd recommend the shortest book you can find on a given subject that has a reasonable balance of explanation and exercises.

For new material, the answer will be completely subject specific, and also whether you are interested in more practical or more theoretical understanding of the given topic.

Yes, I think this is a much better approach to learning math with an application in mind. For example, for learning standard Model of particle physics, discussing general relativity and quantum mechanics, Roger Penrose's book "The Road To Reality" is an excellent guide. Unlike his contemporary Stephen Hawking's infamous book "A Brief History of Time" that avoided math equations like a plague, Penrose explains to you the necessary maths to understand the upcoming materials of the book in the first 300+ pages [1].

[1]The Road to Reality:

https://en.m.wikipedia.org/wiki/The_Road_to_Reality

Some related threads from the past https://hn.algolia.com/?q=ask+hn+math

"Ask HN: I suck at math, where to start?", "Ask HN: How do I learn math/physics in my thirties?", "Ask HN: How to self-learn math?", "Ask HN: Best way to relearn basic math?"

For CS math, I'd recommend MIT's 6.042 https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-...

They have a book on the course website that's pretty good

Mathematics From The Birth of Numbers (Jan Gullberg, 1997)

It's a pretty large tome, but covers all the basics and is a great reference. It goes well with Khan Academy videos for example.

I also wanted to chime in as this list might be helpful: https://shepherd.com/best-books/power-and-wonder-mathematics

Amir Alexander loves math and shared five books about the power and wonder of math. They can be fun as they both teach it and inspire through it.

Lara Alcock shared the best books for studying undergraduate mathematics: https://shepherd.com/best-books/studying-undergraduate-mathe... *She wrote a book on mathematics as a major and has amazing exp.

Garrity’s “All the Mathematics You Missed: But Need to Know for Graduate School” may be of interest. It’s not comprehensive but it does touch on the main ideas that one should know for each topic. It also points out relevant books for each topic, which I found useful.

Not the OP, but oddly enough I ordered this book this morning before I saw this thread. Looking forward to reading it. 20 years ago when I graduated undergrad I had to make a decision... software job or math graduate school. I chose software job.

There are many excellent books that can help you to learn math. Some popular choices for beginners include "Math for Dummies" by Mark Ryan, "The Everything Basic Math and Pre-Algebra Book" by Meg Clemens, and "The Cartoon Guide to Algebra" by Larry Gonick and Boya Li. These books provide a gentle introduction to basic math concepts and can help you to develop the foundational skills that are necessary for success in more advanced math courses. As you progress in your math studies, you may want to explore more specialized books on topics such as calculus, linear algebra, or probability and statistics.

-- ChatGPT

I just use khanacademy.org to freshen up on individual maths, as desired. I'm not going to be able to read an entire book and remember everything.

More time consuming, but maybe a little bit more inspiring, are the videos of lectures at universities, like MITs open courseware (OCW). Edit: They have the advantage that you can combine your topics of interest. With the disadvantage that you have to think about this.

What is Mathematics by Courant and Robbins is surprisingly good. For something a little more specific Pinter's A Book of Abstract Algebra would fit the bill.

Calculus by M.Spivak. Buy a notebook and start solving it's problems. By the time you finish with most of the book you will be a Math god.

My teacher used Spivak in my high school calculus class. It went way over my head. But I re-read it every five years or so and pick up new things every time.

Spivak is rarely the answer to a request for a math book recommendation, unless the request is something like "I've already learned calculus, now I want to really learn calculus."

I certainly didn't learn calculus from it the first time around.

The answer is almost always Schaum's and Youtube videos.

www.mathacademy.com is in beta and another option too.

Ignore all the other answers and skip straight to this one. Math Academy is amazing. It's got everything you could want (mastery based learning, knowledge graph dependencies, assessment tests, a hint of gamification to encourage you to learn more, even spaced repetition reviews) and its coverage and depth of the material is _excellent_.

For specific example, I've literally studied linear algebra probably close to a dozen times in my life, including full courses from two different universities whose names end with "institute of technology", and I'm currently using math academy to review the subject again. I've already encountered several things that are straight up new to me, and the presentation/practice and spaced repetition review of the things I just never managed to lock into my long term memory is already helping me finally own them.

A Concise Introduction to Pure Mathematics.

As a side note, I asked GPT this question and it recommended the following book:

A Beginner's Guide to the Mathematics of Computer Science by J.E. McLeod and J.A. Fekete

I can't find this on Google or Amazon. Does it even exist??

GPT is writing it now, check Amazon again in a few minutes.

You realise GPT is a text generator and not a recommendation system right?

In my experience GPT works incredibly well to get recommendations of similar movies, books, etc.

I think I am free to interact with ChatGPT in any way that I want.. or do you have a set of limitations I (and everyone else) should use?

I'm not limiting you, I'm just pointing out the obvious.

I don't care what you do

Courtesy: ChatGPT

"How to Ace Calculus: The Streetwise Guide" by Colin Adams, Joel Hass, and Abigail Thompson. This book is designed to help you (re)learn the key concepts and techniques of calculus, which is the study of change and motion in the physical world. It includes lots of examples, exercises, and practical tips to help you master the material.

"The Joy of X: A Guided Tour of Math, from One to Infinity" by Steven Strogatz. This book is a friendly and accessible introduction to math, covering a wide range of topics from basic arithmetic to advanced calculus and beyond. It is written in a conversational style and includes lots of examples and illustrations to help make the material more engaging and easy to understand.

"Algebra for Everyone: In-Depth Coverage, Examples, and Exercises" by James Brennan. This book is a comprehensive guide to algebra, which is the study of equations and formulas. It covers all the key concepts and techniques, including linear equations, quadratic equations, polynomials, and factoring, as well as more advanced topics like algebraic fractions and equations.

Overall, the best book for you will depend on your specific goals and interests. If you want to focus on a specific area of math like calculus, a book like "How to Ace Calculus" could be a good choice. If you want a more general introduction to math, a book like "The Joy of X" or "Algebra for Everyone" might be more suitable.

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My personal recommendation: All the Mathematics You Missed: But Need to Know for Graduate School

2/3 books actually exist, good job ChatGPT.