[stiff]

Feynman also said the following (in the "The Character of Physical Law" lectures):

Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics. Newton's statement of the law of gravitation is relatively simple mathematics. It gets more and more abstruse and more and more difficult as we go on. Why? I have not the slightest idea. It is only my purpose here to tell you about this fact. The burden of the lecture is just to emphasize the fact that it is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics.

[reagency]

This is very important. Many students hit a wall when physics passes beyond lay intuition and whatever may they already know well. Advancing in mathematics is essential to feeling comfortable in advanced physics.

[batou]

I discovered this last year after arrogantly jumping into the first volume of Feynmans Lectures on Physics.

50 pages in, I decided to take a step back and read a calculus book first, but wait my algebra and trig are crap so back to the basics. So yesterday I hit LCM and GCD applications and factoring which are very basic. So, I'll probably resume the initial book in a couple of years or so...

[timnic]

Math is wide and deep. You won’t need to cover every topic in math to get going with physics. If you really are interested in physics there are many things in math, which are, well, less important (for doing basic physics). For example LCM, GCD and factoring. I guess, these things are somewhat important in Computer Science, but I never encountered them in a physics problem. So to get started with physics, I would suggest that you focus mainly on analysis (differentiation and integration) and vector algebra. As an addition maybe the basics of complex numbers. This can be learned relatively quickly.

With these you should be able to follow the Feynman lectures or watch the very fine „Theoretical Minimum“ series by Susskind (http://theoreticalminimum.com)

[batou]

Thanks for the pointers. Much appreciated.

I'm doing a full review of mathematics at the moment. Not in depth, more of a "here's an application of the GCD function" so I know what tools to use to solve specific problems. All this is beneficial for the day job as well who expect to see some value from my time spent even though I'm not being totally honest with the objective to them. Realistically I want to think abstractly in the terms of mathematics and develop some intuition.

Was completely unaware of the Theoretical Minimum series. Thanks for that.

Edit: I'm reading Mathematics: From the birth of numbers by Jan Gullberg as a text. Wonderful book. Covers just about everything and is beautifully written by a non mathematician with no assumptions spared and no education target. In fact the forward is mainly bitching about the education system. Slightly worried I will get distracted by this book but that's never a loss!

[timnic]

I do not know "Mathematics: From the birth of numbers" but judging from the Amazon quick view it seems to cover a lot of ground (BTW: one thing I missed in my list are the basics of differential equations).

Over 1000 pages is quite a long read, though. I never managed to read a (science) book as big as that from cover to cover myself. One thing I learned through the years is to never use only one book for learning. Books have different styles and not every style fits to every student. Additionally one book might be good at one specific topic and weak on another. So nowadays I always use a couple of books (or online resources) to learn a new topic.

[batou]

Its huge yes but a lot of it is fluff and history. It does serve to keep it interesting however.

Quick page shot to show the scope and density: http://i.imgur.com/sV1WYFd.jpg

I have a number of other books as well that I use as a reference as well so no problems there (calculus for the practical man has some different insights). Oh and betterexplained.com.

[laxatives]

On a related note, Mary Boas's text, Mathematical Methods in the Physical Sciences does a great job of giving you the necessary bag of tricks to learn all of undergraduate level physics (and probably much more) without diving too deep into any single topic. It should be sufficient to give you lots of intuition until you decide to pursue something at much greater depth (although doing that alone, and without a professor/PI/expert of some sort is realistically, almost definitely a waste of effort).

[selimthegrim]

You will certainly need them if you have any interest in quantum information.

[semi-extrinsic]

If one has any interest in quantum field theory, I would add complex analysis (countour integrals in particular) to that list.

[ivansavz]

Perhaps my math book can help you learn the basics a little faster: http://noBSgui.de/to/MATHandPHYSICS/

One suggestion: make sure you don't just read about math, but also try solving exercises and problem. These are very important for actually learning the material.

[batou]

Thanks - that looks excellent. I will definitely take a look at your book this evening.

Agree with solving problems; this was what was missing from my school education. Literally rote and box ticking with zero applications.

[gaze]

I think just as much as it's important to have intuition is to have a healthy relationship with your intuition. Knowing when to trust it and when not to. Intuition often happily leads you very far down the wrong path. Math can, too, obviously, but doing math properly involves many self checks. You frame the problem in many different ways and can see if they line up. Your intuition is just the way you see the world. If the way you see the world happens to be wrong, you'll think the wrong thing. For instance, I might intuitively think that if I digitize a band limited analog signal I'm throwing something useful away... that you're throwing away the data between the samples. There's clearly wiggles there... those wiggles must encode something! It turns out though that a digitally sampled band limited signal can be perfectly reproduced. Perfectly. That's totally counter-intuitive, by which I mean there's little real world experience that would tell you otherwise!

So, I think you should think about intuition, math, whatever else you have in your pocket as tools. They give the right answer when used correctly and sometimes give the wrong answer even when you're sure you're using them correctly. I think though that intuition CAN be more insidious because it's what you've experienced! It HAS to be true, you think.