Hi guys. Thanks for the helpful posts. When I think about my self-development goals, I think it comes down to being able to understand some of the lower level functionality enough to be able to modify something if needed. I don't feel like I need to build my own physics or graphics system from the ground up. Problems, like graphics, sound, and physics appear to be almost completely "solved" in this day and age, so I don't see . But I'd like to be able to delve into existing libraries and have an idea what the heck is going on. I'm assuming that a decent foundation in mathematics would help, but I guess it does ultimately depend on what exactly I"m trying to mess with.

I'll still take a look at the recommended resources. Thank you!

@rbc13183

My general recommendation is this for people who are looking to improve their math abilities:

Study linear algebra, and real analysis. This is THE place to really begin mathematics.

These two fields will lay down the algebraic, analytic, and logical foundation from which to build. Once you've waddled through these waters, you will emerge a different thinker, with a new appreciation for mathematics, and you'll be able to guide your own learning path moving forward.

To this end, I will go a step further and recommend http://www.amazon.com/dp/03879825...tackoverfl08-20#reader_0387982582 (Chapters 1-5 most importantly), and http://www.amazon.com/dp/0387950605/?tag=stackoverfl08-20.

@zoo

Thanks for all the insights about math. It really boils down to what you talked about, that feeling when you now know and can move on to the next subject.

I think I need to brush up on some High School math before I delve into the books you suggested, am I right?

Overall this series has been amazing for the reasons you stated in your first post, digging deeper. That was always the missing link for me when I tried other tutorials, I really want to understand to see behind the curtain and get a good grip.

I asked Casey on the stream the other day if he'd read the book "GEB" (Godel, Escher, Bach) by Douglas Hofstadter -- it's a fascinating and detailed look at the structure and meaning between math, art, and music. I would recommend it for a more.. philosophical and theoretical view on how all these disciplines intertwine.

It's not an easy read though as it is very in-depth and detailed. I'll definitely need to read it again sometime to fully grasp what the author is saying. :lol:

My nickname, "Pseudonym", was chosen 25 years ago when I was reading GEB as an impressionable teenager.

The closest I came to juvenile delinquency was cracking the copy protection on games. I decided I needed a hacker handle, so I picked one that was self-referential. It seemed funny at the time.

Also note my .sig at the bottom of this post. It's a self-replicating Perl program.

@ongaku

I'd encourage just diving right in and when you hit something you don't know, turn elsewhere to try to understand it (basically, prerequisites on an as-needed basis). (Or post a question here, I'll try to explain if I see it and can help.)

That said, flipping through the amazon previews quickly, it looks like you'll be off to a head start if you have some familiarity with (1) logical proofs and (2) set theory & notation. (How one acquires such understanding is left as an exercise for the reader. ^_^)

Of the two zoo mentioned, the analysis book might be more accessible.. but real analysis was my favorite course, so my perception is probably biased ;).

It opens with this,

Toward the end of his distinguished career, the renowned British mathematician G.H. Hardy eloquently laid out a justification for a life of studying mathematics in A Mathematician's Apology, an essay first published in 1940. At the center of Hardy's defense is the thesis that mathematics is an aesthetic discipline. For Hardy, the applied mathematics of engineers and economists held little charm. "Real mathematics," as he referred to it, "must be justified as art if it can be justified at all."

Thanks everyone for the suggestions.

@midnight_mero

That's actually the way I usually approach learning. First I dive into to the subject at hand just to tinker with it and try to make something. Afterwards, this creates the questions I will need to ask people, google, books (in no particular order) to actually learn.