Aids for more advanced mathemathics for visual learners?

[Saman]

Hi All. I just wanted to start this thread for people to please, please kindly share any sources they know of to help out some of us more predominately visual learners to maybe finally start to have an easier time understanding some of the more advanced mathematical concepts out there - like for instance visually understanding the square root of 2 or irrational numbers vs rational numbers, etc, etc, etc, which most of you probably thinks is basic stuff but just wait till you want to try to understand more difficult stuff and you don't really understand the basic stuff I am just tired of doing this when it comes understanding the whys and hows that they chose to go about doing this or that in more advanced math stuff, that is trying to really understand the big picture and their building blocks that lead to more complex stuff rather just memorizing useless equations that lead to no understanding, which is what they made many of us do in school - so frustrating and useless when you are mainly a visual learner, or so I think! :( Yes I did take calculus up to college level and I was a B student, that is way back then, but now I don't remember anything and that is because really didn't understand anything but just some forgotten equations that they taught us to use mechanically over and over again! Math is so essential to learning EVERYTHING that I can't ignore my lack of sincere understanding of it anymore.

Anyways, end of my rant. So in a nutshell does anyone know of any websites, for starters, that start from the beginning and progress up to more advanced stuff in mathematics, visually? And please excuse my lack of education

 

[John G]

Ark mentions Tony Smith's site in the transcripts.

Here's a good entry level point for the site:
http://www.valdostamuseum.org/hamsmith/play456.html

There's some pictures if you follow the links. Ark is mentioned in one of the links too.

Here's some pictures and links into Smith's website here too (via a paper I wrote):
http://vixra.org/pdf/0910.0023v2.pdf

Even though this is Smith's model, the math is used in similar ways by lots of people. Smith's D4 has a 6-dim gravity used by Ark and others. This D4 is also related to SU(5) that is used in a mainstream model for the other forces. D5 relates to SO(10) which is a known way to view a 10-dim spacetime. E6 is used for matter/antimatter in string theory and string theory also uses E8 for quantum physics. E8 is also being looked at by loop quantum gravity researchers.

Smith like Ark, also uses Clifford Algebra (I think Smith and Ark and Laura met at a Clifford Algebra conference). You can think of Clifford Algebra as an information space from which the more physical spaces of spacetime/matter/forces come from.

 

[StrangeCaptain]

Websites? not sure... Do some google surfing.

Books?

Take a look at the books on this page under the "Elementary" category. Most of these books I don't know, but it is somewhere to start. I have personally seen and flipped through the Gelfand book on algebra, and it does seem to try to impart as much understanding as is possible at that stage.

_http://www.ocf.berkeley.edu/~abhishek/chicmath.htm#e:algebra

If you could get through an elementary book on each of geometry, algebra, and trigonometry and you are still interested in a more visual approach to math, or perhaps what you will find you mean, in a more "geometrical" approach, then you could try to read Newton's original works. I have not read them, and I doubt I will. However, I have the impression from other authors that his way of doing calculus was rather different than the modern way seen in textbooks. He had a very strong geometrical intuition about things and not just because he was a genius. He did a heck of a lot of work on geometry that most folks just don't do anymore. He thus had a rather more geometrical way of doing calculus than the more symbolic modern approach.

Having said that, at a beginning level there is a point where you just have to accept that certain rules are just that way and get comfortable applying these rules until you have the machinery necessary to do more. The first "proof" I ever saw that 2+2=4 was in the introduction of a book meant for master's degree students in mathematics.

Also I would encourage you to ask yourself why you are interested in math. Not to dissuade you... It is just that it is a long and difficult road, and answering that question might help you know how much time and energy you would want to allocate to such a pursuit.

 

[Palinurus]

I specially registered to give you a starting hint with the following link: _http://demonstrations.wolfram.com
Also worth your while seems the overall website of the same author(s) _http://mathworld.wolfram.com notably (see to the left) the subsections recreational mathemathics and/or Mathworld/classroom. Enjoy!

 

[Vulcan59]

Hi Palinurus,

Thanks for the links.

Welcome to the forum. :) We recommend all new members to post an introduction in the Newbies section telling us a bit about themselves, and how they found their way here. Have a read through that section to get an idea of how others have done it. Thanks.

 

[Saman]

Thank you All for your replies. I think they will help all of us who are visual learners greatly. SOOOO much food for thought from all of you, but yes, I won't be spending a life time trying to understand all of it either when time is so short - just general understanding is fine since I don't intend to go all the way back to the ABC of mathematics with notions of trying to prove 2+2=4 etc,. So yes Patience I do take your advice to heart. I was just reading SHOTW and something that was supposed to be simple, Ironcially by Netwon (!) wasn't simple to me. Hence the stimulus for choosing to post this thread. Peace