hilomath.com— These pages contain the text of the book Inner Algebra. Its premise is that mathematicians use their mind in certain ways that result in math being easy for them, and most people can learn to do the same.
Jan 18, 2006View in Crawl 4
Looking at the examples on the site, I thought, "well, I already do that ... and that ... and that", hoping to find something I've missed. I've tutored mathematics before and I am amazed at the simple tricks that I've figured out (and/or forgotten I've been taught), that those I've tutored had no idea existed. So, I digg this site; not everything is obvious, especially things that I've stared at for way too much time to figure out in the first place. Not everyone obsessively looks for patterns in things, and I'm sure this will help some kids out there and probably my SO, if she'd care to learn it in the first place.
gamil said: What just algebra? ah well, I guess it can apply to Calculus as well. But then again, I've already mastered seeing functions and doing their derivatives in my head. Heck, I actually SEE the derivative being written in my handwriting, on the page that the problem is writen, and fitting it into the available space on the page.YES! That's just the way to go about it, I think. Another thing to point out, of course, is that the human mind and imagination is much more expressive than what we can write on paper. So by visualizing, we have the potential to do things that would be awkward to do if we wrote them down, but might help us do something better mathematically (for example, moving chunks around). Those two ideas are basically the foundation of what is taught in the book.A lot of it follows fairly easily once a person has the ability to visualize well. I kind of always had it, like most of you who have posted, but I have met plenty of people (some of them quite intelligent) who did not seem to consciously visualize at all. That's why the chapter on visualization is in there.PS to justinvt: Thanks for the very nice compliment!PPS to all: If anyone wants to discuss this more, my email address is on the website - feel free to get in touch.
I wonder just how much of "analytical thinking" is really just a learned set of semantic transformations, some of which can be visualized as demonstrated in this book. Is most of it thus?If so, then develping artificial intelligence should simply be a matter of recognizing and accumulating these transformation protocols, then applying them to language, machine perception and machine movement.HAL, please open the airlock...
I'm really good at History and English[am in the IB program for both subjects], but have always struggled with maths and its applications in Science. No, I never learned to do this stuff in my head and my struggle with math reached its climax sophomore year when I failed Geometry[I know, I know]Now I'm a junior and am getting ready to play catch up by taking algebra 2 and geometry next semester. I like what I read from the site and I just finished placing the order on amazon. Thanks hilomath.
nj10iiJan 19, 2006
I wonder if Algebra would be easier if you contemplated it first on an LSD trip?
auxonJan 19, 2006
Looking at the examples on the site, I thought, "well, I already do that ... and that ... and that", hoping to find something I've missed. I've tutored mathematics before and I am amazed at the simple tricks that I've figured out (and/or forgotten I've been taught), that those I've tutored had no idea existed. So, I digg this site; not everything is obvious, especially things that I've stared at for way too much time to figure out in the first place. Not everyone obsessively looks for patterns in things, and I'm sure this will help some kids out there and probably my SO, if she'd care to learn it in the first place.
snwboardguyJan 19, 2006
This is pretty cool. I've kinda always done something like this though this just went into more detail and explained what I would do.
selphishnerdJan 19, 2006
I'm going to be honest...I didn't know anybody didn't do this stuff. Maybe thats why I have a hard time explaining things when I tutor.
ashisJan 19, 2006
"Math suks!"Man.....Math should be declared as act of terror!Its a torture!
hilomathJan 20, 2006
gamil said: What just algebra? ah well, I guess it can apply to Calculus as well. But then again, I've already mastered seeing functions and doing their derivatives in my head. Heck, I actually SEE the derivative being written in my handwriting, on the page that the problem is writen, and fitting it into the available space on the page.YES! That's just the way to go about it, I think. Another thing to point out, of course, is that the human mind and imagination is much more expressive than what we can write on paper. So by visualizing, we have the potential to do things that would be awkward to do if we wrote them down, but might help us do something better mathematically (for example, moving chunks around). Those two ideas are basically the foundation of what is taught in the book.A lot of it follows fairly easily once a person has the ability to visualize well. I kind of always had it, like most of you who have posted, but I have met plenty of people (some of them quite intelligent) who did not seem to consciously visualize at all. That's why the chapter on visualization is in there.PS to justinvt: Thanks for the very nice compliment!PPS to all: If anyone wants to discuss this more, my email address is on the website - feel free to get in touch.
jimbo92107Jan 20, 2006
I wonder just how much of "analytical thinking" is really just a learned set of semantic transformations, some of which can be visualized as demonstrated in this book. Is most of it thus?If so, then develping artificial intelligence should simply be a matter of recognizing and accumulating these transformation protocols, then applying them to language, machine perception and machine movement.HAL, please open the airlock...
Closed AccountJan 22, 2006
I'm really good at History and English[am in the IB program for both subjects], but have always struggled with maths and its applications in Science. No, I never learned to do this stuff in my head and my struggle with math reached its climax sophomore year when I failed Geometry[I know, I know]Now I'm a junior and am getting ready to play catch up by taking algebra 2 and geometry next semester. I like what I read from the site and I just finished placing the order on amazon. Thanks hilomath.
hfilbyFeb 24, 2006
I was quite disappointed myself.