So I’m getting a good grade in algebra, but I don’t really feel like I have an intuitive grasp of the under laying logic. Quadratic equations are something I’m starting to get but it still looks a lot more like voodoo than logic to me.
What really works good for me are books written by authors who are passionate about their subject. Further I need more than “do this, do that”. I need an intuitive grasp of why doing that works, and how it works. Further things that really help me learn are the stories behind the discoveries. Like what lead to them and how they were used. Stuff like that creates a lot more memories and mental reminders when it’s needed.
Algebra Unplugged, by Kenn Amdahl and Jim Loats, is a bit cutesy, but might be the kind of thing you’re looking for.
If you want the “stories behind the discoveries,” the Algebra volume in John Tabak’s History of Mathematics series is a pretty good basic introduction to the history of algebra.
You’re probably not ready for it, but to really got a solid grasp on why what you’re doing works (for some things), what you need is a calculus book.
I remember being amazed when I took Calc 1. The formulas they just handed out to you in Algebra (especially things like Area of a Circle or formulas for speed/distance/acceleration) we found from scratch.
It’s also worth noting that, if you have specific questions or topics you’re puzzled about, you could try asking here. You’d probably get some good answers (and/or links to good online explanations) before the thread devolved into math-geeky quibbling.
For example, what about quadratic equations looks like voodoo to you? Solving them by factoring? completing the square? the quadratic formula? or what?
You might like Algebra by Israel Gelfand. It starts off slow, but he really makes you think about why things are true. I found the first 55 pages online here:
I just watched the quadratic formula video. It looks to be a good place to check up, on things. Thanks!
Modern branches is okay. I like learning new things. When I was a a kid I read this book Chaos: Making a New Science. I wish I hadn’t lost it. I didn’t understand it very well then but it left an impression on me. Strange attractors, the butterfly effect, the futility of meteorology beyond a week because of the butterfly effect, and oh yeah self organizing systems. I don’t understand why those aren’t taught to kids in the first grade. You just can’t understand biology without the concept. Take rain forests, a metric buttload of plants and animals all crammed in every spot they can fit, all interacting in inarticulately complex ways. The whole system seems like it should fall apart, it’s a biological clown car, more in than there is room, but it doesn’t. Self organizing systems. Lot’s and lots of strategies, defenses, random happenings all changing but averaging to the same thing, until something alien to the system comes along and knocks it off it’s tilt, but given enough time and it’ll adapt and revert back to it’s complex hum. Or the problem of measuring the English coast. The closer you zoom in to the details in it’s irregular shape the longer it is. It’s a real life fractal. So much stuff like that.
Thanks for the suggestions I’ll check them out!
Well you were right about it starting off slow with part one having the chapter about rows of apples, but part three is about where I’m at. Getting ready to do a test about logarithms tomorrow so that stuff is very relevant. Should be some productive study during lunch, thanks!
I have in the past. It was very helpful. When I started quadratics I didn’t even know FOILing. A kind person showed me foiling and it clicked it was just an abstract version of grade school multiplication. Just variables took the place of the ones column, and tens column, and stuff. I try not to flood GQ and have been asking a lot of programming questions lately. Plus I like to read anyway.
Quadratics are starting to make a lot more sense now that I saw how factoring works
I manged to test past the intro class, and in the intermediate class the first chapter was things like factor x^2 + 3x -18 = 0which works out to (x-3)(x+6) = 0. If you go at it in that order is bazaar. where did the negative 3 and positive 6 come from? However it finally clicked if you foil (x-3)(x+6) you get x^2-3x+6x-18 which simplifies to x^2+3x-18. Basically quadratic equations are like rectangles that have small equations for the width and height which made it seem a lot simpler.
and typing this, it’s finally clicking why factoring them gives you the x-intercepts, because ax^2 + bx + c actually equals 0y which just simplifies to 0, so people leave the y out even though it’s a very elucidating y that the whole world should be told about every single time. They need to know. It’s a very important y. because if y is 0 then logically x must equal the x axis intercepts.
I guess I’m thinking quadratics are confusing out of force of habit.
I think the problem is
Taking Calc I and II next fall and winter. It’s good to know there’s explanations coming, because I want some. Tried peeking ahead at a trig book. Apparently a lot of this stuff is reproducible with something called the Cartesian plane. Looks exciting!
