Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20070915 03:05:30
...now whatI've finished high school, and I'm taking a few years off before college, the problem is: I love math. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #2 20070915 03:42:51
Re: ...now whatWell, you can do one of two things (or both really). You can either prepare yourself for introductory math courses at the college level or start to study pure mathematics. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20070915 04:08:59
Re: ...now whatI think I too like "pure maths." I liked calc, but only the mathematical parts, not the application. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #4 20070915 05:17:50
Re: ...now whatAn introductory course in linear algebra would also cover transpositions, determinants, properties of determinants, solving systems of equations, and perhaps even an introduction to eigenvalues and eigenvectors. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20070918 09:40:40
Re: ...now whatI think you should study parametric equations, or maybe I should, come to think of it. Last edited by John E. Franklin (20070918 09:50:24) igloo myrtilles fourmis #6 20070918 12:48:05
Re: ...now whatI touched on in breifly in my Precal class, but it didn't really impress me. Maybe a second go would be a good idea. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #7 20070918 14:17:23
Re: ...now whatIt's never a bad time to study number theory , if you can't find anything else to do, investigate that #8 20070919 01:46:10
Re: ...now what
How would I go about that? Do you know of any good books? There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #9 20070919 02:28:35
Re: ...now whatAs I've said other places, I highly recommend you take an intro to proofs course before studying number theory. It is certainly possible to go straight into it, but you'll have a much easier time if you do proofs first. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #10 20070919 04:06:40
Re: ...now whatDo you know of any (nontextbooks) books that would be a good place to start with intro to proofs? What's in an intro to proofs class? I've read many proofs (mostly famous ones) and they didn't seem to difficult to follow. Is there something more to it? Last edited by bossk171 (20070919 04:07:07) There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #11 20070919 05:09:12
Re: ...now whatProofs isn't about following them. It's about coming up with them. A proofs class starts out in basic logic and truth statements, goes on to methods of proving. Through it, you learn basic definitions in math (positive, even/odd, divisible, etc). Then an introduction to set theory, functions, relations, and cardinality. Also normally included is operators and other things such as that, "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #12 20070919 06:34:13
Re: ...now whatMaybe I'm not fully understanding the depth of what you're saying, but I feel like all of this is stuff I already know. Last edited by bossk171 (20070919 07:53:56) There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #13 20070919 09:00:37
Re: ...now whatWell, the easiest thing to do is try a sample problem: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #14 20070919 12:27:24
Re: ...now whatPoint made. I don't understand a word of that. There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction. #15 20070919 12:42:47
Re: ...now whatRight now I'm reading two books Last edited by Identity (20070919 12:44:30) #16 20070919 13:39:41
Re: ...now whatJust to let you know that was a "I have a firm grasp on everything that should be learned in an intro to proofs course" type question. It is probably a bit advanced for someone who has just taken a proofs course, although not be too much. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 