I have a cs degree and I couldn't do the simplest of high level math at this point. I said it was pointless all through my years as a student, and turns out im absolutely correct.
dullard
Elite Member
- May 21, 2001
- 26,004
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Ok I give up. Proofs now in this thread.
1 = 1. (Do I have to count this as a rule?)
1 = 1 + 0. (The add by zero rule.)
X * 1 = X * (1+0) (The do the same thing to both sides rule.)
X = X * (1+0) (The multiplication by 1 rule)
X = X + 0 * X (The distributive rule)
0 = 0 * X (The do the same thing to both sides rule.)
See how my simple rules did your proof?
In math a definition is a specific thing. Without a proof 0*X=0 is a conjecture and nothing more. You can't just define 0*X=0. A definition does not require a proof, a conjecture does require one to be true. Now with the Axioms of the Reals and definitions you can solve and prove basically everything that has to do with the reals, and 99.9% of the things you encounter can be solved with just the 5 Additive Axioms and 5 Multiplicative Axioms. Though you are right this is off topic from the OP question. Even my question prove 0*X=0, and what you said X^0=1, could be proven using these 10 axioms. With these 10 axioms you can even do calculus as long as you know the difinition of things in Calculus.
dullard
Elite Member
- May 21, 2001
- 26,004
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<- Dullard is clearly an applied math person.
MySos is clearly a theoretical math person. The two groups probably will be battling for the rest of time.
Not trying to diss you, but people like that need to get their head out of their as$. We have millions of American's who can't pass a 6th grade math test to save their life. And then math people come in and say things like "you can't use 0 * 4 = 0 since you haven't proved it yet". I hereby define 0 * X = 0. People from now on can use that without worry of proof! If you have zero apples in each hand, then you are holding zero apples in your hands! And if they need the proof, they can scroll up two posts.
We need people to spread math knowledge, not complain about the philosophy of the meaning of a word such as "definition".
I agree that something needs to be done, we are lagging to far behind in the world. If I was in charge this is what children would be learning. 1st grade: Addition, Subtraction, Multiplication, and Division. 2nd: long division, large multiplication, fraction, and decimals; 3rd: the axioms of the real, and proving the things they learned in 1st and 2nd grade. 4th grade Pre-Algebra; 5th Algebra; 6th grade Geometry; 7th grade Algebra 2; 8th grade Pre-Calculus and Trigonometry; 9th-10th: Calculus, and Statistics; 11th: Linear Algebra, 12th: Differential Equations. This should be mandatary. We do everything to make sure students are given the resources necessary to learn these things. If we made students learn like this we wouldn't have a problem with 6th grades who can't pass a basic math test.
"You're not getting the problem wrong because you don't understand the calculus. You're getting the problem wrong because you're using illegal mathematics in the algebra"
Though in the past few weeks it's "You've been complaining about not being able to use a calculator for the past 14 weeks, and now I'm handing you one and telling you to use it, and now you're complaining that the calculator is giving you wrong answers."
Though in the past few weeks it's "You've been complaining about not being able to use a calculator for the past 14 weeks, and now I'm handing you one and telling you to use it, and now you're complaining that the calculator is giving you wrong answers."
My friend sucked at Maths too and she knew that she did (sux). So she took some classes @ her local community college and it helped her a great deal -- she worked hard, wasn't afraid to ask questions in class and actually managed to get an A in the class. She doesn't suck as much because of her renewed confidence and knowing that she can relearn something that she thought that she couldn't muster 
Try taking courses, or buy a high-school maths book and do the exercises without using a calculator. And overall, be patient with yourself! Learning is not an overnight deal.
Try taking courses, or buy a high-school maths book and do the exercises without using a calculator. And overall, be patient with yourself! Learning is not an overnight deal.
TheLonelyPhoenix
Diamond Member
- Feb 15, 2004
- 5,594
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99.9% is a very high number. You really think that only 1 in 1000 people who hate math will have to take calculus? I bet it's closer to 1 in 5. Same with logarithms and triganometry. Sure, most people don't use them every day, but almost every person in this coutry has had to deal with those two concepts by thier 18th birthday.
You might be able to reduce 8th grade algebrea to 10 basic rules, but you cannot do it with all of math below the Ph.D. level.
I think that the problem with math education is bad teachers. They were never taught right to begin with and pass on the bad techniques to their students...and the cycle continues.
I know too many students who focus on just trying to memorize facts and miss the whole point. Sure, memorization will get you through grade school, and even maybe most of university, but it most certainly won't do you any good in life.
I know too many students who focus on just trying to memorize facts and miss the whole point. Sure, memorization will get you through grade school, and even maybe most of university, but it most certainly won't do you any good in life.
i agree, math teachers suck. i had mostly good math teachers (all except middle school), so i did alright, but i still dont completely understand a lot of the stuff (soph in engineering at duke). I think one problem is that teachers just expect kids to not understand the stuff, and not enough time is paid to seeing the "big picture" so we know where we are going with stuff.
btw, does anyone know of a good linear algebra book? i took it this last semester, but i dont understand it very well; was wondering iif anyone knew of anything to help me out.
btw, does anyone know of a good linear algebra book? i took it this last semester, but i dont understand it very well; was wondering iif anyone knew of anything to help me out.
dullard
Elite Member
- May 21, 2001
- 26,004
- 4,618
- 126
I'm proud to be the first response in that thread, and proud that I've never returned. I wonder how many of those thousand posts are responses to my post. Probably none, but I'll never know.
About 1 in 4 Americans take some form of college math. Lets say about a third of those take a calculus or calculus prep course. That'll leave you with 1/12 of Americans that have even taken that course. I'm assuming the people who hate math and are convinced they suck didn't take it in highschool either. But, here is the important issue you are missing: even if you do the occasional calculus problem, the vast majority of math you will come across doesn't use it. For every derivitive I take, I do 100 algebra problems. I'm an engineer, other professions will have a lot more algebra/to calculus ratio. Crude math: 1 - 1/12 of Americans * 1% of problems are calculus related = 99.9% of typical problems are not calculus related.
You seem stuck on those logarithms and triganometry problems. Ok, use my rules or don't, but solve this: g(10)=? And show your steps.
Done yet?
Oh wait, you don't know the definition of g(x). I agree that my 10 rules cannot solve this problem without one more piece of data - the definition of g(x). With each problem you solve, you do need more than my 10 rules, you also need to know the definition of the functions. If you don't have the definition of log(x), then you can't solve it - with ANY method. That is taken as a given for the person doing the problem. Duh. But once you have the definition, you can solve them with my 10 rules in the vast majority of problems that people like the original poster will have.
No where did I say that all sub-PhD math can be done with 10 rules. I said sub-PhD math is quite easy. Then, seperately, I said the 10 rules will solve most of those problems if you know the definition of the problem you are working with. You combined those two separate ideas into one idea to twist my words outside of their original meaning. Of course you need to know the definitions of the problem as well as those 10 rules.
Linear Algebra Done Right by Axler is fairly good, but you'll probably want to read from another book to supplement the fairly short section on determinants. I read bits of Linear Algebra Done Wrong by Treil for a better treatment of determinants -- it's free in pdf here: http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf
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