Archived: How to become a Math Wizard

[1337Hendrix]

So you clicked on this thread. Clearly you have some motivation to become better at Math. Well, this is the thread for you!


[SIZE="3"]The Keys to Math Wizardry[/SIZE]

1. Start Small. No matter what your subject is, complex partial differential equations to high school algebra, you will not get anywhere by starting at the back of the book or with the hardest problems you can find. Harder problems are built on concepts and techniques that the problem creator assumes you already know. Thus, it is your job to first learn the concepts and techniques. Read the book, and do simple problems first. They will reinforce what you have learned already and help you build the confidence to tackle ever harder problems.

2. Read the book. The best way to learn the concepts, and expose yourself to the theorems, is by reading the book. I know, most of us HATE to read the book, and thus go right to the problems, but if you want to solve problems you need to understand the concepts behind them. Read slowly, and if you don't understand a word or a sentence, go find out what it means. It could be the reason you don't understand why or how the next theorem introduced works or has any relevance at all.

3. Do the homework. Do the homework again. Do the homework again and again. The only way you will learn problem solving skills is to solve problems. You will see that even if you did the problem yesterday, you might not be able to solve it that easy today. Of course, the goal is to get to the point where you can solve the problem without much difficulty.

4. Go to class. The instructor might be able to explain things much better than the book can. If you have any questions you were not able to resolve yourself, class is the time to ask. Do not be afraid that your question is stupid, because there are probably many more students in the class stuck on the same thing who do not possess the courage to actually speak up about it.

5. Reference. By nature, some textbooks and some authors just suck. They are unclear and seem to pull solutions out of some magic mathematical hat. The good news is, you do not have to stick to that text if you feel that way. Ask your instructors, or other people who have been or are in your boat, and see if they can recommend you any books that have a knack for explanation, or a comprehensive solutions guide to a variety of pertinent problems. (They might even let you borrow!) For instance, one of the best calculus books around is "The Calculus Lifesaver" by Adrian Banner, and I have yet to find a course which uses this book as its main text.

6. Study Together. Go find a friend who is taking your course or one like yours and study together. Multiple researchers have shown that learning is reinforced when you have to explain it to someone else, plainly because you really have to know what you are talking about to get it across. Also, you will benefit if you are on the student end of such peer instruction. Think about it as someone giving you pieces to your puzzle while you are giving pieces to them for their own. Sometimes all it takes is a certain someone to say just the right words which makes it all click in your head. You will undoubtedly make good friends in the process.

7. Get Help. Usually there will be someone or somewhere at your school which provides tutoring services or assistance programs. It is not shameful to ask for help. There is no reason to struggle because of something as ridiculous as your ego. Go see your teaching assistants or your instructor. If they have office hours, show up every time you are stuck. It really helps to get to know those giving you your grades...that is...as long as you are nice.

Well, I hope that helps!

[zingalong]

Thanks, this is great advice and has filled me with inspiration to hit my math class running once university starts!:biggrin:

[Mantikore]

i find that in the more complicated forms of calculus and algebra, there are a limited number of possible scenarios that every problem is a member of. ive got a good teacher that would do examples of all the possible question types

[zingalong]

^^^ Throughout the 12 (and counting) years of schooling i have done, i have never once had a teacher which i considered "good". I always had to figure everything out for myself which didn't really benefit me in the long run. I only hope to "god" that once i start university ill get some decent professors who can properly prepare me for exams.

[Irukanji]

I had a few great teachers. Sure, they were the typical maths teachers, but if you kept quiet, and actually tried to learn, then they'd help you do whatever you wanted

[iSoap.eNet]

I've decided to minor in math (major is biology). I'm thinking Trig to Pre-Cal to Cal 1-3. This sounds correct?

[1337Hendrix]

Originally Posted by iSoap.eNet

I've decided to minor in math (major is biology). I'm thinking Trig to Pre-Cal to Cal 1-3. This sounds correct?

Usually Calc 1-3 are prereqs to the minor.

You will probably be required to take a course in differential equations and/or linear algebra, and a few other higher level math courses of your choosing.

Every school is different, and I'm just generalizing.

[Bender]

Hendrix, i've never seen you hear before. But if you name is referring to the guitarist, I already love you.

Jimi Hendrix > Barrack Hussian Obama

[Mathematics]

You forgot to mention to learn that 0.9 recurring = 1 and also to learn that the plane will take off but the wheels will spin twice as fast.

[JChifty]

Play chess, all logic is good.

[Zay]

Download a TTC torrent. They give great lectures. You can also download MIT courses for free(legally), but it won't help you much if you don't have a foundation.

[The Jitterskull]

If you do math you should be doing programming. They complement each other perfectly and will make you 1.0x10^inf times better.

[eunux]

Originally Posted by Nightside Eclipse

If you do math you should be doing programming. They complement each other perfectly and will make you 1.0x10^inf times better.

Well, of course! Computer science is a subset of mathematics.

[The Jitterskull]

Originally Posted by eunux

Well, of course! Computer science is a subset of mathematics.

So many univ. math students don't know how to use computers, or even program. Its sad

[Trauntj]

isn't this common sense pretty much?

[Ping Crosby]

Originally Posted by Mathematics

You forgot to mention to learn that 0.9 recurring = 1 and also to learn that the plane will take off but the wheels will spin twice as fast.

stuff like this is why i keep coming back.
knowledge is beautiful.

[Ben Katz]

Originally Posted by Mathematics

You forgot to mention to learn that 0.9 recurring = 1 and also to learn that the plane will take off but the wheels will spin twice as fast.

What do you mean about the wheels spinning? Are you referring to velocity? I now know why .9 repeating equals nine. That still blows my mind.

[Mantikore]

Originally Posted by Ben Katz

What do you mean about the wheels spinning? Are you referring to velocity? I now know why .9 repeating equals nine. That still blows my mind.

hes referring to the two age old scientific internet debates that rage on various forums. some forums have even banned its discussion because of the shitstorm it creates

-does 0.9 repeated = 1?
-if a plane on a treadmill was moving in one direction, and the treadmill was moving the other way, would the plane lift off?

[grencez]

Mathematics is always challenging for everybody. It is a great humbler. This being the case, I don't understand how being a "wizard" is even possible.

In any case...
Treat and learn mathematics as a tool. Do science, use math. Put simply - adding for the sake of adding is silly, but adding up your dollars makes adding worthwhile.
And projecteuler.net is pretty cool.

[L33tz]

.9 repeating does equal one. It is simply a flaw in our way of displaying and using numbers and perhaps the way we think that causes it to appear.

[Rizzo in a box]

lol. "how to be a math wizard: learn math" the end.

[crazzyass]

Originally Posted by Mantikore

hes referring to the two age old scientific internet debates that rage on various forums. some forums have even banned its discussion because of the shitstorm it creates

-does 0.9 repeated = 1?
-if a plane on a treadmill was moving in one direction, and the treadmill was moving the other way, would the plane lift off?

On the first one: yes.

Second one: no, assuming that the plane's velocity is being cancelled out.

[HuffRaid]

the planes wheels are simply the point of contact against the tarmac however they are frefloating and will spin to any velocity until they fail... assuming the wheels can spin to an infinate velocity the plane will pull itself forward regardless of the backwards motion of a dynamic tarmac because the prop is attached to the fuselage of the plane

there IS friction on the wheels bearings or whatever plane wheels use to negate friction to spin at a high velocity however...for assuming the tarmac is retreating at a rate of 30 meters a second and the prop is providint a rearwards thrust propelling the plane at 30 meters a second the wheels would be spinning at a rate that would propell the plane at 30 meters per second were the tarmac static. the wheels were they the point of propulsion as in a car...would be need to spin twice as fast to achieve the same velocity. however as a planes propulsion is a turbofan/prop/jet that is not its point of contact whilst a land vehicles propulsion is the same as its point of contact, should lead to a conclusion that the plane wil propell itself forward inducing the wheels to simply spin at twice the speed were the tarmac static


the wheels spin freely, the plane pulls itelf forward lift is achieved, flight is possible.

[The Jitterskull]

Easy:

1. Get an A+ in your comp sci class

Done

See? That was easy. One step, you will think so linearly that math becomes easy.


Experience to validate: I did this and I've gotten A+ in every math course and calculus at university.

[SIdt]

Originally Posted by The Jitterskull

Easy:

1. Get an A+ in your comp sci class

Done

See? That was easy. One step, you will think so linearly that math becomes easy.


Experience to validate: I did this and I've gotten A+ in every math course and calculus at university.

You either are not being taught good mathematics courses, or have been taught a fucking amazing decades-long computer science course covering chaos, multivariable nonlinear analysis, spectral theory, number theory, advanced group theory, spherical harmonics, Green's functions, complex nonlinear fourier analysis, order theory, proof theory, model theory and hypercomplex analysis to name but a few.

[Crazy Polymath]

Great post! Luuuuuuuuurve math.

For those interested in the .9 repeating=1 proof

let x=.999999...

10x=9.99999....

Subtract x from both sides

9x=9

Therefore, x=1

You can do this with any repeating decimal to find out how to express it as a fraction.

For example

let n=.2727272727....

100n=27.2727272727....

Subtract n from both sides

99n=27
n=27/99
n=3/11

[:Evo:]

Originally Posted by Crazy Polymath

Great post! Luuuuuuuuurve math.

For those interested in the .9 repeating=1 proof

let x=.999999...

10x=9.99999....

Subtract x from both sides

9x=9

Therefore, x=1

You can do this with any repeating decimal to find out how to express it as a fraction.

For example

let n=.2727272727....

100n=27.2727272727....

Subtract n from both sides

99n=27
n=27/99
n=3/11

no

[Crazy Polymath]

Originally Posted by :Evo:

no

Um... care to explain?

Don't go abusin' the picard.

[:Evo:]

Originally Posted by Crazy Polymath

Um... care to explain?

Don't go abusin' the picard.

the only "way" (i guess you could say) that .999... is equal to the value of 1.0 is in the display of calculators that just simply round to the nearer value.

the math that was done above does not prove anything at all, especially that any repeating value is equal to anything but its self. Mostly because that math was *wrong*

here:

let x=.999999...

okay, we'll let x equal that

10x=9.99999....

okay now we have an equation, lets solve for x...

Subtract x from both sides

9x=9

wrong, subtracting x from both sides is done as follows:

10x=9.99999....

(10x) - (x) = (9.99999....) - (x)

9x = 9.999999 - x

this proves nothing, or shows nothing.


Therefore, x=1

also, incorrect...

if you wanted to solve for x, you just would have had to divide by "10" (or whatever coefficient is in front of the variable there), so you would get:

10x = 9.99999....

(10x)/10 = (9.999..)/10


now... here is where I would like you all to listen...

everybody... PLEASE TAKE OUT your Ti-83+ or Ti-89 calculators...

enter each of the following in and see what you get as an answer:

9/10

9.9/10

9.99/10

9.999/10

9.9999/10

9.99999/10

9.99999999999999999999/10

as you can see, the only reason that last entry is "equal" to one is because the value and amount of the final value that it increases by per iteration is so so so (let me fully express the word "so") infitesimally small, that the calculator reached its bounds of sigfigs and rounds it up... thats it. done.

you can spend eternity doing those calculations above by hand and you'd never reach the value of one (1), you would literally get an infinite amount of *.9s*

hope that clears stuff up. btw i only use picard when warranted.

[Crazy Polymath]

wrong, subtracting x from both sides is done as follows:

10x=9.99999....

(10x) - (x) = (9.99999....) - (x)

9x = 9.999999 - x

this proves nothing, or shows nothing.

Actually, since we've already stated that x= .9999....

And

9.999...
-.999...
9.000...

Therefore, 9x=9, as the right hand side of the equation we simplified above.

The reason this isn't intuitive is because the .9 represented literally repeats infinitely (not just a lot) and we're inherently not equipped to deal with infinity intuitively.

[NamelessNom4d]

I wish it wasn't so time consuming and frustrating to practice math. The key with all types of math is to practice like a motherfucker. Things become second nature when you do them for the 9002nd time...

[:Evo:]

Originally Posted by Crazy Polymath

Actually, since we've already stated that x= .9999....

And

9.999...
-.999...
9.000...

Therefore, 9x=9, as the right hand side of the equation we simplified above.

The reason this isn't intuitive is because the .9 represented literally repeats infinitely (not just a lot) and we're inherently not equipped to deal with infinity intuitively.

wrong, since

10x = 9.9999

subtract .9... from both sides leaves you with not 9x = 9 but:

9.000001x = 9

you still have an infinitely repeating decimal. what *you* are doing is just assuming that x is already equal to "1" when youre subtracting it from 10, but you cant do that since that is incorrect AND you cant use what your "proof" is supposed to prove before you actually prove it.

youre wrong here.

[Bin "Fuck Towers" Laden]

Originally Posted by :Evo:

wrong, since

10x = 9.9999

subtract .9... from both sides leaves you with not 9x = 9 but:

9.000001x = 9

you still have an infinitely repeating decimal. what *you* are doing is just assuming that x is already equal to "1" when youre subtracting it from 10, but you cant do that since that is incorrect AND you cant use what your "proof" is supposed to prove before you actually prove it.

youre wrong here.

well look at this then

1/3=.3333...
2/3=.6666...
3/3=.9999...


3/3=1

.9999....=1

[kroz]

^^^ no your a juggalo cock sucker!

[:Evo:]

Originally Posted by Bin "Fuck Towers" Laden

well look at this then

3/3=.9999...
wrong

3/3=1
correct

.9999....=1
wrong

you have it right the second time. I don't understand why this concept is so hard for so many people to grasp. 3/3 is not .9999... 3/3 is 1. thats it.

1/3 and 2/3 equal their respective never-ending number because thats what their values are: an infinite number of sigfigs.

what youre telling me is the equivalent of:

2/4.000...001 = 4.999

2/4 = .5

therefor, 4.999 = .5

which is *not* correct.

[Crazy Polymath]

Originally Posted by :Evo:

wrong, since

10x = 9.9999

subtract .9... from both sides leaves you with not 9x = 9 but:

9.000001x = 9

you still have an infinitely repeating decimal. what *you* are doing is just assuming that x is already equal to "1" when youre subtracting it from 10, but you cant do that since that is incorrect AND you cant use what your "proof" is supposed to prove before you actually prove it.

youre wrong here.

I'll put it this way. .999...-.999...=0

No matter how many nines there are, 9-9 will always equal zero. 9.999...-.999...=9, because everything after the decimal point is now zero. I'm not sure how you're getting that final "1", but it doesn't exist: there's only an infinity of zeros.

I have a feeling you just want to argue, which is something I'm frankly sick of doing, so I'll refer you to Wikipedia and if that doesn't satisfy you seek a higher authority.

http://en.wikipedia.org/wiki/0.999...

[:Evo:]

Originally Posted by Crazy Polymath

I'll put it this way. .999...-.999...=0

No matter how many nines there are, 9-9 will always equal zero. 9.999...-.999...=9, because everything after the decimal point is now zero. I'm not sure how you're getting that final "1", but it doesn't exist: there's only an infinity of zeros.

I have a feeling you just want to argue, which is something I'm frankly sick of doing, so I'll refer you to Wikipedia and if that doesn't satisfy you seek a higher authority.

http://en.wikipedia.org/wiki/0.999...

no.

9-9 = 0... cool story.

10-.999 = 9.001
10-.999...= 9.00...01

thats where the one comes from. dumbass.


youre too much of a lazy, self-absorbed idiot to realize that I am wrong so you shell it off as you "not wanting to argue" and refer me to wikipedia

even though I've clearly refuted each of your points in a logical manner to continue this debate, not argument. grow up kid.

[Crazy Polymath]

Originally Posted by :Evo:

no.

9-9 = 0... cool story.

10-.999 = 9.001


thats where the one comes from. dumbass.


youre too much of a lazy, self-absorbed idiot to realize that I am wrong so you shell it off as you "not wanting to argue" and refer me to wikipedia

even though I've clearly refuted each of your points in a logical manner to continue this debate, not argument. grow up kid.

"10-.999...= 9.00...01"

That is not the problem in question--it's also not the right answer unless there are a finite amount of nine. I've given you a proof for this, and you have tried to point out flaws in the individual step, where there are none. Math is not always intuitive: it's the proof that counts. You have not refuted my points, you've failed to understand them.

9.999...-.999...=9 is the problem you have said is inaccurate, as a part of my proof.

The other side is 10x-x, which is always 9x no matter the value for x.

Do you not accept those?

If you do, I can prove validly that .999 repeating for infinity=1. If you do not, speak to a math teacher, because I'm done.

[Rust]

Originally Posted by :Evo:

even though I've clearly refuted each of your points in a logical manner to continue this debate, not argument. grow up kid.

No, you haven't refuted anything. You're wrong. Crazy Polymath is completely correct. The problem is those aren't really formal proofs.

The formal proof (or the most popular one anyways), is representing 0.999... as a geometric series, and showing it converges exactly to 1.

[Crazy Polymath]

Originally Posted by Rust

The formal proof (or the most popular one anyways), is representing 0.999... as a geometric series, and showing it converges exactly to 1.

Interesting, I didn't know this! What differentiates that from mine as a formal proof?