## Search found 221 matches

Mon Nov 01, 2010 4:19 am UTC
Forum: Mathematics
Topic: My idea on why math is hard...
Replies: 28
Views: 4003

### Re: My idea on why math is hard...

There's a nice quote (which I'll misquote here and not attribute since I can't remember his name) by a Mathematician that talked about Math being impossibly hard while you try to learn it, and then after you 'see the light' and figure out that problem/idea/proof it becomes so trivially easy that you...
Wed Sep 29, 2010 4:59 pm UTC
Forum: Mathematics
Topic: Ideas for a "Quadratic Equation" class demonstration/game?
Replies: 13
Views: 7211

### Re: Ideas for a "Quadratic Equation" class demonstration/gam

One would think that if they already knew the equation they would have already done the derivation.

Kirby wrote:If they already know the equation, then you could derive it for them by completing the square.
Mon Sep 13, 2010 5:08 am UTC
Forum: Mathematics
Topic: Which is it? (straight line or circle through a portal?)
Replies: 33
Views: 5035

### Re: Which is it?

antonfire wrote:It's a straight circle.

Maybe it's bi, with hetero-circular leanings.
Tue May 11, 2010 6:02 am UTC
Forum: Mathematics
Topic: Taylor Series
Replies: 15
Views: 3231

### Re: Taylor Series

Taylor series can be thought of as a method to determine what the power series for a function is. the 1/(1-x) trick is great when it works quickly and easily... but that's not always the case. So let me get this straight: the Taylor Series is NOT a series in and of itself, but a method of FINDING a...
Mon May 10, 2010 5:04 am UTC
Forum: Mathematics
Topic: Taylor Series
Replies: 15
Views: 3231

### Re: Taylor Series

Taylor series can be thought of as a method to determine what the power series for a function is. the 1/(1-x) trick is great when it works quickly and easily... but that's not always the case. With taylor series we start off by assuming that a function does have a power series representation (center...
Wed Apr 21, 2010 5:56 am UTC
Forum: Mathematics
Topic: Wanted: punch line for joke
Replies: 15
Views: 3566

### Re: Wanted: punch line for joke

avoiding the math punchlines I'll just go with the:

Are we talking 12 oz soda or those wimpy 8oz cans?
Mon Mar 08, 2010 7:19 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 493571

### Re: What's the derivative of x?

BlackSails wrote:Why is it 0? X could very easily be a function of y.

For example, [imath]x=f(y)[/imath] where [imath]f(\cdot)[/imath]is the "append \ to the argument" function.

Other fun uses of this function are [imath]f(P)=R, f(O)=[/imath]Q, and [imath]f(|\,|)=[/imath]N.

Spoiler:
Linearize that.
Wed Dec 09, 2009 8:34 am UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66753

### Re: Wrong on the Internet: John Gabriel

I keep going back to his knol... I don't know why, maybe I feel sorry for the guy. I keep wondering if he's inflating his own ratings on the page or if he's really convincing some people that he knows what he's talking about. I hope it's him; I don't want to think about his writing misleading people...
Wed Nov 18, 2009 9:43 pm UTC
Forum: Mathematics
Topic: Fundamental Theorem of Calculus
Replies: 16
Views: 2560

### Re: Fundamental Theorem of Calculus

It's refreshing to have people want to know why a theorem works, especially when you want it enough to go and research it a bit and to ask others for some help. In the School where I've taught Calc I I've only had a very small handful of students who felt this way, most seem to just want the bare mi...
Fri Nov 06, 2009 9:09 pm UTC
Forum: Mathematics
Topic: What aspect of a fn causes integration by parts to fail
Replies: 16
Views: 2575

### Re: What aspect of a fn causes integration by parts to fail

the classic \int e^x \sin(x) \, dx class of problems where you do some integration by parts (twice) and get back the original integral, do some algebra and solve for the integral A simpler (less error-prone) approach would be to differentiate it twice. I'll admit that I don't know that tric...
Fri Nov 06, 2009 8:29 am UTC
Forum: Mathematics
Topic: What aspect of a fn causes integration by parts to fail
Replies: 16
Views: 2575

### Re: What aspect of a fn causes integration by parts to fail

Here is an "analogous" problem using only algebra. Let's solve for x! I'll start off with just an x . Of course we may write x=x . Now I'll add and subtract the same thing to the right hand side: x=x+1-1 . I'll subtract x from both sides and get 0=1-1 . Just as when you did integration by ...
Mon Sep 28, 2009 6:01 am UTC
Forum: Mathematics
Topic: Limits with square roots
Replies: 6
Views: 2262

### Re: Limits with square roots

(mr-mitch beet me to the punch!) Notice that what you did with the log's was unnecessary. In your first step you moved the half power out of the log, then did some more steps including the "key step" of getting that "divide numerator and denominator by x" involved, and finaly put...
Thu Sep 10, 2009 6:55 am UTC
Forum: Mathematics
Topic: Favorite math jokes
Replies: 1452
Views: 493571

### Re: Favorite math jokes

Monika wrote:
HINT: Use l'Hôpital's rule , multiple times if necessary.

I would argue that this is the math equivalent of a pun.

::groan::

And I would argue that it's just a bad hint.
Thu May 28, 2009 10:16 pm UTC
Forum: Mathematics
Topic: Integrals trig substituation
Replies: 4
Views: 740

### Re: Integrals trig substituation

For the limits, usually I drop the limits while doing the substitution then at the end substitute x back in and use the original limits. A number of students fall into a "bad habit" of doing this AND connecting each of their steps with "equal signs". That is they start out doing...
Wed May 20, 2009 2:16 am UTC
Forum: Mathematics
Topic: Calculus: Integration problem
Replies: 25
Views: 2191

### Re: Calculus: Integration problem

How is remembering the derivative of arctan more fundamental? Trig substitution can derive such derivatives. My use of the word fundamental assumes that the curriculum was learned in a certain order. Assuming one learns derivatives before integrals, assuming one learns forward substitutions before ...
Tue May 19, 2009 5:36 pm UTC
Forum: Mathematics
Topic: Calculus: Integration problem
Replies: 25
Views: 2191

### Re: Calculus: Integration problem

this is not a trig substitution problem. x = \sqrt{3} \tan \theta + 2 . Perhaps a more accurate statement would be there is a more fundamental tool to evaluate this integral, namely recalling the derivative of arctan and using a "u-substitution". However for the majority of students (at l...
Sat May 02, 2009 6:16 am UTC
Forum: Mathematics
Topic: Help with a Math Problem
Replies: 11
Views: 1756

### Re: Help with a Math Problem

NathanielJ wrote:I'm a little surprised that the name "Samuel" was still available on these forums. Neat.

Fri May 01, 2009 7:10 pm UTC
Forum: Mathematics
Topic: A polynomial problem
Replies: 2
Views: 680

### Re: A polynomial problem

Tibixe wrote:
Can you solve this problem?

Yes. Next.
Fri May 01, 2009 7:08 pm UTC
Forum: Mathematics
Topic: Help with a Math Problem
Replies: 11
Views: 1756

### Re: Help with a Math Problem

Taly and Marc open a Registered Home Ownership Savigs Plan that pays 6% iterest compouded semi-annually. For 4 years, they invest \$500 every 5 months in the plan. Determine the amount of interest they earn. Solution may be found by reading your text book and finding the appropriate formula to plug ...
Mon Apr 27, 2009 9:05 pm UTC
Forum: Mathematics
Topic: Any significance to this fact Re: FLT
Replies: 5
Views: 938

### Re: Any significance to this fact Re: FLT

I was all set to read something about faster than light travel and then I get Fermat instead. Oh well. Significance is all in the eyes of the beholders, and the more supporting evidence you have... the more people will see things as significant. One "general" way this may be achieved is by...
Mon Apr 27, 2009 6:19 am UTC
Forum: Mathematics
Topic: Congruent regular hexagons and distinct compartments
Replies: 2
Views: 4564

### Re: Congruent regular hexagons and distinct compartments

Here's one solution.
Fri Apr 24, 2009 10:38 pm UTC
Forum: Mathematics
Topic: Balls and buckets problem
Replies: 3
Views: 741

### Re: Balls and buckets problem

There are n buckets, each initially containing one ball. Balls are thrown, and must land in one of the buckets. The probability that a ball will land in a particular bucket is the ratio of the number of balls in that bucket to the total number of balls. How many balls must be thrown so that there i...
Wed Apr 22, 2009 2:05 pm UTC
Forum: Mathematics
Topic: Simple trig function
Replies: 10
Views: 985

### Re: Simple trig function

for some values of y you can find solutions, for example x=y=0 is a solution. for most y values though you'll likely be looking at a numerical scheme to approximate a solution.
Tue Apr 21, 2009 4:04 am UTC
Forum: Mathematics
Topic: Simple Exponent Question (highschool math)
Replies: 11
Views: 1413

### Re: Simple Exponent Question (highschool math)

Anyways, the question were were given was to write the expression 2 x + 5 as just 2 (?) (Two to the some exponent) This leads to the same answer as before but here's another way to find that answer. All you do is write down what you want. 2^x + 5= 2^{(?)} and solve for the (?...
Mon Apr 20, 2009 2:25 am UTC
Forum: Mathematics
Topic: [Request] Cramer's Rule Help
Replies: 14
Views: 2307

### Re: [Request] Cramer's Rule Help

What cramers rule is, is a way to solve a system of linear equations by turning it into a (generally) harder (to compute numerically) bunch of determinants, then doing some division. Since it's "harder" why use it, you may ask... Third paragraph in the wiki article gives a little answer to...
Sun Apr 19, 2009 9:24 pm UTC
Forum: Mathematics
Replies: 4
Views: 869

I enjoy investing my time to help people most when they need the help because they are lazy. It's a waste of my time to help somebody that puts forth effort on their own.
Sun Apr 19, 2009 6:20 pm UTC
Forum: Mathematics
Topic: Something I've been wondering...
Replies: 2
Views: 640

### Re: Something I've been wondering...

The short answer is that when you add up infinitely many things (in this case the lengths of all your little pieces) strange things can happen. You're also dealing with two types of convergence. On the one hand your "staircase" is converging to the straight line. On the other, as you point...
Sat Apr 11, 2009 6:56 am UTC
Forum: Mathematics
Topic: The MOST comprehensive math reference poster one can purchas
Replies: 18
Views: 2740

### Re: The MOST comprehensive math reference poster one can purchas

A link would be lovely :D Other's have left good things since then but I fixed my post above to include the link I intended to leave the other day. Silly me. OP, what do you mean by "300-400 level math"? A practice that some schools in the US still follow is to list freshman level classes...
Fri Apr 10, 2009 4:05 pm UTC
Forum: Mathematics
Topic: The MOST comprehensive math reference poster one can purchas
Replies: 18
Views: 2740

### Re: The MOST comprehensive math reference poster one can purchas

Here's a link to a list of links that each have math posters of some sort or other. The ones I looked at don't seem to have quite what your looking for as a single poster, but maybe you can pick and choose a few of them to get the sort of spread of topics you want. edit: Well that was bad. As was po...
Sat Apr 04, 2009 11:46 pm UTC
Forum: Mathematics
Topic: Pendulum question
Replies: 3
Views: 747

### Re: Pendulum question

Don't forget though a pendulum is a dynamical system with some fixed points. As such the probabilities of being at certain angles depends on what time interval you are looking at and whether or not it's a forced pendulum. If it's not forced and you look at it a long time after it's initial condition...
Sat Apr 04, 2009 4:43 pm UTC
Forum: Mathematics
Topic: Function extrema in general
Replies: 9
Views: 1613

### Re: Function extrema in general

Uh, if x is in V , how can f(x) fail to be in f[V] ? I'm still trying to decode the rest of your definition, but this at least doesn't seem right to me. You're right I should have said fail to be in the interior of f(V)... or as bray mentioned I really should have just remembered the word b...
Sat Apr 04, 2009 4:39 pm UTC
Forum: Mathematics
Replies: 8
Views: 1312

the tree wrote:it's simply because all mathematicians are complete bastards who want to confuse you for thier own amusement.

Don't tell other people this. It's supposed to be a trade secret.
Fri Apr 03, 2009 8:03 am UTC
Forum: Mathematics
Topic: Function extrema in general
Replies: 9
Views: 1613

### Re: Function extrema in general

I don't think you need a partial order either... at least not to find extrema. As long as you don't want to classify them as "min" or "max" or somesuch I think what you might try using as the definition of x an extreme value for f is that every open set U containing x has an open...
Wed Mar 25, 2009 6:42 am UTC
Forum: Mathematics
Topic: Laplace Transformations
Replies: 3
Views: 1033

### Re: Laplace Transformations

A common "first use" for Laplace transforms is in differential equations. You can take a differential equation, transform it into an algebra equation, solve that, then transform your answer back.
Mon Mar 23, 2009 4:33 am UTC
Forum: Mathematics
Topic: Cutting up apples
Replies: 9
Views: 1317

### Re: Cutting up apples

at each step is the interval chosen uniformly and randomly from the k+n intervals or is the distribution actually on the numbers within the intervals. i.e. are bigger intervals more likely to be chosen or at step n does each interval have a 1 in n+k shot?
Sat Mar 21, 2009 4:05 pm UTC
Forum: Mathematics
Topic: Uncountably many vertical asymptotes?
Replies: 18
Views: 2159

### Re: Uncountably many vertical asymptotes?

Okay, suppose you have uncountably many left-vertical asymptotes, i.e. a set of numbers x i for i \in I (with I uncountable) so that the limit \lim_{x \rightarrow x_i^-} f(x) = \pm \infty . For each asymptote at x i , take an open interval (a_i,x_i) that contains no other asymptotes. (There...
Thu Mar 19, 2009 6:41 am UTC
Forum: Mathematics
Topic: Here's a fun problem...
Replies: 27
Views: 3735

### Re: Here's a fun problem...

(made by a association of mine) A man on the street asks you to play a game of chance; ...What amount of money should you be willing to pay to play the game? Nothing. If a random man on the street "offers" to let you play -- You should really assume that the game is either rigged or skewe...
Fri Mar 13, 2009 5:23 pm UTC
Forum: Mathematics
Topic: Pi Day
Replies: 49
Views: 6179

### Re: Pi Day

I honestly do not understand a how anyone can logically think dd/mm is good, and I would love to hear your reasons if you care to share. Three units of measure years, months and days that have a relation, namely 1year > 1 month > 1 day. So when saying all three it seems sensible to either say the b...
Thu Mar 12, 2009 6:03 pm UTC
Forum: Mathematics
Topic: What is wrong with this differentiation?
Replies: 19
Views: 2851

### Re: What is wrong with this differentiation?

Say what? Can you tell me what this is equal to? \sum\limits_{i=1}^{5/3}\sin{i} Using the method above set y(i)=3i and then \sum\limits_{i=1}^{5/3}\sin{i} = \sum_{y(1)=3}^{y\left(5/3\right)=5} \sin \left(\frac{y}{3}\right) = \sin\left(\frac{3}{3}\right)+\sin\...
Thu Mar 12, 2009 4:05 am UTC
Forum: Mathematics
Topic: Fix My Broken Integration
Replies: 5
Views: 925

### Re: Fix My Broken Integration

The Idea behind partial fraction decomposition still works. It's just (sometimes) much harder to find the correct numerators AND once you do find the correct numerators the two (or more) pieces you have are not always easy to integrate.