Mathematics

Hi, I'm considering beginning studying mathematics as an autodidact. For those of you who are knowledgeable in mathematics, i'm hoping you can help me with some of my questions. To give you some background information, i'm thinking of working through this curriculum to the best of my ability. Also, i have studied at a public high school level of calculus, but it is my understanding that, because of this fact, regressing a little might not be a bad idea. 1. Is it unwise or too difficult to pursue mathematics alone (besides having you gals and guys, i mean), given that i'll still be seeking the best textbooks available? 2. Is Philosophy of Mathematics okay t…

I'm not sure if there is a thread on this. If so, I don't know where it is. The question is, what is 00 and why?

At last, the first problem! Your posts will not appear until the competition winner has been announced. Please read the rules thread before posting a solution in this thread. This week, there are two problems (as a bonus ) for you to pit your wits against. If I can't see any correct proofs or people are struggling a lot within a decent amount of time, then I will post a couple of hints here. Problem 1: Trigonometry Values (Angles stated are in degrees.) Calculate the exact value of cos(72), and hence find the value of cos(36)-cos(72). This is a fairly simple question, but a proof is required. It's aimed at the majority of users here. Problem 2:…

Can someone explain to me what equilibrium points are when dealing with diff EQs and slope fields and such? Nathan

Let K[m,n] be a complete bipartite graph and let M and N be the set of vertices with |M| = m and |N| = n such that every edge is incident on one vertex in M and one vertex in N. I have three questions: 1. If v and w are in M, how many paths are there from v to w of length j? 2. If v and w are in N, how many paths are there from v to w of length j? 3. If v is in M and w is in N, how many paths are there from v to w of length j? For questions 1 and 2, if j is odd, the answer is 0. For question 3, if j is even, the answer is also 0. (I can prove this if anybody is interested). For question 1, assume j is even and let P = (v[0], v[1], v[2], ..., v[j]) be a path…

I wrote a small program that generates alot of regularity: $pattern= "#################################################################################################"; $r=1; for(0..366000) { $x=1/($r**2); $r=$r+0.01; @t=split/\./,$x; $t[1]=~m/^..(.)..(.)../; $p=$2.$1; print $p.' '.substr($pattern,0,$p)."\n" } You can see the result by entering c:>perl this.pl > rw and browsing through rw with word at 10% size (choose normal view) Is this a fractal or chaos or something unknown ? it is the combination of a formula and a simple logical operation that extracts a couple of digits of the pr…

Four suspects of a crime made the following statements to the police: Andy: Carl did it. Bob: I did it. Carl: Dave did it. Dave: Carl lied when he said i did it. 1.) given that one of them "did it" and that exactly one of them told the truth, who did it? 2.) given that one of them "did it" and that exactly one of the statements was false, who did it? 3.) If exactly two answers were true, who could have done it?

Can anybody make any sense of this??? A thought experiment illustrates this. Imagine a company, United Differences (UD), operating in a community that is 25 percent black and 75 percent white and 5 percent homosexual, 95 percent heterosexual. Unknown to UD and the community is the fact that only 2 percent of the blacks are homosexual, whereas 6 percent of the whites are. (The numbers are fictitious and chosen for illustration only.) Making a concerted attempt to assemble a work force of 1,000 that "fairly" reflects the community, the company hires 750 whites and 250 blacks. However, just five of the blacks (or 2 percent) would be homosexual, whereas 45 of th…

The equation of a circle [math](x-h)^2+(y-k)^2=r^2[/math] where (h,k) is the center and r is the radius. The equation of the circumference has no bearing on if it is or isn't a circle. When a circle spins, the circumference shortens and the radius stays the same. Is a circle, spinning near c, still a circle?

Is there a web site giving out a lot of difficult questions about the additional mathematics or just mathematics? I appreciate who helps me very much. I want to have far more troublesome questions:P

Here is a simple statement which I've yet to prove satisfactorily: Adding/deleting loops, parallel edges and edges in series does not affect the planarity of a graph. If a graph is planar, then removing anything from it does not create any edge crossings, so the graph remains planar. If a graph is not planar, then adding anything to it will or will not create any edge crosssings, so the graph remains unplanar. Now I have to show that adding (removing) loops, parallel edges and edges in series does not affect the planarity of a(n) planar (unplanar respectively) graph. This is were I stopped. I'm trying to think of a good argument which shows that a planar grap…

When setting up the balls before a break in a typical game of pool, the 'J' arrangement of the balls is preffered by most players. I use it operating under the assumption that it will give the most even distribution of red/yellow(stripe/dot) balls. Is there anyway to mathematically verify this if so how would one approach such a problem. I assume there will be a fair amount of probablitistic anaylsis but I cannot think for the life of me how such a problem should be undertaken. Is there a more logically sound intial layout that will insure a more even distribution. Any thoughts?

Is any one here familar with the hexadecimal system if you can you help me understand it?? Do you take the number divide by 16 the quotient is the 1st charcter and the remander is the second?? E.X. [math]173/16[/math] is 10 with remainder 13 so the hex number world be AD right??

Here are a few challenge problems to solve (I don't know what the difficulty of this board is so I would appreciate comments) 1. u and w are in degrees. tan(U)=1/2 and tan(w) = 2 find tan(u-w) 2. There are 20 switches in two columns each with 10 in them. Each switch is either on or off. If exactly 5 must be on in each column what is the number of distinct ways the switches can be set? 3. A metal plate of constant thickness is cut into a rt. triangle. The coordinates are (0,0), (2,0) and (2,1). The plate is balanced on a fulcrum on the side which connects (0,0) and (2,0). Find the x coordinate of the balance point of the fulcrum.

For finding the roots, like root(x^2), What's the value? Is that if x > 1, ans=x x<1, ans=-x x=0, ans=0? But when we do quandratic equations, (x^2)=4 x =2 or x=-2? Should we rearrange the steps as x^2=4 x=2 or -x=2?

I have learned that Dave plays trombone - I play flute. My mother was a very accomplished organist and could play 2 manuals, pedals, and change stops simultaneously. Where am I going with this? How much does mathmatical abilitity enhance musical ability and vice-versa? Think about it. You're sightreading - it's syncopated, you have to mentally compute the measure in advance to know how it will come out. If you're sight reading, and you're good at it, you're reading at least 4 measures ahead of what you're playing. Throw into the mix that the key signature and the time signature may be changing. It's challenging when you're dealing with one line of music. …

e^x=x Anybody got a solution for this? I'll post the solution later, unless someone comes up with a better one and some sort of proof for it.

I posted this on PF but it didn't get very far: Suppose {a[n]} is an increasing sequence and whenever m divides n, then a[n] = a[n/m] + d where m is a positive integer and d is a real number. Show that a[n] = Θ(lg n). I can show that a[n] = O(lg n). All I need to do is show that a[n] = Ω(lg n). This is where I'm stuck. Any hints?

I'll have: Analysis II: Hilbert spaces, Banach spaces, L_p spaces, Lebesgue measure & integration, etc. Textbook: Real Analysis by Royden Abstract Algebra III: noncommutative rings, modules, some categories, functors, tensor products, etc. Textbook: Algebra by Thomas Hungerford Set Theory: this is directed studies so I'm not sure what I'll do, except it'll probably be with the book by Kamke & the book by Suppes.

I need some closure on this one: In how many ways can the vertices of an n-cube be labeled 0, … ,2ⁿ - 1 so that there is an edge between two vertices if and only if the binary representation of their labels differs in exactly one bit? Let G be an appropriately labeled n-cube. Pick an arbitrary vertex v in G. How many ways can one change labels of the vertices appart from v in G and still mantain the properties of the n-cube? Because of the nature of G, there are n incident edges on v with n adjacent vertices. The labels of these vertices differ from the label of v by one bit. If one swaps the labels of two of these vertices and makes the appropriate swaps elsewher…

My math teacher gave us this problem. You're selling stamps. One costs 3 cents and the other costs 5 cents. People can buy as many stamps as they wish. If x is how many 3 cent stamps someone buys, and y is how many 5 cent stamp someone buys, 3x + 5y represents the price of both of them. What is the lowest price of combined stamps, 3x + 5y, so that every price after that continues at an interval of 1 cent. The next problem is what if you have m cent stamps and n cent stamps. What is the lowest combined price so that every price after that continues at an interval of 1 cent? My English may be vague and incorrect, so tell me if you need clarification.

Hey, can anyone help me understand finding an degrees of an angle in a triangle? and how to use it to find the other sides, etc. Does anyone know of anyways to learn trig easy? thanx

whats everyones mathematics skills? And what areas of maths do you reckon have helped you the most?

Given a solid sphere, construct its diameter using compass and straightedge.

Here's a teaser from my old school days. My maths teacher posed this problem to the class, and gave us five minutes. I came up with the highest number, and the teacher scoffed at my result. After expliaining my result, one student agreed with me, but the teacher said that I was wrong, and he would devote no more class time to the problem. To this day, I'm still frustrated at this teacher as I'm certain that I was the only one with the correct solution. Anyway, thirty years later, I'm after some vindication, so here it is:- Given a set of equal arm scales, like the Justice scales, and the following weights :- 1kg, 3kg, 9kg and 27kg, how many different weights can be …