Mathematics

I'll probably be taking math class at local college in my senior year. I know that the best way to choose class is to contact with the college's math department but I wonder what you guys think will be a good class to take. I know some NT, combinatorics, algebra, trig, geometry, and hopefully be able to learn some graph theory/invariant sometime in future before my senior year. I personally do not like calculus much so good tip? Also, if I take class at local college, will this go as a part of my regular transcript or count as "AP" type credit? Thanks.

Hey, i am little puzzled by this question.... i get that none of the sets (a,b or c) are orthogonal when taken over -infinity to infinity. am i doing something wrong, i would have thought at least one of them would be orthogonal...??? this is the problem in question: the inner product i think i am meant to be using is: <f|g> = ?f*g where the thing on the left (f*) is complex conjugate of f. the combinations i tried were: (a) cos(x) & 3sin(x) (b) 1 & (-x+1) © x * 4x^{3} i would have thought that cos(x) & 3sin(x) would be orthogonal...?? or is it that i am not meant to be integrating from -infinty to infinity? (that is …

any suggestions? I think have to use partial fraction decomposition but I don't seem to get anywhere...

Hey everyone, i am having a bit of trouble trying to do this question. how do i show that they are linearly dependent ? i tried using the wronskian but this doesnt work does it? (because just because the wroskian is 0 on the interval it doesnt neccessarily mean that the two functions are dependent, right?) this is what i have done so far: (a) for 0<t<1 |t| = t so f(t) = t^2.t = t^3 = g(t) therefore f(t) and g(t) are linearly dependent on 0<t<1 for -1<t<0 |t| = -t so f(t) = t^2.-t = -t^3 = -g(t) therefore f(t) and g(t) are linearly dependent on -1<t<0 for -1<t<1 because f(t) is a different mult…

I hope I am not bothering you guys with too many questions and post I am clueless, tried changing it to csc^2(x)csc(x) but doesn't help neither does csc(x)(1+cot^2(x))

hey all, just having a bit of trouble with this problem... i have done a little bit on it, just thought i'd let you guys look at it first, because i havent been able to type up my solution yet. Cheers guys & gals Sarah

this problem, I don't even have a clue where to start...

I not sure which maths forum to stick this in so I'm putting it here I don't mind if it gets moved though. I was thinking about this earlyer and its been bugging me for a while now. Say you have two numbers 1 and 2 isn't there an inifnate amount of numbers between them? Like 1.999' So how can we ever get from one to the other? Does that make sense I'm going crazy here!

Hey, I'm currently struggle with these two proofs, if anyone can help me I would be very thankful. 1. prove that one of the roots of x^3+ax^3 +bx + c = 0 is the negative of another if and only if c=ab. 2. Prove that if the diagonals of a quadrilateral divide it into four triangles of equal area, then the quadrilateral is a parallelogram.

I have a assignment due by Friday and ive done most of it but a few problems are really killing me and I was wondering if I could get some help and by help I mean the answers lol to some problems if u can help me I will be greatly apprciative. 3. Find the length of arc S, if r= 10 and its like a 0 with a line in the middle = pie over 6. 4. Find the area A of the sector if the 0 with the line in the middle = pie over 4 and r = 6 5. If the latitude of Chicago is about 42 degrees and the radius of the earth is about 4000 miles, how far is Chicago from the eaquator? (use pie = 3.1416) please can some one help me its a matter of life and death lol.

From now on, I will use this thread to inquire my math questions that I have. I don't want to create a new thread for everytime when I have a single, small math question. Waste of time in my opinion. Also, to let everybody know, those math questions will never be my homework. They are just some bogus math questions that I see around or on the Internet. IT'S NOT MY HOMEWORK. Awhile ago, I just found this old Fermat Competition booklet in my bedroom that I entered last year (A Canadian National Math Contest), and I have this question. When [math]a=\frac{1}{2}[/math] and [math]b=\frac{2}{3}[/math], what what does [math]\frac{6a + 18b}{12a + 6b}[/math] equals? I…

how to solve this: sin(z)= i where z =x+iy. (or if we have sin(z) = ni where n belongs to N(natural number) in general. It's a question of a quiz and I don't know what kind of equation it is) Thanks in advance

Hi all, i am having a lot of trouble trying to do this problem, as my textbook does not discuss circuits and it is only covered in 3 very brief lecture slides. if anyone would be able to point me to some good websites on how to do these type of problems or be able to help me in any other way that would be great! Thanks guys & gals! -Sarah

Hello, Recently I stumbled across a math problem, that I hope you can help me with. It is really about defining a planetary orbit from very little data, but since all orbits are ellipses I might as well post it here too (it has also been posted in the astronomy subforum). I'm building a simple 2D program that simulates gravitiational attraction between celestial bodies. The program is strictly Newtonian - it calculates all movement using F = G*(M+m)/d^2 - but I'd like to calculate backwards so to speak and find the details about any orbit's eccentricity, orbital period, orbit centre and foci ect ect. All the data I have is: -body's velocity vector length …

terrence mckenna derived the FRACTAL TIMEWAVE out of the KING WEN sequence of the I CHING. i have looked at his math and it is very complicated and i do not understand, plus I know nothing about FRACTALS except that they relate to the structure of CRYSTALS. it is my theory that the universe is really just one big giant CRYSTAL and i think terrence mckenna went a long way to prove that with the timewave. he says that history is feeding back on itself and that time resonates over and over again and that these resonances are increasing and will reach infinity in THE YEAR 2012 WHICH IS THE END OF TIME. he does not explain what happens in 2012 but says that man…

Hi I hope someone can help me. Are there any good websites for learning logic? I've just been trying to figure out antecedents and consequents and the two valid ways and the two invalid ways of arguing them. I'm confused by the following sets of propositions: If I buy the correct ticket then I'll win the Lottery. I'll win the Lottery only if I buy the correct ticket. The consequents and antecedents are reversed from one the the other, yet one of them can be a true statement and the other not?

if y_1 and y_2 are the answers of this equation: (d^4 y/dx^4) + 4 y = f(x) then what's y_2 - y_1? I used laplace Transform! Thanks in advance

I'm currently in a linear algebra class and we are doing a massive amount of proofs, something that is foreign to me. Every time I'm asked to do a proof my effort turns into a narrative argument, and my problem isn't knowing why something is true or not. I piece it together in my mind and can argue it, and if I had to teach somebody whether or not something is true I have faith in my abilities to do so, but I'm having difficulty providing any type of valid mathematical proof. What's lost on me appears to be the logic behind the language of proofs and what assumptions can be made when doing them. A lot of proofs make perfect sense to me when I read them, but somet…

how many times would you have to shuffle a deck to wind up with all the cards in the original order?

a friend of mine said there was a way to prove 4 is more than 5 could anyone please explain?

I really dont know where to go with this one. A boat sails across a straight river of uniform width W, starting from a point O on one bank of the river. The velocity of the river at a distance y from the bank is u(y)=ay(W-y), where a is a positive constant. The boat travels at a constant speed v relative to the current and steers a course set at a constant angle p between 0 and pi. in the downstream direction. a) show that the velocity of the boat is (u+vcosP)e1+(vsinP)e2. b)at what time does the boat reach the other bank? c) show that when the boat has reached the other bank, the downstream distance it has travelled is equatl to [math]\frac{aW^3}{…

Hi, i hav a problem which i am unable to solve. it is from the chapter on trigonometry here goes: A vertical rod is fixed in a horizontal rectangular field ABCD. The angular elevations of its top from A, B, C and D are alpha, beta, gamma and delta respectively. Show that: cot^2 alpha - cot^2 beta=cot^2 delta - cot^2 gamma plzz help me with this and post the solution as soon as possible

In one of Terry Pratchett's Discworld novels he describes the Proverbial Quantum Butterfly as having infinitely complex wings that had an infinite edge and therefore an infinite area. A friend of mine disagree's with this and says that as Koch's snowflake fits can fit into a circle with a finite area, the snowflake itself must also have a finite area, although I agreed with that at first but then I figured that sometimes things are not that simple, as with Gabriel's Horn and the other stuff I don't understand. So if something has an infinite perimeter, then does it have to have an infinite area?

Hey guys, tis my first entry so apologies if I seem a little nervous! My friend and I were having a healthy debate on rather silly physics theories as we do. My friend then suggested the existance of irrational dimensions. This seemed far more silly than any other but i found some proof off a website i cant remeber the address of. I would like to open this thought up to debate - irrational dimensions or at least non-integer dimensions (like 4.3rd dimension or the e'th dimension) Thanks all!! Perry.

Hey, I read this question a while ago and was wondering if anyone could come up with proof for this question. Let a1,a2,a3,a4, and a5 be any distinct positive integers. Show that there exists at least one subset of 3 of these integers whose sum is divisble by 3. (Use the fact that every integer can be writtein in the form of 3k, 3k+1, 3k+2, where k isa int). Thanks, this question has been bothering me for quite some time now