Linear Algebra and Group Theory

The defenition of point is very abstract, it is defined as an entity with a position in space but has no length, height or width. So please explain to me how can you diferrentiate the no. of points in a line segment of two different lengths, which are of course infinite but they are visibly different. Can I find a more plausible defenition. HELP!

Hi Everyone, I just learnt this game and ever since have been thinking about it. But couldn't figure it out with that garbage bag over my shoulder. So, I decided to post it here, but was a bit confused with where to post it. So, here it is - 1. First take 52 cards. 2. Tell Someone to think of a card in his mind. (Don't seperate the card, just think of it) 3. Then make three sets of card - I mean two sets will have 17 cards and one will have 18. (Make the sets like when u distrubute cards when u r playing a game , don't just take 17 , then 17 and then 18. Distribute them) 1 1 1 2 …

First off, I can't cope with anything much beyond high school math, but given that restriction, can anyone enlighten me as to what a modular form is and why they are marvelous mathematical objects? I managed to read all of Simon Singh's book on Fermat's Last Theorem without gaining any insight into what a modular form is. Funnily enough, I just looked on Amazon and the first reviewer, who is clearly a mathematician, enjoyed the book but complains about precisely this point- if you don't know what a modular form is then you miss the main idea behind the proof. (P.S. Such is my ignorance that I don't even know whether this is the best subforum for this question. Mod…

Skipping the mathematics....explain Chaos and it relation to the real world.

I am using the http://www.aleks.com/ system in class and was wondering two things. Has anyone used this system and can tell me what to expect from the students and two what are some good notions to carry into a classroom filled with mostly 20 year old kids who are in remedial algebra in college?

And lots of it. http://pi.autopron.org/pi Enjoy.

Australian aborigines use a "Moiety" system which avoids in-breeding when living in small nomadic groups. It is universally understood by local people and they consider the system mathematically obvious. Non-aborigines find it confusing. (Take a look at the attachment). It's not complicated in a cultural context, e.g. at a barbecue, "So your name's Christopher. How do you do? Please introduce me to your wife Stephanie and your kids Emile and Emily." This is because every Christopher you've ever met has a wife called Stephanie. All Christophers have sisters and brothers called Christopher or Christine. All their Children are called Emile and Emily. All their f…

is there a connection. Could one do a college level project on the two subjects and their corralation?

I'm bored, so here's a nice piece of maths: Simplify sqrt(2 + sqrt(3)) - sqrt(2- sqrt(3)). A few of you may have already seen this - if so, don't spoil it for the others. It's not supposed to be hard, but it's fairly nice.

does anyone here have an algorithm for random number generation? I know there are analogue ways (electonic) to produce this. and various digital ways using shift registers to generate a number sequence that doesn`t reoccur till so many 1000 steps. but is there an equasion/algorithm that will do this? I considered the use of Pi, as that seems to go on forever. is there an algorithm to calculate Pi?

I'm starting the class monday. For those who have taken it, then what's it like? how is it compared to calc 1&2? i dunno, just start talking about calc 3. -edit- sorry about this being in the number theory forum, i'm sure you all know where I MEANT to put it. =P my mistake

i saw something similar to the regular argument used to prove 1=2 the other day, and i thought i'd share it in here since these forums seem a little dead on the maths side sometimes it goes like this: (cos(x))^2 = 1 - (sin(x))^2 then, 1 + cos(x) = 1 + sqrt(1 - (sin(x))^2) squaring, (1+cos(x))^2 = (1+sqrt(1 - (sin(x))^2))^2 now when x = 2*pi/3: (1-1/2)^2 = (1 + sqrt(1-3/4))^2 1/4 = (1+sqrt(1/4))^2 therefore 1=9 i haven't looked at it much, as mainly i find these things tedious, but i thought it was quite neat so here you are. enjoy

Reply #3 quote: Personally I think pi, the ratio between the diameter of a circle and its circumference, is much more amazing, and appears in a much wider variety of places, but we all recognise it as 'part of the woodwork', so it's invisible. MrL Jakiri wrote that. I found the statement so tantalizing I must as him or anyone to elaborate. Tell me of the wonder of Pi.

Could it be that the make-up of atoms and other sub-atomic particles are actually like fractals? That is, a pattern going on for infinity?

On the following: three men enter a hotel and ask a clerk for a room for the night the clerk tells them that the cost for the room is $30.00. each of the three pays $10.00 (totalling $30.00). the manager later sees the guest book and realizes that he know these men and decides to give them a discount. he tells the clerk to refund the guys a total of $5.00. the clerk takes out $5.00 and thinks to himself, how do i divide $5.00 between three people? ultimately, he decides to give the guys $1.00 each ($3.00 total) and keep $2.00 (totalling to $5.00 as the manager requested). where the problem occurs is when you try to add it all together and you try to muliply and b…

i couldn't find where to put this one so i put it here. there is a math problem that i had heard once before that puzzled me. i'm not a math genious and hell, i have a hard time understanding algebra at times. the only way i can explain this one is by telling the story as i heard it. i haven't tried to find an eaisier way of explaining it so here goes. bear with me. three men enter a hotel and ask a clerk for a room for the night the clerk tells them that the cost for the room is $30.00. each of the three pays $10.00 (totalling $30.00). the manager later sees the guest book and realizes that he know these men and decides to give them a discount. he tells the clerk to …

Using the Bailey-Borwein-Plouffe algorithm, it is possible to calculate any digit in the hexadecimal expansion of pi without calculating any of the preceeding digits. :pi: = :lsum: (4/(8n+1) - 2/(8n+4) - 1/(8n+5) - 1/(8n+6))*(1/16)n for n=0 to :inf: Is there ever a hope of formulating an equivalent in decimal form? What does this say about whether pi might have an ending?

Dear frands! Prompt please references to works in which it was considered the Schrodinger equation with stochastic (random) Gaussian delta-correlated potential which time-dependent and spaces-dependent and with zero average (gaussian delta-correlated noise). I am interesting what average wave function is equal. U - potential. <> - simbol of average. P(F) - density of probability of existence of size F. Delta-correlated potential which time-dependent and spaces-dependent: <U(x,t)U(x`,t`)>=A*delta(x-x`) *delta(t-t`) delta - delta-function of Dirack. A - const. Zero average: <U(x,t)>=0 Gaussian potential (existence of probabili…

I have another math question. i was wondering if other fields of mathematics are used in physics besides calculus. I know geometry is used in physics but i dont know how much algebra is used in it. i was wondering if it would be useful to learn all types of math besides only calculus such as algebra and geometry and if it would be worth the effort in order to understand physics and higher mathematics in general. i didnt know exactly where to put this so i just put in the algebra section.

If x is a positive integer, what is one possible value of the units digit of 103^2x after it has been multiplied out. What does that mean?

Just for fun. Proof: Suppose that a=b. Then a = b a^2 = ab a^2 - b^2 = ab - b^2 (a + b)(a - b) = b(a - b) a + b = b a = 0 -- 1$ = 100c = (10c)^2 = (0.1$)^2 = 0.01$ = 1c -- Proof: 1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1 Also one can disprove the axiom that things equal to the same thing are equal to each other. 1 = sqrt(1) -1 = sqrt(1) therefore 1 = -1

I have a friend who started out many years ago studying mathmatics, game theory and topology. It has always interested me, however as a Dyslexic I have some obvious issues to work around. Is anyone here a fan of Topology? Bill

Not sure what forum this goes under, so someone will have to move it to the right area. Could someone explain to me fibonacci numbers? I tried google, but all I came up with was a bunch of sites that show how cauliflower has rows that spiral outwars, and so do pine cones My calculus teacher mentioned something about the ratio between your forehead and your bellybutton, and belly button to your toes is always the same for every person. Fibonacci was in the same sentence, but I didn't catch what he was trying to say about them (distracted w/ the fine specimen of female beside me). From what I can gather they are numbers that commonly occur throughout nature??

I Love Math! My daughter, age 9, has a book of Mensa puzzles for kids. She hit me with this one: A guy recycles candle stubs and can make 1 new candle out of 7 stubs. How many candles can he make out of 679 stubs? The solution is simple: Stubs, Candles Made, Leftover Stubs 679, 97, 0 97, 13, 6 19, 2, 5 7, 1, 0 Answer: 113 So, I’m teaching myself calculus and I know that I can find a general solution for this problem. Well…not quite. I know that the answer is a series: f(x) = { (x/(7^1)) + (x/(7^2)) + (x/(7^3)) + ... + (x/(7^n)) } Testing the series with some actual values I get: x, f(x) 679, 113.120 15,139, 2,552.103 3,020,302, 503,…

I just want to let everyone know that I have won the USAA National Mathematics Award! I have never heard of the USAA before the other day, but believe me, I was honored. I think this is my first award ever!