Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #11226 20130606 06:17:45
Re: Linear Interpolation FP1 FormulaSo far I did Q1, Q2, Q3, and am about to finish Q5 when I start under mock exam conditions again. #11227 20130606 06:22:32
Re: Linear Interpolation FP1 FormulaThat is very good! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11228 20130606 06:23:32
Re: Linear Interpolation FP1 FormulaThanks  do you agree that those are the easiest? #11229 20130606 06:25:51
Re: Linear Interpolation FP1 FormulaI hope not, I have not looked at the others yet. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11230 20130606 06:27:15#11231 20130606 06:30:14
Re: Linear Interpolation FP1 FormulaNope, I am wondering how to do them. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11232 20130606 06:31:08
Re: Linear Interpolation FP1 FormulaHi zf. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11233 20130606 06:32:28
Re: Linear Interpolation FP1 Formulamaths helper . co . uk / oxb . htm (remove spaces) #11234 20130606 06:38:35
Re: Linear Interpolation FP1 FormulaThat is a better link , I can download it. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11235 20130606 06:39:09
Re: Linear Interpolation FP1 FormulaYeah it's the best link to use, although some of the links stopped working recently... #11236 20130606 06:47:27
Re: Linear Interpolation FP1 FormulaI am looking at 1. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11237 20130606 06:49:59
Re: Linear Interpolation FP1 FormulaI thought you might like that question, it is similar to some GF problems we did... #11238 20130606 06:52:19
Re: Linear Interpolation FP1 FormulaThat is what I am doing with it. It is a partition problem actually. We can look at it when you are done, if you like. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11239 20130606 07:06:04
Re: Linear Interpolation FP1 FormulaSure, that would be great. #11240 20130606 07:28:12
Re: Linear Interpolation FP1 FormulaYou are doing STEP II, year 2012? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #11241 20130606 08:17:40
Re: Linear Interpolation FP1 FormulaYes, I just finished that one, haven't checked my answers yet though. Thought it was quite a nice paper, lots of accessible questions not requiring that much work. Hopefully the mark scheme will not be harsh. #11242 20130606 08:32:01
Re: Linear Interpolation FP1 FormulaJust done marking... lots and lots of silly errors but definitely a solid 1 or possibly a low S if I got a generous examiner. Happy times! I am just glad I did not embarrass myself. #11243 20130606 11:17:16
Re: Linear Interpolation FP1 FormulaThat is very good. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11244 20130606 11:18:43#11245 20130606 11:30:12
Re: Linear Interpolation FP1 FormulaYes, I have not looked at it because I just got back home. It was like 110 or something over there. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11246 20130606 19:47:58
Re: Linear Interpolation FP1 FormulaI am interested in seeing how you did it  given that they asked for the coefficient of x^k for (relatively) small k, I just used arithmetic. #11247 20130606 19:56:16
Re: Linear Interpolation FP1 FormulaHope I can remember it offhand. Correct me if I make some silly mistake. is that correct? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11248 20130606 19:59:26#11249 20130606 20:18:10
Re: Linear Interpolation FP1 FormulaIf we think of this as a partition problem then that has the polynomial representation of. This is the generating polynomial for the number of ways you can form a sum using sixes and threes. We can now enumerate the possibilities by filling in the 3 polynomials. You can have (4 sixes)(0 threes) 1 way (0 threes)(4 sixes) 1 way (3 sixes)(1 six)(0 threes) 1 way (1 six)(3 sixes)(0 threes) 1 way (2 sixes)(2 sixes)(0 threes) 1 way (2 sixes)(1 sixes)(2 threes) 1 way (1 sixes)(2 sixes)(2 threes) 1 way (3 sixes)(0 sixes)(2 threes) 1 way (0 sixes)(3 sixes)(2 threes) 1 way (1 sixes)(1 sixes)(4 threes) 1 way (2 sixes)(0 sixes)(4 threes) 1 way (0 sixes)(2 sixes)(4 threes) 1 way (1 sixes)(0 sixes)(6 threes) 1 way (0 sixes)(1 sixes)(6 threes) 1 way (0 sixes)(0 sixes)(8 threes) 1 way total ways 15. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #11250 20130606 20:27:35
Re: Linear Interpolation FP1 FormulaOh I see, so you treated (1  x^6)^(2) as the square of a geometric series. That looks pretty neat. The binomial expansion of it has the triangular numbers as coefficients (and then I used the same method as you, pairing up the exponents). 