crasic
Reputation
1,408
Top tag
Next privilege 2,000 Rep.
 Nov2 comment What is the expansion of $(1 + x)^n$? In binomial expansion its written as the sum over all the terms, that is $(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k$ Nov2 comment What is the expansion of $(1 + x)^n$? It will be 1^n + x^n, that is, assuming n is prime and we are in a field with characteristic n ! Oct30 comment Real world uses of hyperbolic trigonometric functions Lorentz transforms can be understood as hyperbolic rotations. The caternary curve (a dangling string/chain) is really just cosh Oct30 comment What should the high school math curriculum consist of? Statistics. it was an optional class in my HS, but if there is anything in math that is used more often and more maliciously to defraud people and persuade the public opinion I can't think of it. People should be aware of the limitations and the meaning of statistical results. Oct30 comment Simple Sequence Problem: Walk in the park Use the chinese remainder theorem to solve the set of congruences. The days are prime for a reason :D Oct30 awarded Citizen Patrol Oct30 awarded Critic Oct28 revised Intuitive way to understand covariance and contravariance in Tensor Algebra added 1768 characters in body; added 52 characters in body Oct28 comment Intuitive way to understand covariance and contravariance in Tensor Algebra Thanks for the response. I wasn't implying I use the matrix picture for calculations, it was just my intuitive way to understand what a mixed rank-2 tensor represents. Oct28 comment The determinant is the integral of algebra. The integral is the determinant of analysis I don't see how this is a good parallel,definite integrals can be understood as linear functionals acting on the space of integrable functions, and thus can be injected into linear algebra. But I find it hard to see how one can generalize the integral and determinant into general idea. IMHO they have many many more differences than similarities (the determinant is distinctly non-linear for instance). Oct28 comment Intuitive way to understand covariance and contravariance in Tensor Algebra Would it be fair to say that a (m,n) tensor $X_{*m}^{*n}$ takes n vectors to and m-tuple of vectors? What does this map do with covectors? Oct28 asked Intuitive way to understand covariance and contravariance in Tensor Algebra Oct28 comment StarCraft II: Ladder math Statistical equations have the nasty habit of introducing lots of symbols, numbers, and integrals. In the end though, it a pretty simple expression. Also, I dont think the phi's are meant to represent totient functions. Oct28 comment Two basic question on set theory Using your own logic, how can you get 62 proper subsets out 2^6 total subsets? Why are you subtracting two and not one? Oct28 comment Two basic question on set theory You could also get there directly, by asking how many subsets you can make out of {2,3,4,5,6} which 2^5 then subtract the one which is the whole set and get 2^5 - 1 = 31 Oct27 comment How safe is it to ignore low probability events? my point is that in most cases, a MTTF estimate includes a huge number of assumptions about what you know about the system. In a mathematically "closed" problem like SHA-256 you can be confident in these assumptions. But in most cases, multiple failure pathways are overlooked. Oct27 comment How safe is it to ignore low probability events? If the totalitarian principle is to be believed then everything not forbidden is compulsory Oct27 comment Difficulty in Mathematical Writing I understand your pain. I have lost many marks on exams a d assignments because my proof writing style is too informal. Oct27 comment How safe is it to ignore low probability events? Failure rates estimates are entirely unreliable. take for example, the Space Shuttle. Official stated MTTF is >10K launches. As both Feynman (who was on the Columbia disaster investigation committee) and reality showed, the real number is close to 50. Oct27 awarded Commentator