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 Nov 4 comment Is speed an important quality in a mathematician? @mike too true unfortunately. I've lost many points on exams that had I had more time to think I would have solved completely. There must be some middle ground between the free for all of a take home exam (there are not very many questions you can ask on an undergraduate exam that won't be proven in some book) and the stressful race of a sit-in exam. Nov 4 comment Is speed an important quality in a mathematician? It sure helps on mathematics exams! Nov 3 accepted Finite rings of prime order must have a multiplicative identity Nov 2 revised Finite rings of prime order must have a multiplicative identity added 68 characters in body Nov 2 asked Finite rings of prime order must have a multiplicative identity Nov 2 accepted Intuitive way to understand covariance and contravariance in Tensor Algebra Nov 2 answered Proof that polynomial multiplication works Nov 2 comment What is the expansion of $(1 + x)^n$? In binomial expansion its written as the sum over all the terms, that is $(x+y)^n = \sum_{k=0}^n \binom{n}{k} x^{n-k}y^k$ Nov 2 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 ! Oct 30 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 Oct 30 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. Oct 30 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 Oct 30 awarded Citizen Patrol Oct 30 awarded Critic Oct 28 revised Intuitive way to understand covariance and contravariance in Tensor Algebra added 1768 characters in body; added 52 characters in body Oct 28 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. Oct 28 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). Oct 28 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? Oct 28 asked Intuitive way to understand covariance and contravariance in Tensor Algebra Oct 28 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.