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Prove that the manifold $SO (n)$ is connected The question really is that simple: Prove that the manifold $SO (n) \subset GL (n, \mathbb {R})$ is connected it is very easy to see that the elements of $SO (n
What is the relationship between SL (n) and SO (n)? I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la
Boy Born on a Tuesday - is it just a language trick? The only way to get the 13 27 answer is to make the unjustified unreasonable assumption that Dave is boy-centric Tuesday-centric: if he has two sons born on Tue and Sun he will mention Tue; if he has a son daughter both born on Tue he will mention the son, etc
Fundamental group of the special orthogonal group SO(n) Also, if I'm not mistaken, Steenrod gives a more direct argument in "Topology of Fibre Bundles," but he might be using the long exact sequence of a fibration (which you mentioned)
The Tuesday Birthday Problem - Mathematics Stack Exchange In case this is the correct solution: Why does the probability change when the father specifies the birthday of a son? (does it actually change? A lot of answers posts stated that the statement does matter) What I mean is: It is clear that (in case he has a son) his son is born on some day of the week
Representation theory of $SO (n)$ - Mathematics Stack Exchange Regarding the downvote: I am really sorry if this answer sounds too harsh, but math SE is not the correct place to ask this kind of questions which amounts to «please explain the represnetation theory of SO (n) to me» and to which not even a whole seminar would provide a complete answer The book by Fulton and Harris is a 500-page answer to this question, and it is an amazingly good answer
Diophantus Lifespan - Mathematics Stack Exchange "The son lived exactly half as long as his father" is I think unambiguous Almost nothing is known about Diophantus' life, and there is scholarly dispute about the approximate period in which he lived