s.b

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seen Oct 9 '12 at 3:52

Sep
14
awarded  Commentator
Sep
14
comment homeomorphism question relating to the topological 3-sphere
You are talking about the usual construction of $S^{3}$ the one asked is bit unusual. In general there are many ways to triangulate a surface (and here break up a solid into polyherdral parts: essentially a CW complex). If you keep track of the smaller parts and their intersections you can decompose the solid into more manageable parts. The question is showing the sphere is two solid tori.
Sep
13
comment The matrix exponential: Any good books?
For finite dimensional matrices you are essentially talking about exponential maps on lie groups. So look up any elementary nook on lie algebras and lie groups (may be it is worthwhile to consider compact lie groups first). Off hand I can think of M.Artin's Algebra, Bump's Lie Groups.
Sep
13
comment Notation Issues
I am guessing here, but most likely $S^{\star}X$ would be the space of Schwartz Bruhat functions on $X$. If you do not know what that is it is better to work with a healthier substitute and you can assume $S^{\star}X$ is space of smooth (infinitely differentiable) compactly supported real functions on $X$.
Sep
13
comment What branch of mathematics is most needed in the industry or how one can make living with mathematics (apart from teaching)?
I think you need to define relevant job more clearly. If you wish to maximize your chances at a financial institution studying economics or perhaps mathematical economics is more useful. Studying mathematics for that purpose is not the most efficient route.
Sep
13
comment Proving that there are infinitely many primes with remainder of 2 when divided by 3
Use Dirichlet's theorem on primes in Arithmetic progressions. Well it is an overkill but you don't have to do anything.en.wikipedia.org/wiki/Primes_in_arithmetic_progression
Sep
13
comment I've heard that some kinds of mathematics are so abstract, what's the point in it?
I do not understand if you mean abstraction of programing languages in a concrete technical sense or a rather loose figurative sense. But, mathematics is no more abstract to a mathematician than playing a (difficult) piece of music to a pianist. Of course to an outside r it looks strange and esoteric.
Sep
13
comment Connectedness of centralizer exercise
Look at any discussion on Spec of a commutative ring (like exercise to the fist chapter of Atiyah Macdonald).
Sep
13
comment Connectedness of centralizer exercise
As you computation shows, the points lying in the centralizer of t in Sp(4) is an algebraic variety over $K$ (same in the Gl4 case but slightly more complicated). The relevant topology topology is the Zariski topology. More concretely, look at the ring $ K[x_{1}. \ldots, x_{8}]$ and quotient it by the ideal $(x_{1}x_{7} -x_{5}x_{3}, x_{1}x_{8} + x_{2}x_{7} - x_{3}x_{6} -X_5}x_{4})$ and show that the resulting quotient has idempotents.
Sep
13
answered Some question on filtrations
Sep
12
answered What's a good place to learn Lie groups?
Sep
12
answered Trivilisations of Vector Bundles
Sep
12
answered Suggestions for further topics in Commutative Algebra
Sep
12
answered How many subsets are there in a set of size $n$? No combinatorics
Sep
12
awarded  Editor
Sep
12
comment Derivative of $f(s) = \frac{1}{\prod_{k=1}^{n}(x_k-s)}$
sorry ! typo fixed.
Sep
12
revised Derivative of $f(s) = \frac{1}{\prod_{k=1}^{n}(x_k-s)}$
added 26 characters in body
Sep
12
answered Local Isomorphism on Topological Groups
Sep
12
awarded  Teacher
Sep
12
answered Derivative of $f(s) = \frac{1}{\prod_{k=1}^{n}(x_k-s)}$