network profile
| bio | website | |
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| visits | member for | 8 months |
| seen | Oct 9 '12 at 3:52 | |
| stats | profile views | 39 |
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Sep 14 |
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Is the set of integer coefficient polynomials countable? An integral polynomial gives a function from $\mathbb{Z} \rightarrow \mathbb{Z}$. A power series doesn't. A polynomial is a finitely generated algebra over the co-efficient ring a power series is not. |
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Sep 14 |
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Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? A hlibert space is still a vector space...what do you mean by a operator which is not linear? |
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Sep 14 |
awarded | Commentator |
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Sep 14 |
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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. |
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Sep 13 |
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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. |
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Sep 13 |
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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 $X$. |
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Sep 13 |
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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. |
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Sep 13 |
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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 |
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Sep 13 |
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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. |
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Sep 13 |
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Connectedness of centralizer exercise Look at any discussion on Spec of a commutative ring (like exercise to the fist chapter of Atiyah Macdonald). |
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Sep 13 |
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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. |
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Sep 13 |
answered | Some question on filtrations |
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Sep 12 |
answered | What's a good place to learn Lie groups? |
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Sep 12 |
answered | Trivilisations of Vector Bundles |
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Sep 12 |
answered | Suggestions for further topics in Commutative Algebra |
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Sep 12 |
answered | How many subsets are there in a set of size $n$? No combinatorics |
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Sep 12 |
awarded | Editor |
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Sep 12 |
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Derivative of $f(s) = \frac{1}{\prod_{k=1}^{n}(x_k-s)}$ sorry ! typo fixed. |
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Sep 12 |
revised |
Derivative of $f(s) = \frac{1}{\prod_{k=1}^{n}(x_k-s)}$ added 26 characters in body |
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Sep 12 |
answered | Local Isomorphism on Topological Groups |
