James S. Cook
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 Jul 21 reviewed Reject Get amount of submatrixes from $a \times b$matrix Jul 21 reviewed Reject How is the derivative geometrically inverse of integral? Jul 20 comment Push-forward of vector fields by local isometries Thanks for this answer, I'm hoping to guide a promising student through the Smooth Manifolds book next year, this helps! Jul 20 revised Push-forward of vector fields by local isometries added 4 characters in body Jul 20 answered Push-forward of vector fields by local isometries Jul 20 comment Push-forward of vector fields by local isometries I would assume that the key word here is "local". We know for a local isometry the map $\phi$ is regular (meaning the local coordinate representative has full rank) hence $\phi$ suitably restricted gives a diffeomorphism from an open set $\mathcal{U}$ to another corresponding open set $\mathcal{V} = \phi (\mathcal{U})$. This is the inverse function theorem for manifolds. Jul 20 comment How to see that SL(2,C) is simply connected? Well, now answering (2.) is easy, $M$ is simply connected because $\text{Sl}(2, \mathbb{C})$ is simply connected ;) Jul 18 reviewed Approve Proof question: Prove that 2^(odd integer) + 5^(odd integer) + 2 is a multiple of 3, and 4^(any integer) + 1 can be expressed as 5n, 5n + 1 or 5n + 2. Jul 18 reviewed Reject Maths Puzzle: Partitioning a set into two disjoint sets Jul 17 revised Can the following tensors be contracted? name mispelt Jul 17 revised Natural Coordinate Functions name mispelt Jul 17 comment Continuous map $\mathbb{R}^n\rightarrow\mathbb{R}^n$ math.stackexchange.com/questions/57686/… gives you a bit in the direction of understanding that differing norms on a finite dimensional topological space (like $\mathbb{R}^n$) give equivalent topologies and hence limits. Also, see page 67-68 of supermath.info/AdvancedCalculus13.pdf Jul 15 comment “Grouping” differential equations and the appropriate methods for solving them Very well then, you'll see them soon enough. Best wishes on your exam. Jul 15 comment “Grouping” differential equations and the appropriate methods for solving them you're missing exact equations. Maybe this wasn't covered yet? Jul 15 reviewed Approve Giving two equal line segments AC and BD so that they bisect each other at E. Prove that quadrilateral ABCD is a Rectangle. Jul 15 comment Proving that $\vec F=yz(2x+y+z)\hat i+zx(x+2y+z)\hat j+xy(x+y+2z)\hat k$ is conservative field why not just find $U$ for which $\vec{F}= \nabla U$ then it is immediately true that $\nabla \times \nabla U=0$ and you have the potential to boot. Jul 15 comment Isn't this article in wikipedia wrong? (Multilinear form) on page 350 of Jacobson's Basic Algebra I he says there is a distinction between alternate and skew-symmetric. In particular, to show skew-symmetric implies alternate he notes: $b(x,x)=-b(x,x)$ implies $2b(x,x)=0$( which fails to prove $b(x,x)=0$ in the characteristic two case). Nevermind, I see you appreciate this point already and Jacobson agrees with your conclusion about the other direction. Jul 14 reviewed Approve Evaluate$\int_{-2}^2\int_{y^2-3}^{5-y^2}dxdy$ Jul 14 reviewed Approve Finding all groups of order $7$ up to isomorphism? Jul 14 comment Example tensor representation Thanks! I hope you have more questions, these are fun.