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Feb
5
reviewed Approve How are 10-20 digit multiperfect and hemiperfect numbers efficiently computed?
Jan
28
comment Subtle error with a module endormorphism on $\mathbb{Z}_8 \times \mathbb{Z}_8$
Isn't the problem your assumption that if you sum a function over one set of residues and then an "isomorphic set of residues," you'll get the same answer both times?
Jan
25
comment Particular on the structure of a weight $L$-module $M$, with $L$ semisimple Lie-algebra.
No. Consider the adjoint rep of sl3: the outer weightspaces are 1-d and the zero weightspace is 2d so there is no way the map induced by the action of $e_\alpha$ from $M_{-\alpha}$ to the zero weight space can be onto.
Jan
19
awarded  Nice Answer
Jan
12
revised decomposition of $\mathbb{C}[A_3],\mathbb{R}[A_3]$ and $\mathbb{F}_{p}$ into simple algebras
typos
Jan
6
reviewed Reject Maclurin series for $\sin^2(x)$
Jan
2
awarded  Yearling
Dec
31
reviewed Approve Solutions to the heat equation, spatial or time decay?
Dec
29
comment Inverse of character table
Look at the orthogonality relations for group characters, they tell you that the character table is nearly an orthogonal matrix. That tells you the inverse.
Dec
17
comment A coordinate free book on linear and multilinear algebra defining determinants using exterior algebra
@Jxt921 Axler's Linear Algebra Done Right, which does not define the determinant via exterior powers (indeed it doesn't mention the exterior algebra at all).
Dec
17
comment What is a classic introductory text in representation theory?
"representation theory" is a pretty big topic, and it would be helpful if you could pin down what you want to know a bit (rep theory of finite groups? of associative algebras? geometric rep theory? of Lie algebras and algebraic groups?). That said, Fulton and Harris's book is classical and at times combinatorial so might be what you're looking for, though it doesn't suit everyone.
Dec
8
awarded  Revival
Nov
29
answered Proof that the number $\sqrt[3]{2}$ is irrational using Fermat's Last Theorem
Nov
24
comment Understand it or burn
Read "How to solve it" by Pòlya (even if you only remember his suggestion to ask yourself "can I solve an easier problem?" you still have something valuable). Try not to be too stubborn with problems you are stuck on: often you are taking the wrong approach, and no amount of thinking about that wrong approach will make it right. Start the problem from scratch with the rule that you must not attack it the same way as before.
Nov
24
comment Epsilon-delta definition of limit on empty/singleton domain
There isn't a "true definition," rather there are many different ones appropriate to different contexts. I agree that a reasonable definition of one-sided limit that applies to functions $f:[0,\infty) \to \mathbb{R}$ should say $\lim_{x \to 0^+}f(x)=0$ in the example you gave. Possibly the calculus text is assuming $f$ is defined on a neighbourhood of $c$ (then that iff result would be true).
Nov
24
comment Epsilon-delta definition of limit on empty/singleton domain
Yes, or just requiring $D$ has $c$ as a limit point, or that it contains $(a,c)$ for a one-sided limit -- it depends on the applications and the people the definition is being taught to.
Nov
24
comment Epsilon-delta definition of limit on empty/singleton domain
The standard way to avoid this is to only define limits for certain sets $D$, for example ones containing a punctured neighbourhood of $c$. There's no sensible way to define the limit as $x \to c$ of a function $f:\{c\}\to \mathbb{R}$ if you adopt the usual convention that $\lim_{x \to c} f(x)$ should be independent of $f(c)$.
Nov
21
answered Tensor algebra and symmetric algebra
Nov
20
comment Why does the fundamental theorem of calculus work?
+1, but it would be good to have some brackets in the first sum so it was clear you're not summing that o(1)
Nov
17
comment Property of minimal projective resolution
You're welcome. The key thing when you are stuck like this is to go back and question your assumptions about the way to approach the problem (e.g. you wanted to use Fitting on $P_n$, but maybe $P_S$ was easier). Polya's How to Solve It is worth a read.