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2h
comment Understanding Tensor product of modules
Please reread your question and fix LaTeX errors, e.g., write $\times$ instead of $x$ and insert the missing subscript.
9h
answered An easy example of a non-constructive proof without an obvious “fix”?
12h
comment Definition of complex conjugate in complex vector space
Maybe section 4 of math.uconn.edu/~kconrad/blurbs/linmultialg/complexification.pdf would be helpful.
16h
comment Question about a topology proof
You should include complete information, like the definition of $H$, in your question to keep it self-contained. Just imagine someone came up to you and asked "Is $h$ prime?" How would you answer that?
16h
revised Question about a topology proof
added 2 characters in body; edited title
1d
comment Who first found the value of $\int_{-\infty}^{+\infty}e^{-x^2}dx$?
@DavidK, try googling "Laplace 1774" instead and you will find better sources.
1d
revised Who first found the value of $\int_{-\infty}^{+\infty}e^{-x^2}dx$?
added 242 characters in body
1d
answered Who first found the value of $\int_{-\infty}^{+\infty}e^{-x^2}dx$?
Jan
22
comment Cyclicity of Aut ($ Z_n $)
The groups involved are so small that you should just check them directly. That is why your (homework?) problem does not have something like $U_{121}$ in it. (There are general theorems about when $U_n$ is cyclic, but it's good practice to work with the elements of the small groups to see if any are cyclic so you get some computational practice.)
Jan
21
comment Theorems discovered without observation
That $\sum_{n \geq 1} 1/n^2 = \pi^2/6$ was never conjectured before Euler found the value. Of course people before Euler could numerically estimate the series, but the decimal estimate gave no hint about such a nice closed form expression.
Jan
21
comment Theorems discovered without observation
It's a bit excessive to say "we all know" how the quadratic reciprocity law was found through experimentation.
Jan
21
comment Real world uses of hyperbolic trigonometric functions
If A occurs in B, and B in general is very important, it doesn't make A important: most of the meaty applications of B need not involve A. Therefore the appearance of hyperbolic trig functions in calculus along with the importance of calculus does not really show why hyperbolic trig functions are important.
Jan
20
comment Why is topological group not a popular topic?
If you are looking for an area of math that cares about topological groups that are not necessarily Lie groups, look to number theory and representation theory ($p$-adic groups, adele groups, infinite Galois groups,...). The development of analysis on general locally compact groups, by Weil, was motivated by such topological groups in number theory.
Jan
19
comment Why “even number of elements in Group” in this question is given?
You can't just "let" $a$ be its own inverse. There may not be such an element besides the identity. In fact, take any finite group you know with an odd number of elements and you can check by direct calculation that it has no solution to $a^2 = e$ other than the identity. In other words, the condition that $G$ have even order is not just sufficient for the equation $a^2 = e$ to have a solution besides the identity, but it is necessary as well.
Jan
18
comment Paradox of Field & Integral Domain in Venn Diagram
The fifth amendment is a single law inside the US constitution, but constitutions of all countries are a subset of all laws. Is this a paradox?
Jan
18
comment Why is $(f(x))'$ shortened $f'(x)$
(1) You do not have a balanced set of parentheses in your first equation. (2) How would you denote the derivative of the function at $x=2$? Writing $(f(2))'$ is very bad. Differentiation and evaluation do not commute.
Jan
18
comment Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
A more general partial fraction decomposition is $$ \frac{1}{k(k+1)\cdots(k+m)} = \frac{1}{m!}\sum_{j=0}^m \binom{m}{j}\frac{(-1)^j}{k+j}. $$ This is proved in one of the answers to mathoverflow.net/questions/193611/binomial-coefficient-identity/….
Jan
18
comment Calculate $ S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}. $
The sum in the question is finite, not infinite.
Jan
18
comment Embed finite field in algebraic closed field
It's not economical if you think about the time invested in proving algebraic closures exist (even just for finite fields).
Jan
18
comment Embed finite field in algebraic closed field
You do not need that property to prove two finite fields of the same order are isomorphic. None of the basic theorems about finite fields (existence, uniqueness up to isomorphism based on order, cyclicity of the nonzero elements, being perfect,...) require using algebraically closed fields.