2,120 reputation
21344
bio website anhhuy.ch
location Switzerland
age 22
visits member for 4 years, 1 month
seen 2 mins ago

My name is Anh Huy Truong and I am currently studying mathematics at the ETH Zürich.


Dec
16
comment Why is the axiom of choice not taught from the start to mathematics undergraduates?
Every lecturer in my first year courses explicitly stated that they were using the axiom of choice, so I think it depends on the lecturer/university?
Dec
9
comment A question about surjective functions.
I did use comments to point out what I disagree about. If you have only seen the use of $f^{-1}$ in the sense of the inverse function, I suggest you look up the "preimage" of a function.
Dec
9
comment A question about surjective functions.
I downvoted because I disagree with your answer.
Dec
9
comment A question about surjective functions.
OP is looking for a surjective function f such that $f^{−1}(f(A))\neq A$. Only applied to sets, the use $f^{-1}(Y):=\{x\in X|f(x)\in Y\}$ is rather popular.
Dec
9
comment A question about surjective functions.
I think it might be a bit pedantic but @Leox never explicitly said that $f^{-1}(x) = \sqrt{x}$ is supposed to be the inverse function of $f(x)$.
Dec
5
comment A simple way to evaluate $\int_{-a}^a \frac{x^2}{x^4+1} \, \mathrm dx$?
@Venus: To evaluate $\int_{-\infty}^\infty \cos(x^2) \, \mathrm dx$, substitute $t = x^2$ and use $t^{-1/2} = \pi^{-1/2} \int_{-\infty}^\infty e^{-tu^2} \, \mathrm du$. Then use Fubini's theorem.
Feb
16
comment How can I find a non-negative interpolation function?
Do you have any idea what the constant you use to subtract depends on in order for the resulting function to being non-negative?
Feb
16
comment How can I find a non-negative interpolation function?
I was thinking about using the logarithm method after all by simply adding a constant to my values (e.g. $y_i + 1$) and then taking the logarithm. However, when I then take the exponential of the resulting interpolating polynomial, is there a formula to find the constant I have to subtract in order to get back? In the examples I tried out I could not find any regularity and most importantly the constant $-1$ does not work. :-(
Feb
16
comment How can I find a non-negative interpolation function?
I think the dirty solution will be best suited for my problem. I have values $y_i = 0$ which rules out taking the logarithm (or is there a solution for that issue?). However, if I am using Hermite interpolation (i.e. I want to interpolate derivatives as well), what values do I take for the derivatives? Simply the square roots?
Dec
9
comment Showing that a matrix is positive (semi-)definite
I'm sorry I didn't refer to the paper earlier. I asked for an alternative proof because the proof provided was not very intuitive to me, i.e. I would have never been able to come up with it. Since you came up independently with basically the same proof: Is there any logical reason for introducing that matrix and decomposing the matrix $D$ as in your answer? Is it just experience or is there a deeper reason? I have never seen this kind of decomposition yet which is why it was rather odd for me.
Dec
9
comment Showing that a matrix is positive (semi-)definite
@DavidSpeyer: I put it for completeness. Sorry if it confused anyone.
Dec
9
comment Is the matrix corresponding to an equivalence relation positive semidefinite?
My question actually arose from this. I had a graph and the matrix $A$ had entries $1$ if two vertices belonged to the same connected component and $0$ otherwise. However, I did not know about the eigenvalues of a clique (or maybe I just forgot).
Dec
9
comment Is the matrix corresponding to an equivalence relation positive semidefinite?
Sorry, I misread. That makes a lot more sense now.
Dec
7
comment Showing that a matrix is positive (semi-)definite
@Casteels: Was there a comment that is deleted now?
Dec
5
comment Showing that a matrix is positive (semi-)definite
@Casteels: I'm sorry I completely forgot. The diagonal entries are 1.
Nov
22
comment Planning a mockup maths class for high school related to river reactivation
(or just of river regulation, sorry, I missed the 5 minute edit time span)
Nov
22
comment Planning a mockup maths class for high school related to river reactivation
@WillieWong: It is the inversion of canalisation of a river.
Aug
21
comment Proving Sylow's first theorem
Which implication are you talking about?
Aug
21
comment Proving Sylow's first theorem
Yes, $S_i$ is not necessarily a subgroup. That is the point of the equation $\operatorname{Stab}_G(S_i) = S_i$: As the stabilizer IS a subgroup, it implies that $S_i$ is too.
Aug
21
comment Proving Sylow's first theorem
Aren't order and cardinality of sets the same thing?