10,316 reputation
1031
bio website danshved.wordpress.com
location Moscow, Russia
age 28
visits member for 2 years, 1 month
seen 5 hours ago

I'm a graduate student at MIPT, Russia. My thesis is in the theory of groups, but I like lots of other things too )


5h
awarded  Caucus
Oct
30
awarded  Yearling
Oct
27
comment Given $z_1, z_2$ prove that $4z^2_1+9z^2_2 = 0$
Also, even with De Moivre, there's no need to use approximate values written as decimal fractions. Write precise expressions, there's less of a chance to make a mistake that way.
Oct
27
comment Given $z_1, z_2$ prove that $4z^2_1+9z^2_2 = 0$
Too lazy to check, but did you calculate the $\cos$ and $\sin$ on a calculator? If so, there's a high risk of a degrees-radians mixup.
Oct
26
comment showing $\psi: R\to \mathbb C$ is ring isomorphism.
@kittuu It would be a good idea to edit your question and add this information, to make it easier to read for future visitors.
Oct
26
comment showing $\psi: R\to \mathbb C$ is ring isomorphism.
@kittuu Please note the discussion under Sami Ben Romdhane's answer below. You should probably indicate what kind of isomorphism you want: one of rings, of vector spaces over $\mathbb{R}$, or of $\mathbb{R}$-algebras.
Oct
26
comment showing $\psi: R\to \mathbb C$ is ring isomorphism.
@manthanomen True, but the OP didn't clearly state that he wants a ring isomorphism. Maybe he wants an $\mathbb{R}$-algebra isomorphism, in which case one indeed needs to check that $\psi$ preserves multiplication by elements of $\mathbb{R}$.
Oct
26
comment showing $\psi: R\to \mathbb C$ is ring isomorphism.
One should also check that multiplication is preserved !
Oct
25
answered For every prime of the form 6x-1 are there comparable number of primes of the form 6x+1
Oct
22
comment What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
@AsafKaragila I don't see how Hayden is beeing too literal. His answer clearly shows that at least two field structures are possible: one isomorphic to $\mathbb{R}$, the other to $\mathbb{C}$.
Oct
22
comment What are all different (non-isomorphic) field structures on $\mathbb R \times \mathbb R$
What you're asking is to list all the fields with cardinality $2^{\aleph_0}$. There are lots of those.
Oct
22
comment Is there any easy way to see that elementary matrices commute in $\text {Mat}_{n \times n} (\mathbb F)$?
Another argument why this isn't so. Each nondegenerate matrix is a product of elementary matrices. If elementary matrices commuted, all nondegenerate matrices would commute! This would be way too good to be true.
Oct
20
comment Prove that $e^x \ge$ its Maclaurin polynomial with n terms
Did you mean $x \geq 0, n \in \mathbb{N}$ in (c)? It looks weird otherwise.
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
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Oct
18
comment $\mathbb R[x]/\langle x^2+1\rangle$ is a field
@mcmat23 you probably mean that every non-zero prime ideal is maximal :-)
Oct
18
answered $\mathbb R[x]/\langle x^2+1\rangle$ is a field
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
added 1 character in body
Oct
18
revised A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
added 394 characters in body
Oct
18
answered A boy's father is 25 years older than him. The sum of their ages is 31. How old is the boy?
Oct
18
revised If a is not relatively prime to n prove modulo property
added 282 characters in body