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I have a B.Sc in computer science and a B.Sc in mathematics from the Technion.

I am interested mainly in abstract algebra and I hope to start graduate school soon to continue study some advanced topics in this area.

Currently I am going over Abstract Algebra by Dummit and Foote to recall old topics and fill some gaps I have, while working full time as a programmer.


14h
comment Value of $z$ so that the series converges
Maybe try to write this as two sums (one with $z^n$ and one with $\frac{1}{z^n}$), see when those converge for starters
1d
comment Probability of drawing the king of hearts and a red card
What have you tried ?
1d
comment The number of positive integers whose digits are all $1$, $3$, or $4$, and add up to $2k$, is a perfect square
This is described in the oeis link along with other descriptions (as well as in the other comment)
1d
comment The number of positive integers whose digits are all $1$, $3$, or $4$, and add up to $2k$, is a perfect square
oeis.org/A006498
1d
comment Irreduciblility of $x^3 + 9x + 6 $ in $\mathbb{Q}[x]$
It is worth mentioning that this is basically the proof of the rational root theorem applied to this case
Aug
16
comment Proving that a number is non-negative?
Have you considered adding them up and seeing if they are a square ?
Aug
15
comment The Galois group of a polynomial
If I recall correctly Dummite and Foote define that a polynomial is separable iff every irreducible factor of it is separable so $f$ is separable iff $g$ is by this definition
Aug
9
comment Is “$a + 0i$” in every way equal to just “$a$”?
If we wish to be exact - they are not the same, but the concept of isomorphism arises, as Bill commented
Aug
9
comment Notation for show that a variable is binary?
$\mathbb{Z}_2$.
Aug
8
comment Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group
@Arthur - I have used this fact so I could use the second isomorphism theorem
Aug
8
comment Proving that the intersection of a Sylow p-group with a normal subgroup is also a Sylow p-group
@Arthur - Yes, I have seem to forgot to write it down
Aug
7
comment A subgroup of functions under multiplication
You should use more informative titles
Aug
5
comment A Group That Span A Space
You should use the word set instead of the word group - the reason is that a group is a mathematical object that is different then a set (I can understand the confusion, in my first language the word group can translate into something very similar to a set)
Aug
5
comment The Size Of A Vector
Do you mean to ask about what is the largest blocked subspace ?
Aug
5
comment Prove that $(a+b\sqrt[3]{2}+c\sqrt[3]{4})^{-1}$ with a,b,c∈Q is a number of the form $d+e\sqrt[3]{2}+f\sqrt[3]{4}$ with $d,e,f∈Q$
This is not true if I recall correctly it is the same iff $a$ is algebraic. e.g for $a=\pi$ the two are not the same
Aug
5
comment Prove that $(a+b\sqrt[3]{2}+c\sqrt[3]{4})^{-1}$ with a,b,c∈Q is a number of the form $d+e\sqrt[3]{2}+f\sqrt[3]{4}$ with $d,e,f∈Q$
Why do you use square brackets ? wouldn't it be better to use regular brackets to indicate this this is a field and not just a ring ?
Aug
4
comment Prove that intersection of finite index subgroups has finite index.
Note that in this solution you have used $|K|$ such as in $\frac{|G|}{|K|}<\infty$ but if $G=\mathbb{Z}$ and $K=2\mathbb{Z}$ then this is somewhat problematic.
Aug
3
comment Solutions of of $x^{76}=1$ in $U_{77}$
@user167668 - By definition. For example it is not empty because $1\in S$
Jul
31
comment Complex numbers in polar form
@Gummybears - Yes! You can use the notation of the exponent as others have if you wish - then you use the rules you already know (such as how to multiply them)
Jul
31
comment Complex numbers in polar form
@MJD - Thanks for the edit. I don't have the \cis command in Lyx but its on Math.SE (apparently)