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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.


12h
comment $27 | (2x+1)^2 \implies 2x$ is a multiple of 9?
@MJD - Why not post this as an answer ?
21h
comment Why is any subspace affine?
This looks like the definition of convexity not of affinity..
2d
comment For all $X \subseteq \mathbb{N}$ there exist $n \in \mathbb{N}$ with $|X| < n$.
Yes. And for your choice there are infinite number of subsets, given any k there is the subset of all element smaller than k. So there is at least one subset per Natural number and thus infinite number of subsets
2d
comment For all $X \subseteq \mathbb{N}$ there exist $n \in \mathbb{N}$ with $|X| < n$.
Yes. And for your choice there are infinite number of subsets, given any k there is the subset of all element smaller than k. So there is at least one subset per Natural number and thus infinite number of subsets
Oct
18
comment Prove that a matrix with a given characteristic polynomial is diagonalizable
$-3$, not $ 3 $
Oct
17
comment If $A,B$ are subgroups of the group $G$, then $A\cup B\leq G\Leftrightarrow (A\subseteq B \vee B\subseteq A)$.
I don't get your last point "but that also comes to a contradiction" - Why ? Both $A$ and $B$ have the same identity element and that's fine
Oct
16
comment Does every vector space have an inner product?
I edited the first inline, please see that this is what you meant
Oct
16
comment Showing $\operatorname{Aut}(\mathbb{R})$ is abelian
You mean Aut(R) is trivial ? in the second line you wrote R is the trivial group..
Oct
16
comment If $m^n = n^m$, why does $m$ to be a factor of $n$?
Maybe someone can correct me, but the only option for this to happen is $n=4,m=2$
Oct
16
comment What can we say? Variance = Mean
Note that if $X$ is discrete RV you can have problems moving from the first to the second line - this is since there is a positive probability that $X-\mu=\pm \epsilon$
Oct
15
comment Prove that a function is continuous in R^2
Can you deal with some of the $y_0$ ?
Oct
14
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
Yes. that is $v=(1,0)^T$ imply $0v=0$ - not the other way around as you wrote it
Oct
14
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
No - it is indeed a solution, but $0v=0$ does not imply $v=(1,0)^T$ , it doesn't say anything about $v$
Oct
14
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
Oh sorry, but then I would argue that if $a=-b$ the implication is not correct
Oct
14
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
If $a=b$ we get the zero matrix so the implication that $v=(1,0)^T$ in the first line is not correct
Oct
14
comment Eigenvectors of $\left( \begin{array}{ccc} a & 0 \\ 0 & -b \end{array} \right)$
assuming $a\neq b$ otherwise there are two independent solutions
Oct
14
comment Prove sequence $S_n$ converges
possible duplicate of $\sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}$, or the limit of the sequence $x_{n+1} = \sqrt{c+x_n}$
Oct
14
comment A real matrix whose eigenvalues have all negative real parts
I don't know about the ODE part but as a linear algebra claim it is false - actually your method shows any non invariable matrix with eigenvalues with negative real parts can be an example
Oct
13
comment How to find $(Ker(A^{*}))^{\perp}$
@ECE - the basis for the perpendicular space is not 'everything else' - it is a set with only two vectors (it is rather a basis for 'everything else')
Oct
13
comment What is a “formal definition” of a set?
I removed the Formal Languages tag. Tag wiki is - Formal languages are studied in computer science and linguistics. They are usually defined using various types of grammars (e.g. regular, context-free) and automata (e.g. deterministic and pushdown automata, Turing machines). There is a hierarchy of formal languages, which is based on the type of grammars and automata which can be used to generated them.