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visits member for 3 years, 11 months
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Sep
11
comment Cant understand some definitions of abstract algebra, can you help me please?
I don't know the reason for the term "over", but it is used to indicate the field from which the scalars for the scalar multiplication are chosen. In a similar vein, if one talks about the finite dimensional space $F^n$, then one considers this space as being "over $F$" in the sense that the $n$-tuples have entries that come from $F$.
Aug
31
comment A Book for abstract Algebra
I'm currently using Pinter's book in my abstract algebra course because it is well-written, inexpensive, and has great exercise sets that break sometimes difficult discussions into manageable pieces.
Aug
24
comment Does every group have a 'cyclization'?
@Alexander - It certainly seems every group has a trivial one, which is why I don't think the trivial case is very interesting. I'm kind of distracted by other obligations at the moment, but it seems that $\mathbb{Z}$ has both itself and the trivial group as cyclizations.
Aug
24
comment Does every group have a 'cyclization'?
It might make a better question to ask what groups have nontrivial cyclizations, since not all have non-trivial ones.
Aug
24
comment Does every group have a 'cyclization'?
@Bryan - I assumed you wanted a non-trivial cyclization.
Aug
24
answered Does every group have a 'cyclization'?
Aug
2
comment Convergent or divergent $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+1}}\left(\frac{n}{n+1}\right)^n$?
@Nick - One thing to remember with textbook answers is that it is not usually possible, because of space limitiations, to give complete, rigorous answers. So, you get the telegraphic version that says "essentially", i.e., asymptotically, your series is a constant multiple of a divergent series, the harmonic.
Jul
27
comment If one number is thrice the other and their sum is $16$, find the numbers
One number is $x$, the other $3x$. They add to 16, so ... .
Jul
2
awarded  Curious
Jun
30
comment Is Matrix $A^2$ invertible if $A$ is invertible?
Follow Thomas' advice. And what do you know about the inverse of a product of invertible matrices?
Jun
25
comment Is it true that “there is no such thing as the square root of minus one”?
@Andre Nicolas Our mathematical conventions are so economical. Perhaps we subconsciously apply Occam's (or, Ockham's) Razor in making these decisions.
Jun
25
comment How is $\mathbb{F}_4$ generated?
@Omnomnomnom - Didn't mean to repeat you. I must have been composing my comment while you were posting.
Jun
25
comment How is $\mathbb{F}_4$ generated?
$x^2+x+1$ is the only irreducible quadratic in $\mathbb{F}_2[x]$.
Jun
17
answered What's the advantage of defining topologies on open sets rather than closed sets?
Jun
13
awarded  Good Answer
Jun
7
comment Why is an injective holomorphism on $\mathbb C$ biholomophic?
- By holomorphism do you mean a ring homomorphism $\mathbb{C} \rightarrow \mathbb{C}$ that is a holomorphic map?
Jun
2
answered Reference Request: Vector valued Taylor formula
Apr
30
comment Calculus Question Problem
Try implicit differentiation. If I'm awake, you should get $\frac{dy}{dx}=\frac{3x^2-1}{3y^2-2}$. Now substitute 2 for $x$ and 3 for $y$ to get the slope of the tangent. The normal is perpendicular to the tangent.
Apr
16
comment Factoring the quintic polynomial $x^5+4x^3+x^2+4=0$
@Michael T - Nothing other than learning at an early age (doing lots of integrals and other things) that it sometimes pays to split one term into the sum (or product sometimes) of two terms. Writing the coefficient on $x^2$ as $1+4$ creates a nice sequence of coefficients: 1, -1, 1; 4, -4, 4; and the rest just flows from there. As gt6989b said above, if you do enough of these things, you develop an intuition. Some of these things are as much art as science.
Apr
11
comment Find the total distance that the particle travels over the given interval?
Subtract the integral on the intervals where the function is negative, and add the integral on the intervals where the function is positive. You're trying to integrate the absolute value of your function over the interval. You might also check your arithmetic. I did the integrals quickly, so I could have messed up, too. I got 545/18 for the first, and 12 for the second.