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bio website ie.linkedin.com/in/aymanh
location Dublin, Ireland
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visits member for 3 years, 11 months
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awarded  Enlightened
1d
awarded  Nice Answer
Nov
11
revised Signs of solutions to a quadratic equation
edited tags
Nov
5
comment Exact sequence of sheaves from the exactness of sections
Exactness of the sequences of sections immediately results in exactness of the sequence of sheaves. Compute each $\ker$ and $\operatorname{im}$ and verify this.
Nov
3
awarded  Enlightened
Nov
3
awarded  Nice Answer
Nov
2
comment Proving the continuity of a homotopy
Note that $D^2$ deformation retracts onto a point on the boundary. By composing this map with carefully chosen maps, you get your desired homotopy.
Nov
1
comment Interpretation of input to solve the differential equation
You don't have to use the partial derivative. Just think of $y$ as a function of $x$ and compute $df(x, y)/dx$ as usual. See total derivative on Wikipedia.
Nov
1
comment Interpretation of input to solve the differential equation
This is borderline off topic. Anyway, try Dt[f[x, y], x].
Nov
1
comment Show that a function is limited and constrained?
Well, $x^2 + y^2 \le 1$ implies that all points are inside the unit circle, so it is bounded.
Nov
1
comment Exact sequence of $A$-modules
This is also proved in detail in Dummit & Foote.
Nov
1
comment Show that a function is limited and constrained?
I assume by constrained you mean bounded. This is false in general. Consider the case in which both $f$ and $g$ are constant.
Oct
31
revised Maps between direct limits and functoriality of $f^{-1}:Shv(Y) \rightarrow Shv(X)$ and $f_{*}:Shv(X) \rightarrow Shv(Y)$
Fixed CD usage
Oct
31
comment Proving Irreduciblity in Polynomial Quotient Rings
@walkar Happy to help.
Oct
31
answered Proving Irreduciblity in Polynomial Quotient Rings
Oct
18
comment Homomorphism between 2 abelian groups sending one given element to another given element
Not necessarily. The only homomorphism from $\mathbb Z / (n)$ to $\mathbb Z$ is the trivial homomorphism.
Oct
17
answered What is the definition of contractible space? (It is not a duplicate)
Oct
17
comment What is the definition of contractible space? (It is not a duplicate)
@NajibIdrissi I don't think they are equivalent in general. Chapter 0 in Hatcher's book has a couple of examples of spaces such that the identity map is nullhomotopic, but not nullhomotopic relative to a point.
Oct
17
comment Best way to learn material dealing with cosets, quotient groups and the isomorphism theorems
In my opinion, D&F does a wonderful job explaining these topics, or anything covered in the book for the matter. It takes time and practice before these topics become second nature to you. I suggest that you keep going, and solve as many exercises as you can. If you want another book, Artin is frequently recommended here.
Oct
17
comment Is $ \mathbb{Q}(i) \cong \mathbb{Q}(2i) ? $
@JC574 That's wrong, I'm afraid. $\mathbb Q(i)$ does not contain an element $x$ such that $x^2 = -2$.