6,464 reputation
520
bio website dedekindsparadise.wordpress.c…
location Sheffield, United Kingdom
age 26
visits member for 2 years, 10 months
seen 2 days ago

Hey, I am currently a PhD student at the University of Sheffield. My interests are in algebraic number theory and related fields.

Check out my academia page for some of my papers/talks. I welcome any suggestions on how to improve them.

(http://sheffield.academia.edu/DanielFretwell)


Dec
17
comment Are Primitive Dirichlet Characters linearly independent.
Essentially by the orthogonality relations for such characters it must be that each coefficient is $0$ (inner product the above relation by each character in turn and all terms disappear except one each time, allowing you to conclude that the coeff is $0$).
Dec
13
comment Two conjectures regarding $\varphi(n)$
Before making a conjecture you should always test it. You clearly haven't done this since an extremely small counter-example exists. As mentioned below $\phi(6) = 2$ and this divides $6$...
Dec
13
comment Solving a linear Equation!
Your argument should be, "If $x\neq 0$ then I can cancel from both sides and get $4y = 1$, so that $y=\frac{1}{4}$ is a solution...otherwise $x=0$ so that $y$ can take any value."
Dec
13
comment Solving a linear Equation!
It is sloppy to say $x=x$ since in that case you never allowed for $x=0$. However you have solved the equation wrong.
Dec
9
comment How to calculate $\sigma(x^k)$?
But if you are just referencing the formulae from wiki then it makes more sense!
Dec
9
comment How to calculate $\sigma(x^k)$?
It is proved the exact same way it is proved for $2$ as the base...this is why I couldn't understand your issue so asked how you somehow managed to do that one particular case without seeing how to do the rest.
Dec
9
comment How to calculate $\sigma(x^k)$?
This is what I was trying to get at...the proof is no different at all for other bases.
Dec
9
comment How to calculate $\sigma(x^k)$?
Yes...but how did you PROVE this formula?
Dec
9
comment How to calculate $\sigma(x^k)$?
You appear to know that $\sigma$ is multiplicative so I guess the question is how do you find $\sigma(p^k)$ for a prime $p$. To answer this I need to ask how you found $\sigma(2^k)$.
Dec
9
awarded  Caucus
Dec
7
comment Intuitive understanding of the uniqueness of the Fundamental Theorem of Arithmetic.
Surely for ord$_p$ to be well defined you NEED unique factorisation?
Dec
5
comment Is there a notion in mathematics saying that, in a sense, all finite dimensions are actually infinite dimensional?
Yep, I was answering the first comment :p
Dec
5
comment Is there a notion in mathematics saying that, in a sense, all finite dimensions are actually infinite dimensional?
@WarmFuzzies: A subspace is a subset...When you say "$\mathbb{R}$ is a subspace of $\mathbb{R}^2$" you really mean something like "The set of vectors of the form $(x,0)$ are a subspace of $\mathbb{R}^2$ isomorphic to $\mathbb{R}$".
Dec
5
comment $x^3-3x^2+4x-2$ cannot be factored over $\mathbb R$
Just a little note that your title is inaccurate...the polynomial CAN be factored over $\mathbb{R}$ but not in this special way as asked in the question.
Dec
5
comment Given radius, and many vertices on it, how can I find center of a sphere?
Or look at Simon Watfa's answer here (steve.hollasch.net/cgindex/geometry/sphere4pts.html) for a nice way of doing it given $4$ non-coplanar points on the sphere (it turns this is enough to get a unique sphere).
Dec
5
comment Given radius, and many vertices on it, how can I find center of a sphere?
Assuming the sphere is in $\mathbb{R}^3$ its equation is $(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2$ where $(a,b,c)$ is the center and $r$ is the radius. Just plug in some of the coordinates of your points and get some equations to solve for $a,b,c$.
Dec
5
comment Given radius, and many vertices on it, how can I find center of a sphere?
Isn't this just solving simultaneous equations?
Dec
2
comment How to show that $\cos\frac{2\pi}{n} + \cos\frac{4\pi}{n} + \ldots+ \cos\frac{2\pi(n-1)}{n} = -1$ for all positive integers $n$?
Can you factorise $x^n - 1$?
Nov
6
revised What exactly is a vector line integral?
deleted 130 characters in body
Nov
6
comment What exactly is a vector line integral?
Oh of course, I was being stupid!