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bio website dedekindsparadise.wordpress.c…
location Sheffield, United Kingdom
age 25
visits member for 2 years, 2 months
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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)


Apr
15
awarded  Nice Answer
Apr
8
comment Galois field of order $p^n$
Just as finite extensions of $\mathbb{Q}$ are basically $\mathbb{Q}^n$ with defined multiplications (corresponding to the minimal polynomial the generator satisfies), $\mathbb{F}_{p^n}$ is basically $\mathbb{F}_p^n$ with defined multiplications.
Apr
5
comment Inverse Galois theory and Hilbert class field
Well it is natural to ask for the groups which occur as extensions of an arbitrary number field. As far as I know this question is unsolved.
Apr
5
comment Inverse Galois theory and Hilbert class field
If we COULD drop the condition of being abelian in Q1 surely the inverse galois problem would be solved?
Apr
5
comment Number Theory and Cryptography
First surely we need to know what the book is and what crypto you wish to learn about. It is hard to answer a question that says "I have this book that I don't get, can you tell me how to get it" without knowing some details. Secondly you could simply ask the original question on here!
Mar
16
answered Proving the sum of the harmonic series up to $p-1$ is divisible by $p$
Mar
14
answered linear Combination And The Zero Vector
Mar
9
comment If $A_1$ and $A_2$ are countably infinite, and that $A_1\cap A_2=\phi$. Then prove that $A_1 \cup A_2$ is countably infinite.
It is true without the intersection condition...but that has been added so that you think about proving it this way.
Mar
6
asked Integral elements with predescribed properties in quaternion orders
Feb
27
reviewed Approve suggested edit on NP-complete: One proof to rule them all
Feb
21
awarded  Yearling
Feb
18
answered Let $a$ and $b$ be relatively prime integers. Prove $a^2$ and $b^2$ are prime as well.
Feb
18
reviewed Edit suggested edit on laplace transform of time shift function
Feb
18
revised laplace transform of time shift function
Latex formatting
Feb
17
comment Proof of Divisibility of $n(n^2+20)$ by 48.
Questions like this are designed to make you better at trying to prove things...if you aren't interested in getting to a solution yourself (albeit with the help of a few hints) then why bother with the problem at all?
Feb
16
comment Consider the trace map $M_n (\mathbb{R}) \to \mathbb{R}$. What is its kernel?
You should easily be able to prove that the trace map is surjective...
Feb
7
comment decoding an encrypted text with modulo
Well there is the obvious brute force method. Find all possible $a$'s, find all possible $d$'s and then try all possible decryptions to see which produces meaningful text.
Feb
7
comment How Would Arnold Explain the Jordan Normal Form to a 6 Year Old?
Do you have intuition for diagonalization? If so the JNF is simple to motivate...it is the closest thing to this we can expect for matrices that aren't diagonalizable.
Feb
6
comment Why does $n^2 \equiv 10 \pmod{30}$ imply $n \equiv 0 \pmod{10}$?
Your implication is only true one way...if $n=30$ then $n^2 = 900$ which is not congruent to $10 \bmod 30$. However $n^2 \equiv 10 \bmod 30$ if and only if $n\equiv 0 \bmod 10$ AND $n \not\equiv 0 \bmod 3$.
Feb
4
revised $4qx^3-3qx-p$ is not reducible over $\mathbb{Q}$
deleted 45 characters in body