abstract algebra - Suppose $K/F$ is a Galois extension of degree $p^m$. Then the

Suppose $K/F$ is Galois and of degree $p^m$ where $p$ is a prime of course. Then how can we see that we have an extension $F_0 = F \subsetneq F_1 \subsetneq \cdots \subsetneq F_m = K$ such that $[F...

numerical methods - Prove the exactness of a quadrature rule is the sum of degre

p(x) is a n-degree polynomial and it is orthogonal to all polynomial that has degree m (m<n) or less with respect to the inner product $<f,g>=\int_a^bf(x)g(x)w(x)dx$, where w(x)>0, cont...

The Generating Degree of ℂ p

The generating degree gdeg(A) of a topological commutative ring A with char A = 0 is the... Z[M] is dense in A. For a prime number p, C p denotes the topological completion of an algebraic...

J.D./M.P.P.M. - Admissions - University of Maine School of Law

Maine Law’s J.D./M.P.P.M. dual degree program with the University of Southern Maine's Muskie School of Public Service is an accelerated program that allows students to obtain a Juris Doctor (J.D.)...

Degree of P as a smooth function equals its polynomial degree d .

Let $M,N$ be connected oriented manifolds such that $\partial M=\partial N=\emptyset$. Let $F:M\to N $ be a smooth proper map (i.e. for every $K\subset N$ compact, $F^{-1}(K)$ is compact). We defin...

abstract algebra - An irreducible polynomial of degree $m$ over $\Bbb{F}_p$ rema

I read this proposition from Lahtonen's comments here and I wish to make a proof for that. Let $p$ be a prime and $f$ be a irreducible polynomial of degree $m$ over $\Bbb{F}_p$. Then $f$ remains

How existence of an irreducible polynomial in $F_p(x)$ of degree $n$ guarantees

I read somewhere that if $\pi$ is an irreducible polynomial of degree $m$ then $F_p(x)\ \backslash \left< \pi \right>$ is a finite field of order $p$. What is $F_p(x)\ \backslash \left< \pi \

abstract algebra - Every irreducible polynomial of degree $m$ over $\mathbb F_p$

We consider $F=\mathbb F_p$ for $p$ prime, $f(x)$ an irreducible polynomial of degree $m$ over $F$ and $g(x)=x^{p^m}-x$. I want to show that $f(x)\mid g(x)$. From the fact that the field $A=F[x]/...

M.D./M.P.H.: Degrees & Pathways - UT Southwestern, Dallas, TX

The Doctor of Medicine/Master of Public Health degree (M.D./M.P.H.) is a collaboration between UT Southwestern and UTHealth School of Public Health.

J.D./M.P.H. - Admissions - University of Maine School of Law

Maine Law’s J.D./M.P.H dual degree program with the University of Southern Maine's Muskie School of Public Service is an accelerated program that allows students to obtain a Juris Doctor (J.D.) deg...