La scheda
Yuan Dong
Titolo: La grande bellezza (2013)
Regista: Paolo Sorrentino
Personaggi principali:
Jep Gambardella (Toni Servillo);
Romano (Carlo Verdone);
Ramona (Sabrina Ferilli)
Ambientazione: Roma
Trama: Il film ambientato nella contemporanea Roma
Math 111C, Spring 2015, Problem (9)
(9) Show that the polynomials X 3 2 and X 3 3 in Q[X] do not have isomorphic
splitting elds over Q.
Proof. First note the following: Every polynomial f Q[X] \ Q has a unique splitting eld
(over Q) which is contained in
SUGGESTIONS AND SOME MOTIVATION
FOR REVIEW OF 111B MATERIAL
Prelude, partly doubling up on what I said in class: Whenever we analyze prototypes
of algebraic structures, such as vector spaces, groups, and rings (now elds), we use homomorphisms to compare s
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a positive
prime in Z.
Corollary 2. Let F0 be the prime eld of F . Then:
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, extension eld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a positive
prime in Z.
Corollary 2. Let F0 be the prime eld
KRONECKERS THEOREM, FIRST VERSION
We know: Every embedding : F K of elds induces an embedding of polynomial
rings : F [X] K[X] (i.e., an injective ring homomorphism); it sends any polynomial
d
d
i
i
i=0 ai X F [X] to the polynomial
i=0 (ai )X in K[X].
The
MATH 111C, S 2015, EXISTENCE OF
SPLITTING FIELDS, GENERAL VERSION
Ill start with a reminder. In class, we proved:
Theorem 14 [nite version]. Let F be a eld and P a nite set of nonconstant polynomials in F [X]. Then there exists a splitting eld for P over
MATH 1110 NAME
SECOND MIDTERM
15 May 2015, 10:0010:50 PERM NO.
PLEASE WRITE NEATLY. When giying proofs, be sure to sort out tentative ideas
on scratch paper, and to put down your argument in a logical sequence on the test
paper. The scratch work will not
MATH 1 1 1 C NAME
FIRST MIDTERM
24 April 2015, 10:00-10:50 PERM NO.
PLEASE WRITE NEATLY. When giving proofs, be sure to sort out tentative ideas
on scratch paper, and to put down your argument in a logical sequence on the test
paper. The scratch work Will
Math 111C, Spring 2015, Homework Assignments
All assignments refer to our text, Abstract Algebra, third edition, by Dummit & Foote.
March 30: p.519, # 5
April 1: p.519, # 7, more cleanly stated as follows: Consider the polynomials fn =
x3 nx + 2 Z[x], for
MATH 111C, S 2015, OVERVIEW
Basics
Denitions. Field, subeld, eld homomorphism, prime eld, characteristic.
Theorem 1. For any eld F , either char(F ) = 0 or char(F ) = p, where p is a positive
prime in Z.
Corollary 2. Let F0 be the prime eld of F . Then:
EMPATHY AND VIOLENCE
1
Empathy and Violence: Connecting Characteristics in Psychopathy and Autism Spectrum
Disorder to Criminal Offenses
My signature below certifies that I have complied with the University of Pennsylvania's Code of
Academic Integrity in
In 1922 Benito Mussolini came to power in Italy. To make the capital city a strong symbol of
Fascism, he put forth significant effort into restoring and renovating Rome, with the idea of
transforming it into an imperial city to make a direct link between
Dong 1
Tristan Dong
Instructor: Mehmet-Ali Ata
ARCH 226 Archaeology of Anatolia
Dec 9, 2015
Assyrian Influences on Pre-classical Anatolia: from the Trading Colony to Urartian Art
The arrival of Old Assyrian merchants in the Middle Bronze Age,
originating
3.Commentonthefollowingstatement:Asinterestraterise,stockpricestendtofall.Explain
whydoyouthinkthestatementisrightornot.Searchonlineandfindhistorydataonstockin
dicesandthefederalinterestrate.Isthestatementsupportedbythedata?
When a central bank raises int
Art in Neolithic Anatolia: a Response
Tristan Dong
Oct 3, 2015
During its first survey, limestone slabs of mammoth proportions were discovered in the site of
Gbekli Tepe. Interestingly, these rocks and slabs constituted the upper parts of the T-shaped
pil
A REMARK ON FINITE ABELIAN GROUPS THAT
FEEDS INTO THE PROOF OF THEOREM 22
Auxiliary Proposition. Let A be a nite abelian group. Then there exists an element
x A such that |y| divides |x| for all y A.
Consequence: If A fails to be cyclic, there exists a na