The University of Hong Kong
DEPARTMENT OF MATHEMATICS
MATH3302/MATH4302 Algebra II
Assignment 2 Suggested Solution
In the following, E, F, K are elds.
1. Let : Q C be the identity embedding. Write down all the possible
1
extension embeddings Q( 2, 3 3 ) C
4
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
4.5
70
Modelling with Exponential and Logarithmic Functions
Exponential Models of Population Growth
A population that experiences exponential growth increases according to the equation
n(t) = n0 ert
Where
n(t) = pop
Since t0.05(8) = 1.86 we have
4.3 4
= 0.75 < 1.86
1.2/3
and we accept H0. The pvalue is
p
value = 2P (t(8) > 0.75) = 0.475
Note: We can not calculate this p value
exactly from the table. We calculated this
with a computer program.
Inference on a populatio
Those values of the test statistic for which
H0 is rejected is known as the critical
region.
Those values of the test statistic for which
H0 is not rejected is known as the acceptance region.
The boundary point(s) between the acceptance and critial reg
The University of Hong Kong
DEPARTMENT OF MATHEMATICS
MATH3302/MATH4302 Algebra II
Assignment 1 Suggested Solution
In the following, E, F, K are elds.
1. Let E, K be two eld extensions of F .
(a) Show that E K is also a eld extension of F .
(b) Suppose gc
The University of Hong Kong
DEPARTMENT OF MATHEMATICS
MATH3302/MATH4302 Algebra II
Suggested Solution to Assignment 5
In the following, E, F, K are elds.
1. Let Char (F ) = 2. Show that any degree 2 polynomial in F [x] is
solvable by radicals directly fro
The University of Hong Kong
DEPARTMENT OF MATHEMATICS
MATH3302/MATH4302 Algebra II
Assignment 4 Suggested Solution
Due: Tuesday 1 pm, April 8, 2014.
In the following, E, F, K are elds.
1. Prove that K Emb (K/F ) = F for all u K F , MinPoly F (u) has
at le
The University of Hong Kong
DEPARTMENT OF MATHEMATICS
MATH3302/MATH4302 Algebra II
Assignment 3 Suggested Solution
In the following, E, F, K are elds.
1. (a) Let g(x) = br xr + . + b1 x + b0 K[x], K/F is a nite separable
extension and for all Emb (K/F ),