JSS
Journal of Statistical Software
October 2015, Volume 67, Book Review 1.
doi: 10.18637/jss.v067.b01
Reviewer: James P. Howard, II
University of Maryland University College
Data-Driven Modeling & Sc
Math 225 Homework #1: due 9/9/2016
Let (F, +, .) be a field as given in the lectures. As mentioned in class, certain
conclusions can be inferred from these properties.
Here are some examples with proo
Math 225 Homework #4: due 9/30/2016
1.
We proved in class that every ideal of Z is principal , that is, it has the form
nZ for some integer n.
(a) If a, b Z define (a, b) to be cfw_ma + nb | m, n Z. P
Math 225 Homework #2: due 9/16/2016
1. Let R be a ring with 1. We say that an element in R is a unit if v R such
that u.v = v.u = 1.
(a) Use Q1(c) to prove that if u is a unit then so is u.
(b) Let R,
Orthogonal matrices
1. Let B be an n n matrix with real entries satisfying BB t = I = B t B. Then
in particular AB is a unitary matrix, and we can apply the spectral theorem to it:
there is a unitary
1. Quotient rings and Subrings.
1.1
In class we discussed the following theorems.
First Isomorphism Theorem. Let : R S be a homomorphism of rings with
kernel K. Then there is a homomorphism : R/K S de
Math 225: On the spectral theorem
Suppose N is an n n matrix acting on elements of Cn . The spectral theorem
says that N is normal if and only if there is a unitary matrix U such that U N U = D
where
Math 225 Homework #5: due 10/7/2016
1. Let I be the ideal (X 2 + 3, 5) = cfw_a(X) (X 2 + 3) + b(X) 5 | a(X), b(X) Z[X]
in the ring Z[X]. Let F5 = Z/5Z and define a map
p : Z[X] F5 [X]
by a0 + a1 X + +
1. The rings Z/nZ.
1.1 Let n > 1 be a positive integer. If a Z we write a for the set cfw_a + qn
Z | q Z.
Lemma. We have b a if and only if a, b have the same integer remainder when
divided by n. In
1. Homomorphisms between rings.
1.1 This is an expansion of what was discussed in class. First, let (R, +, .) and
S, , ) be two rings. We do not assume that they are commutative, nor do we
assume that
Math 225 Homework #3: due 9/23/2016
1. Let a, b be two positive integers at least one of which is non zero.
(a) Let k be a third positive integer. Prove from the definition that gcd(a, b) =
gcd(a, b +