Math 521, Lecture 2
Hints for Assignment # 3
Problem 1 Let X be a metric space, and let E X be a subset. The interior of the set E is the
set E o = x E there exists r > 0 so that B(x, r) E . The closu
2. Groups I
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
Groups
Subgroups, Lagranges theorem
Homomorphisms, kernels, normal subgroups
Cyclic groups
Quotient groups
Groups acting on sets
The Sylow theorem
Tryin
I. Algebra
1. Vector Spaces
1A. Linearity.
Denition 1.1. A real vector space (or just a vector space for short) consists of a
set V , a function V V V called addition, and a function R V V called scal
HOMOMORPHISMS
KEITH CONRAD
1. Introduction
In group theory, the most important functions between two groups are those that preserve the
group operations, and they are called homomorphisms. A function
WON Series in Discrete Mathematics and Modern Algebra Volume 2
NUMBER THEORY
Amin Witno
Preface
Written at Philadelphia University, Jordan for Math 313, these notes1 were used rst
time in the Fall 200
MAT 364 Topology
Problem Set 6
due Wednesday, October 13
Problem 1. Determine whether the following sets are compact or not.
Prove your answers.
(a) X = cfw_(x, y) R2 |x 0, y 0, the graph of the funct
MATH 115, SUMMER 2012
LECTURE 13
JAMES MCIVOR
Today we focus on the multiplicative aspects of the integers mod p.
1. Primitive roots in Z/m
For this section, we work in the ring Z/m, so = in this ring
Solution to last chapter 5 activity problem
As we showed in step 3, for a given sample size n, the null hypothesis is rejected if
1.645. We want the probability of this event (the power) to be .95:
M
SUBGROUP SERIES II
KEITH CONRAD
1. Introduction
In part I, we met nilpotent and solvable groups, dened in terms of normal series. Recalling the denitions, a group G is called nilpotent if it admits a