Addendum to the Analysis Module
Charles Peters
I think it is important for you to know the following results. Some proofs
are included and you should read them, but the important thing is that you
be aware of the results themselves.
1. Completeness of Rn

MATH 3334-SUMMARY
VERN I. PAULSEN
Abstract.
1. The Space Rn
First we introduce the basic concepts that are needed to study limits and
continuity in Rn .
n
2
Recall that given x = (x1 , ., xn ) Rn we set x =
i=1 xi and we
call this the norm of x. Given two

PART III. FUNCTIONS: LIMITS AND CONTINUITY
III.1.
LIMITS OF FUNCTIONS
This chapter is concerned with functions f : D R where D is a nonempty subset of
R. That is, we will be considering real-valued functions of a real variable. The set D is
called the dom

PART II. SEQUENCES OF REAL NUMBERS
II.1.
CONVERGENCE
Denition 1. A sequence is a real-valued function f whose domain is the set positive integers
(N). The numbers f(1), f(2), are called the terms of the sequence.
Notation Function notation vs subscript no

PART I. THE REAL NUMBERS
This material assumes that you are already familiar with the real number system and the representation of the real numbers as points on the real line.
I.1.
THE NATURAL NUMBERS AND INDUCTION
Let N denote the set of natural numbers

Probability
Part 3 - Random Variables, Distributions and Expected Values
1. References
(1) R. Durrett, The Essentials of Probability, Duxbury.
(2) L.L. Helms, Probability Theory with Contemporary Applications, Freeman.
(3) J.J. Higgins and S. Keller-McNul

Probability
Part 2 - Basic Rules of Probability
1. References
(1) R. Durrett, The Essentials of Probability, Duxbury.
(2) L.L. Helms, Probability Theory with Contemporary Applications, Freeman.
(3) J.J. Higgins and S. Keller-McNulty, Concepts in Probabili

Probability
Part 1 - Basic Counting Principles
1. References
(1) R. Durrett, The Essentials of Probability, Duxbury.
(2) L.L. Helms, Probability Theory with Contemporary Applications, Freeman.
(3) J.J. Higgins and S. Keller-McNulty, Concepts in Probabilit