Mathematical Review (Really More than a Review)
Economics 380
R. Pope
Introduction
Economists aren’t mathematicians but we use mathematics along with most sciences.
Here are a few quotes to show that it is a process to accomplish the mathematical skill
and comfort we seek.
"Mathematics is the gate and key to the sciences."  Roger Bacon
[Statement without proof but I agree]
"I hear and I forget.
I see and I remember.
I do and I understand."  Chinese Proverb.
[Some don’t hear and forget, some do and don’t understand]
"In mathematics, you don't understand things. You just get used to
them."
 Johann von Neumann
[I’ve been around a long time so maybe I’m used to things that
aren’t comprehensible to youstop me at those times]
"There are two ways to do great mathematics. The first is to be
smarter than everybody else. The second way is to be stupider
than everybody else  but persistent."  Raoul Bott
[What mathematics I know likely came through persistence]
"Black holes are where God divided by zero."  Steven Wright
[Just for fun]
"I recoil with dismay and horror at this lamentable plague of
functions which do not have derivatives.  Charles Hermite
[Most of the time, we will assume not only continuity but
differentiability. However, nondifferentiable examples often teach
us something important]
Most important central ideas of modern economics can be accessed without much
mathematics but do require deductive mathematical reasoning. However, these ideas
can’t be made rigorous and can’t be empirically tested without quantification. Economics
380 formalizes much of the microtheory that one learns in Economics 110. Interesting
theoretical conclusions arise that weren’t evident in Economics 110.
In order to proceed with more formalism, we need to make sure we have the necessary
algebraic and calculus tools. We proceed from review to a few ideas that most of you
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Documenthave not had in math classes: calculus of several variables. We focus most on differential
calculus but integral calculus is important in many areas of economic theory and
application. It will be fun.
Sets (We use notions of sets quite superficially)
A set is a clearly specified collection of elements. It may contain a finitely or infinite
number of elements. The most common set of elements for this class is R the set of real
numbers. A set without any elements is usually denoted
or the null or empty set. The
symbol
is generally used to denote membership in a set. Thus, 2
R
. A subset of
R
is
the set of nonnegative numbers denoted
R
+
. The set of positive numbers is often
denoted R
++
. Thus, 2
R
while zero is not in (
)
R
. An example of a subset is an
interval in
R
. It is open if it doesn’t contain it’s endpoints (a,b) or e.g., all numbers
between 1 and 2 but not including a or b. It is a closed interval (subset of R) if it includes
a and b written [a,b]. For example, all numbers between 1 and 2 including these two
endpoints. An interval can be half open or closed (a,b] as well. There are a number of
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '08
 Showalter,M
 Economics, Derivative, Johann Von Neumann

Click to edit the document details