Instructor: William
H. Hoyt Professor of Economics Office: 335AZ Gatton Business & Economics Bldg. Lexington, KY 405060034 Phone: (859) 2572518 Office Hours: 9:15  10:30, WF Email: whoyt@uky.edu Fax: (859) 3231920 
Syllabus (pdf)  Course Description  Text and Readings 
Grading and Course Assignments  Tentative Course Outline 
Grades and Scores available (by ID)
Friday,
November 5, 2004
Topics:
Constrained
Optimization: Second Order Conditions
Simon & Blume, 19.3
Hoyt, Lecture 10.7
Monday, November 8, 2004
Topics:
Homothetic and Homogeneous Functions
Readings:
Simon
& Blume, 20; Hoyt, Lecture 11
Monday,
November 1, 2004
Topics:
Constrained
Optimization: Minimization
Envelope Theorem,
LaGrange Multipliers
Readings:
Simon & Blume, 18.5,
19.1 – 19.2
Hoyt,
Lecture 10.510.6
Topics:
Second Order Conditions
Monday,
October 25, 2004
Topics:
Constrained
Optimization: Inequality Constraints and KuhnTucker Conditions
Simon & Blume, 18.3
– 18.6
Wednesday,
October 27,
2004

Wednesday,
October 20,
2004
Topics:
Review of
Exam 1
Examples of
Unconstrained Optimization
Constrained
Optimization: Equality Constraints
Readings:
Simon &
Blume, 18.1
– 18.2
Hoyt, Lecture 10: Constrained Optimization
Friday,
October 20, 2004
Topics:
Constrained
Optimization: Inequality Constraints
Topics:
Shape of Functions
Simon and Blume, 21.121.3
Hoyt, Lecture 8.88.9
Topics:
Unconstrained Optimization
in R^{N}
Taylor’s Theorem
Second Order Conditions for
Unconstrained Optimization
Readings:
Simon & Blume, 17.117.5;
30.130.3
Friday,
September 24, 2004
Topics:
Higher Order Derivatives
Implicit Function Theorem
Simon & Blume, 15:115.4
Monday,
September 27, 2004
Hoyt, Lecture 8.78.9
Simon & Blume,
16;21.121.4
Topics:
Gradients
Implicit
Function
Theorem
Readings:
Hoyt,
Lecture 8
Simon & Blume, 14; 15
Matrix Inversion
·
Cramer’s
Rule
^{Euclidean Space
Limits and Open Sets
}
Simon & Blume, 10.510.7; 11; 12.112.5

·Determinants
Inverse
Matrices
·
Cramer’s
Rule
Simon
& Blume, 8.18.4, 10; Hoyt, Lecture 6; Simon & Blume, 67
Friday,
September 10, 2004
Topics:
·
Rank
& Solutions to Systems of Equations
·
Properties
of Determinants
·
Inverse
Matrices
Friday,
September 3, 2004
Topics:
One Variable Case:
Maxima
& Minima
Introduction
to Linear Algebra
For Wednesday, September 8
Introduction
to Linear Algebra
Readings:
Simon
& Blume, 3; 68.4
Hoyt, Lecture 5: Maxima and Minima (see restricted section)
Hoyt,
Lecture 6: Fundamentals of Linear Algebra
Wednesday,
September 1, 2004
Topics:
One Variable Case:
Maxima & Minima
Concavity & Convexity
Economic Applications
Introduction
to Linear Algebra
For
Review:
Rules
for Differentiation
Product
Rule
Quotient
Rule
Chain
Rule
Higher
Order Derivatives
For Friday,
September 3
Introduction
to Linear Algebra
Readings:
Simon
& Blume, 3; 68.4
Hoyt, Lecture 5: Maxima and Minima (see restricted section)
Hoyt,
Lecture 6: Fundamentals of Linear Algebra
Assignment
(Due Friday, September 3, 2004)
Simon
& Blume 2.1, 2.4, 2.5 (p. 1516); 2.8, 2.9 (p. 2122);
2.102.12
(p. 29); 2.16 (p. 33); 2.20 (p. 34);4.1, 4.5 (p. 75)
Monday,
August 30, 2003
Topics:
Course
Outline and Introduction
Vocabulary of Functions
Definition
of Derivative
For Monday, August 30
Readings:
Simon
& Blume, 1.11.2; 2.32.7; 12.1, 12.4; 4
Hoyt, Lecture 3 (see restricted section)
For review: Hoyt, Lectures 1 & 2 (see restricted section);
Simon & Blume 2.12.2; 5
Assignment
(Due Friday, September 3, 2004)
Simon
& Blume 2.1, 2.4, 2.5 (p. 1516); 2.8, 2.9 (p. 2122);
2.102.12
(p. 29); 2.16 (p. 33); 2.20 (p. 34);4.1, 4.5 (p. 75)
Readings:
Simon
& Blume, 3
Hoyt, Lecture 4 (restricted section)

From the University Catalog: An introduction to mathematical approaches to economic theory. Emphasis is on linear models, constrained optimization, and techniques used in comparative statics. Prereq: ECO 488G; MA 113; or the consent of the instructor.
While this description has some truth to it, I would add that the
purpose
of this course, in my view, is not to train you as a mathematical
economist.
Instead it should provide you with basic tools you need for coursework
and research in economic theory and econometrics as well as the applied
fields you will encounter later. With this in mind, I shall try to
tailor
the topics we cover to focus on those techniques and tools that you
need
to advance in the program and use in your own research.

The required
text for the course is Carl P. Simon
and Lawrence Blume, Mathematics for
Economists, Norton, 1994. Occasionally, when I believe another text
might
do a better job of covering a specific topic, I shall make the relevant
readings available to you in the file for course readings in BE 324.
In addition, “lecture notes” that I try to make
available prior to the lecture supplement the text. These are quite
extensive
and detailed notes on which the class lecture is generally based.
However, these
notes should not be used as substitutes for taking notes during class.
These notes will be on the course website, http://gatton.uky.edu/Faculty/hoytw/590/590.html,
in a section of the website that will require a special access code to
access.
The code will be given to you in class. Most of these notes will be in
a
postscript (pdf) format that requires Adobe Acrobat to read. The reader
can be
obtained free of charge at www.adobe.com.

Your grade for the course is based on my evaluation of your performance on problem sets and three exams. Problem sets will be given on daily basis. Problem sets must not be late to receive full credit with late being defined as any problem set I do not receive at or prior to the beginning of class on the date on which it is due. A problem set that I receive within three days of the date on which it is due can receive at the most halfcredit. Any problem set received after that period receives no credit unless the student has an excused absence as defined by the University.
On each problem set a maximum of 50 points is possible. Your total score on problem sets for the course will be based on an average of the scores after discarding your four lowest scores. As the primary purpose of the problem sets is to give you practice, substantial credit will be given for attempting problems even when correct solutions are not obtained. In addition, not all problems on a set will generally be graded. Of course, you will not know in advance which problems will be graded.
While you are
encouraged to work together on the problem sets, I encourage
you to first work on the problems by yourself and then meet with other
students or me to compare answers and perhaps attempt the more
challenging
problems. I do not want the group to write up the solutions to the
problems
 that is the responsibility of the individual. Once you have written
up your solutions to the problem set, do not share your answers with
anyone
else. Remember the purpose of the problem sets is to get you to learn
the
material; to do this it is necessary for you to make an honest effort
to
do the work yourself.
Given the nature of
the material being tested, if
possible, I would like you to allow two and onehalf hours to taking
the two
exams during the semester. This is

Topic 
1. Applications of
Calculus of One Variable 
Maxima and Minima 
Chain Rule 

2.
Linear Algebra: The Basics 
Introduction and Definitions 
Systems of Linear Equations 
Matrix Algebra and
Determinants 
Euclidean Spaces 

3.
Multivariate Calculus

Limits and Set Theory 
Functions in R^{N} 
Partial Differentiation and Differentials 
Implicit Functions 
Comparative Statics 
Concave and Quasiconcave Functions 

4.
Optimization 
Unconstrained 
Equality Constraints 
Inequality Constraints 
Multiplier and Envelope Theorems 
Second Order Conditions 

5.
Analysis 
Limits and Compact Sets 
Weierstrass and Mean Value Theorems 
Taylor Series Polynomials 

6.
Linear Programming 
Examples of Linear Programming 
Convex Sets and Linear Programming 
Duality 

7.
Differential Equations and Dynamic Programming 
First Order Linear Differential Equations 
Variable Coefficients and Variable Term 
Exact Differential Equations 
Nonlinear Differential Equations 
Higher Order Differential Equations 
