Grad MathCamp
Objectives
The goal is to introduce Grad Students to the mathematics that
will be applied to economics
in the Master's program. It is intended to bring students up to date
with the basic mathematical skills needed for a graduate study in
economics.
A Math Proficiency exam is tentatively scheduled on Thur. Sept 8th
from 6pm to 8pm. The exam is compulsory for all new entering graduate students.
The purpose of the exam is to evaluate your math background at the level
of advanced undergraduate differential calculus,
calculus of several variables and its applications, optimization techniques,
intergral Calculus,
and dynamic optimization analysis. You may bring hand written notes to the
exams.
There will be a review session.
I encourage you to ask questions in class. You can also ask me questions any time by e-mail or during my office hours.
Exam
The Math Proficiency exam will be held on
Thursday Sept 8th, 6:00pm to 8:00pm
(Location: TBA )
Required Text
Alpha Chiang and Kevin Wainwright (2005)
Fundamental Methods of Mathematical Economics, McGraw-Hill Irwin
Carl P. Simon and Lawrence Blume (1994) Mathematics for
Economists. W.W. Norton and Co., New York, NY.
Any of the above texts will suffice; although the Simon and Blume is perhaps, one
of
the clearest and most concise modern texts for grad
students in economics. It is rigorous in its
mathematics and presents a variety of
examples and applications that will be useful throughout your graduate
school career. Both will be available in the bookstore and Tisch Library; but
you may also want to check amazon.com (or equivalent) for a used one.
Other Texts
The following texts are also useful:
(i) Dixit, Avinash (1990), Optimization in Economics,
2nd Edition, Oxford university Press
(ii) Hoy et. al, Mathematics for Economists, MIT Press
(iii) Klein, Michael,
Mathematical
Economics Methods for Economics. Available in the Tisch
library.
Lectures: Times and Room
The Math Camp shall run from Thursday Aug 25th till Wednesday Aug 31st.
We shall meet twice a day in Barnum 114: from 10 - 12 noon in the
mornings; and
then from 1:30 - 3:30. in the afternoons
COURSE OUTLINE
August 25th
Review of functions (as used in economics), and their
properties;
Exponential and Logarithm functions;
Differential
calculus (one-variable) and applications
Intro to functions of several variables
Readings:
CW chp 10; SB chp 2-5;
August 26th
Calculus of several variables
Quadratic forms
Static optimization: uncontrained and constrained optimization
(i.e., equality constraints, inequality constraints, mixed
constraints, first and second order conditions)
Readings:
CW chp 7-9, 11-13; SB chp 14, 18-19
August 29th
Envelop theorem and duality
Non-linear programming and
Kunh-Tucker conditions
Integral calculus and sme applications
Readings:
CW chp 13-14; SB Appendix A4
August 30th
Intro to discrete time dynamic analysis (difference equations; stability
analysis)
Intro to differential equations
No classes after lunch: Graduate Student Orientation
Readings:
August 31st
Discrete time dynamic optimization
Continuous time
optimization (optimal control)
Readings:
CW chp. 15, 17-20