MATH
363 -
MATHEMATICAL MODELING
Fall 2004
( 3
credits ) Topics in game theory include: games with perfect information; Nash
equilibrium, mixed strategy equilibrium, Bayesian games; games with imperfect
information; repeated games. Topics in curve fitting include: curve fitting
with polynomials; Hermite method, Lagrange method, least-squares method;
interpolation with piecewise polynomial functions; curve fitting with splines;
smoothing techniques.
Prerequisite:
Math 130
INSTRUCTOR: DR.
DANIEL J. GHEZZI
OFFICE: A-404
E-MAIL: djghezzi@kings.edu
PHONE
#'s:
x
5299
(office)
570 -
674 - 4039
(home - emergencies
only please)
TO
TUESDAY
BE
WEDNESDAY
DETERMINED
THURSDAY
FRIDAY
Other times available by
appointment
COURSE
MEETS: MONDAY, WEDNESDAY, and FRIDAY
TIME: 8:00 am - 8:50 am (compressed schedule : 10:00 - 10:35)
PLACE: MU- 204
The
topics included in this course will be covered through lectures, class
discussions, and homework assignments. In the Game Theory portion of the
course, students will learn how to model real world problems appearing in the
fields of economics, biology, and the social & behavioral sciences. No
prior knowledge of these fields is required. Sound logical reasoning will be
emphasized.
In
the Curve Fitting portion of the course, students will study the various
mathematical methods of fitting a curve to a set of data. They will learn how
to choose an appropriate model for the data and how to use the model to
estimate or predict an unobserved response. After completing this course, the
students will be able to compare and contrast the results given by computer
graphics packages because they will understand the mathematics upon which the
packages are built.
GAME
THEORY TEXT:
“An
Introduction To Game Theory”
by
Martin J. Osborne
Oxford
University Press, Inc. 2004
ISBN
#: 0-19-512895-8
Supporting
materials can be viewed online at:
http://www.economics.utoronto.ca/osborne/igt/
THERE
IS NO TEXT FOR THE CURVE FITTING PORTION OF THIS COURSE.
LECTURE
NOTES AND THE PROFESSOR’S HANDOUTS WILL SUFFICE.
CLASS
POLICIES:
1.) There will be 4 tests. 2 tests on game theory and 2 tests on
curve fitting. The 4th test
will be given during the final exam period at the end of the semester as
scheduled by the registrar.
A
make-up for an exam will only be given in rare cases when:
a.) You have prior
written verification of a valid reason
and
you have notified the instructor prior to the time of the exam
or
b.) You have a confirmable emergency and notify the
instructor as soon as possible
Make-up exams will be more difficult than the
regularly scheduled exam.
2.) Homework will be assigned each week
and "is ordinarily due" at the beginning
of the first class meeting the following week. Some
of the homework problems
will be designated as “work alone” problems. This
means that the student must tackle the problem without any outside help (i.e.
help other than that of the professor). Students can work together on problems
that aren’t designated as “work alone”.
3.) King’s College students ARE expected to attend all classes
and to actively participate.
(See King's College Student Handbook).
Any student who misses more than (3) classes during
the semester could incur a letter grade reduction. The loss of a letter grade
is at the discretion of the instructor. If you are absent from class by reason
of emergency, serious illness, or compelling cause, then you must notify the
instructor as soon as possible and submit a written verification for the
absence.
4.) King’s College students ARE expected to arrive to class on
time and to stay throughout the entire class period. If you arrive after the
roll has been taken, then you must see the instructor after class to have your
name added to the roll.
5.) Students should read the King’s College policy regarding student conduct
and
academic integrity. (See King's College Student Handbook).
6.) The federal government requires that instructors make special
accommodations for students who have a bona-fide disability that impacts on
their ability to learn the course material. Students with certifiable
disabilities should privately inform the instructor so that appropriate
arrangements can be made.
FINAL GRADE COMPUTATION
Homework: 20%
4 Exams 80% {each exam is
worth 20%}
Each
student should read the policy on academic integrity outlined in the King's
College Student Handbook.
Intended
Schedule (subject to change by the professor)
GAME THEORY Completed
By:
Chapter 1:
Introduction
September 2
1.1 What
is game theory
1.2 The
theory of rational choice
1.3 Coming
attractions
Chapter 2:
Nash
Equilibrium: Theory September
17
2.1 Strategic
games
2.2 through
2.5 Examples
2.6 Nash
equilibrium
2.7 Examples
of Nash equilibrium
2.8 Best
response functions
2.9 Dominated
actions
2.10 Equilibrium
in a single population
Chapter 3:
Nash
Equilibrium: Illustrations September 22
Exam #1 Chapters
1, 2, and 3 September 27
Chapter 5:
Extensive
Games w/Perfect Information
Theory October
6
5.1 Extensive
games w/perfect information
5.2 Strategies
and outcomes
5.3 Nash equilibrium
5.4 Subgame perfect equilibrium
5.5 Finding subgame perfect equilibrium
of
finite horizon games
Chapter 6:
Extensive
Games w/Perfect Information
Illustrations
October
11
Chapter 10:
Extensive
Games w/Imperfect Information
October 20
10.1 Extensive
games w/imperfect information
10.2 Strategies
10.3 Nash
equilibrium
10.4 Beliefs
and sequential equilibrium
10.5 Signaling
games
Exam #2 Chapters
5, 6, and 10 October 22
CURVE FITTING
*1 Review
of functions:
derivatives,
integration, graphs October
27
*2 Fitting
curves using polynomials November
12
Exam #3 Topics
*1 and *2 November 15
*3 Linear
Splines
November 23
*4 Cubic
Splines
December
6
*5 Introduction
on Projectors December
10
Exam #4 Topics
*3, *4, and *5 Finals
Week