600-level courses; Spring 1999
Each semester, faculty propose some 600-level courses to possibly be offered
to graduate students, primarily doctoral students. Some of these courses
follow up on 500-level courses, and some are primarily focused on current
research. Depending on several variables, including student interest, these
courses may be offered as regular courses, or they may be offered by faculty
as independent study courses, or the offered course may be withdrawn (i.e.,
cancelled).
The following 600-level courses were offered in the spring 1999 semester:
Course descriptions follow.
Courses from previous semesters: Fall 1998
| Spring 1998
Prerequisite: MATH 510 and at least one additional 500-level
mathematics education class, or consent of department.
COURSE OBJECTIVES: The objectives of MATH 610 are:
to familiarize you with materials and publications for teaching mathematics
with respect to the new Principles and Standards of School Mathematics;
to acquaint you with affective domain research on the learning and
teaching of mathematics; to acquaint you with current curriculum issues of
attitudes, beliefs, appreciations, preferences, emotions, feelings, and values
in mathematics education. This semester's MATH 610-B is an in-depth investigation
of current developments in areas of attitude and beliefs research that relate
directly to mathematics learning, curriculum, and instruction.
TEXTS:
Grouws, D.A., Ed. (1992). Handbook of research on mathematics teaching
and learning.
New York: Macmillan Publishing Company. [RECOMMENDED TEXT]
National Council of Teachers of Mathematics. (1998). Principles and
Standards for School Mathematics:Draft. Reston, VA: NCTM. [RECOMMENDED
TEXT]
Owens, D.T., Ed. (1993). Research Ideas for the Classroom: Middle Grades
Mathematics.
New York: Macmillan Publishing Company. [RECOMMENDED TEXT]
Jensen, R.J., Ed. (1993). Research Ideas for the Classroom: Early Childhood
Mathematics.
New York: Macmillan Publishing Company. [RECOMMENDED TEXT]
Wilson, P.S., Ed. (1993). Research Ideas for the Classroom: High School
Mathematics.
New York: Macmillan Publishing Company. [RECOMMENDED TEXT]
Prerequisite: MATH 532
The course is intended to provide the student with a deeper
knowledge of complex function theory through the study of some topics which
have been of classical interest which also have a current research direction.
In each topical area both some classical results and some questions of current
research activity will be discussed. Topical areas included are to be:
I. Normal families and functions
The Riemann mapping theorem
Montel's theorem
Recent work
II. Bergman spaces
Classical connections
Canonical divisors
III. Univalent and multivalent functions
IV. Value distribution for functions of unbounded characteristic
There will be no text, but appropriate references will be supplied
and, in some instances, put on reserve in Founders Library. Of course, the
current research work is only available through journal articles or preprints.
Prerequisite: MATH 530 and previous exposure to differential
equations
Incompressible and invicid fluids can be modeled by a system
of so-called Euler's equations, which represent the most simple model for
fluids. The theory, as well as the numerical methods, for these equations
are surprisingly not yet complete, particularly for flows in 3-dimensional
domains. An overview of known results as well as of open problems will be
presented in the lectures for this course.
-
Euler's equations
-
Rotation and Vorticity
-
Gas flow in one dimension
-
Euler's equation in two dimensions
-
Estimates in three dimensions and open problems
-
Navier-Stokes approximation
Text: None
References:
-
A.J. Chorin and J.E. Marsden, A Mathematical Introduction
to Fluid Mechanics, second edition, Springer-Verlag, New York, 1990.
-
P.-L. Lions, Mathematical Topics in Fluid Mechanics, Volume
1: Incompressible Models, Oxford University Press, Oxford, 1996.