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Descriptions of Mathmatics

MATH 441
Introduction
to
Numerical Analysis . [3]
Topics of this course include:
numerical linear algebra , interpolation,
numerical differentiation
and integration, solution of
non
- linear equations , acceleration
of convergence and numerical
treatment of differential
equations . Prerequisites: MATH
225, 251, 301 and CMSC 201,
or permission of instructor.

MATH 452
Introduction to
Stochastic Processes. [3]
This is a non-measure theoretic
course. Topics include general
Markov chains (branching
process, queuing processes,
birth and death processes, and
Poisson processes), secondorder
processes (Gaussian
processes and Wiener
processes) and an introduction
to stochastic differential equations .
Prerequisite: STAT 451
or 355.

MATH 456
Mathematical Methods for
Science and Engineering. [3]
Vector analysis and tensors,
Sturm-Liouville problems and
Fourier series, complex analysis ,
integral transforms and
variational calculus. Prerequisites:
MATH 221, 225 and 251.

MATH 465
Introduction to
Artificial Neural Networks.
This course gives a systematic
introduction to artificial neural
networks, which represent a
rather new and fundamentally
different approach to computing
and information processing.
Providing parsimonious universal
approximators for static and
dynamic mappings, synthetic
methodologies for building models
and/or solutions, abilities to
learn from and adapt to environments,
and massively parallel
computation paradigms, the
artificial neural networks have
formed a powerful approach to
solving non -linear or complex
problems in a broad spectrum
of areas including signal
speech/image processing, system
control, pattern recognition,
robotics, financial management,
digital communication, etc. This
course will cover multi-layer perceptrons,
recurrent neural nets,
global minimization for training,
adaptive and robust neural
nets, neural filtering, identification
and control, support vector
machines, self-organizing maps,
etc. Prerequisites: MATH 221,
251, 301 and STAT 451, or permission
of instructor.

MATH 470
Introduction to Actuarial
Mathematics. [2]
This course is intended to prepare
students for Society of
Actuaries Exam Course I Mathematical
Foundations of Actuarial
Science. Prerequisites: MATH
251 and STAT 451.

MATH 475
Combinatorics

and Graph Theory . [3]
General enumeration methods,
difference equations , generating
functions. Elements of
graph theory, including transport
networks, matching theory
and graph algorithms. Introduction
to finite geometries and
block designs. Prerequisites:
MATH 301 or permission of
instructor.

MATH 476
Introduction to Game Theory.
Purely non-cooperative or zerosum
games between two players
are introduced. In simple cases,
solutions of such games use
techniques of saddle points or
other geometric means. VonNeumann’s
Min-Max theorem
assures optimal mixed strategies.
In general, linear programming
techniques must be
employed. Study of convex sets
in Euclidean spaces, in particular
of polyhedra, and polytopes is
necessary for full understanding
of the general case. In non-zero
sum situations with two or more
players, the fundamental results
of John Nash assuring equilibria
in mixed strategies and on arbitration
or bargaining schemes
are studied. For cooperative
games with many players, several
solution concepts are studied,
including Shapley values and
core
allocations. Diverse application
are considered. Purely noncooperative
or zero -sum games
between two players are introduced.
Solutions of such entail
techniques of finding saddle
points or geometric means in
simple cases. Prerequisites:
Math 221 and Math 251.

MATH 479
Mathematics
Problem-Solving Seminar. [1]
Mathematical problem-solving
techniques, mathematical communication
skills. Problem sessions
with problems ranging
from pre-calculus to analysis,
algebra, geometry, combinatorics
and probability. Problems
ranging from quickies to mini
research problems. Students
will develop and reinforce skills
from previous mathematics
courses and will be introduced
to topics from more advanced
courses. Note: Repeatable for
credit. Prerequisite: Permission
of instructor.

MATH 480
Senior Seminar. [1]
Note: Repeatable for credit.

MATH 481
Mathematical Modeling. [3]
Derivation and analysis of mathematical
models of phenomena
from physics, engineering and
other exact sciences. Topics
include stability of equilibria of
dynamical systems with emphasis
on the qualitative aspects of
solutions, phase plane analysis
and linearization of non-linear
systems. Additional topics from
catastrophe theory, bifurcation,
optimization and chaos will be
covered as time permits. Examples
will be drawn from population
dynamics, flywheel governor,
a model for heartbeat,
bang-bang controls, self-sustained
oscillations and morphogenesis.
Prerequisites: MATH
221, 225 and 251.

MATH 482
Non-linear Optimization. [3]
Introduction to convex analysis.
One-dimensional minimization.
Unconstrained optimization in
algorithms, global convergence
and rates of convergence.
Quasi-Newton techniques. Convex
programming: optimality
conditions and duality. Penalty
and Barrier methods. Prerequisite:
MATH 251. Corequisite:
MATH 301.

MATH 483
Linear and Combinatorial
Optimization. [3]
Integer programming. The traveling
salesman problem.
Advanced linear programming
techniques. Complexity. Projective
methods in linear programming.
The Karmarkar method.
Prerequisite: MATH 381.

MATH 484
Stochastic Methods in
Operations Research. [3]
Topics of this course include:
introduction to Markov chains,
Poisson processes, introduction
to queuing theory, Stochastic
programming, introduction to
deterministic and Stochastic
dynamic programming. Prerequisite:
STAT 355 or 451.

MATH 485
Introduction to the
Calculus of Variations. [3]
This course will provide a modern
introduction to basic results
of the classical calculus of variations.
Special emphasis will be
given to the theory of secondorder
conditions. Considerable
attention will be devoted to
physical applications of variational
methods. Prerequisites:
MATH 221, 225, 251 and 301.

MATH 486
Introduction to
Dynamical Systems.
The course will address ideas
from discrete dynamical systems,
including fixed points,
periodic points, bifurcations,
and an explanation of period 3
implied chaos. Fractals such as
Sierpinski’s gasket, Julia sets
and Mandelbrot sets also will
be introduced. Prerequisite:
MATH 221 and 225 and some
programming experience; Math
301 or permission or instructor.

MATH 490
Special Topics
in Mathematics. [1-4]

MATH 495
Topics in Mathematics of
Operations Research. [3]
Introduction to recent and
advanced techniques of optimization
and operations
research. The course will be
redefined from time to time and
will reflect the instructor’s interests.
Prerequisite: Permission
of instructor.

MATH 496
Mathematics Practicum. [1-4]
Under faculty direction, students
will write a report dealing
with mathematical concepts or
techniques utilized or implemented
in internships or cooperative
education or in the workplace.
Note: This course is
repeatable up to four times.
Prerequisite: Permission of
instructor.

MATH 497
Senior Thesis. [3]
The student will be required to
prepare an exposition of either
a significant area of mathematics
or of the results of a student
research project. Typically,
the former will be in connection
with an upper- division course
the student has completed or
independent study (MATH 499).

MATH 499
Independent Study
in Mathematics. [1-4]
Under this heading, a student
may agree to a course with a
particular faculty member on a
topic not covered in the regular
curriculum. The arrangements
with the faculty member must
be made before the student
registers for the course.

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