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# Descriptions of Mathmatics

MATH 215
Finite Mathematics for
Information Sciences.
This course focuses on the
area of mathematics of particular
use in the information sciences.
The basic linear algebra
of matrices used for solutions
of large scale systems of linear
equations is treated. Applications
of matrices such as Leontieff
models of multi-sector economics
and the basics of the
simples method for solving linear
economic optimization problems
are discussed. Fundamental
concepts of probability
including basic combinatorial
methods for probabilistic computations
are studied. An introduction
is given to decision theory.
This treatment is in the
context of Bayesian or statistical
decision theory, though
game theorectic versions may
be discussed. Possible optional
topics may include elementary
Markov chains or the matrix
This course is intended
for IFSM majors only. Prerequisite:
MATH 141, 151, 155 or
380.

MATH 221
Introduction to
Linear Algebra. 
Topics of this course include:
linear equations, Gauss-Jordan
reduction, matrices and determinants
and their properties,
vector spaces and subspaces,
basis and dimension, linear
transformations, kernel and
range, eigenvalues and eigenvectors,
and matrix diagonalization.
Prerequisites: MATH 141,
151, 155 or 380.

MATH 225
Introduction
to Differential Equations. 
Topics of this course include:
solutions of first- and secondorder
linear differential equations,
non-linear exact and separable
equations, integrating
factors, homogeneous equations,
higher-order linear equations.
initial and boundary value
problems, solutions as functions
of the equation parameters,
Laplace transforms, power
series solutions for Bessel and
Legendre equations, difference
equations and numerical methods.
Note: Recommended for
science majors who need a
basic knowledge of differential
equations. Recommended:
MATH 251. Prerequisite: MATH
142 or 152.

MATH 233
Fundamentals
of Geometry. 
In this course, the student will
learn and apply the principles of
geometry as well as recognize
and understand their relevance
to the real world. Topics include
fundamental concepts and patterns;
geometric reasoning and
proof; parallel and perpendicular
lines as they relate to
Euclidean, hyperbolic and elliptical
geometry; triangle relationships
and triangle congruence;
and similarity; investigating
right triangles, polygons,
surface area and volume,
and circles. Throughout the
course, special emphasis is
given to problem-solving techniques.
Prerequisite: MATH
132 or 150 or placement into
MATH 140 or 151.

MATH 251
Multivariable Calculus. 
Topics of this course include:
vectors, lines, planes and surfaces
in three dimensions. Vector
functions and their derivatives.
directional derivatives,
maxima, minima and Lagrange
multipliers. Multiple integrals,
area, volume, surface area,
integration in different coordinate
systems. Line integral,
Green’s theorem, Stokes’ theorem
and divergence theorem.
Prerequisite: MATH 142 or
152.

MATH 290
Special Topics
in Mathematics. [1-4]

MATH 299
Independent Study
in Mathematics. [1-4]
Prerequisite: Permission of
instructor.

MATH 301
Introduction to
Mathematical Analysis I. 
This course is a systematic
study of basic analysis with an
emphasis on formal proofs,
examples and counter examples.
Topics include properties
of the real line, sequences,
series, limits, continuity and differentiation
of functions, and
Riemann Integration. Highly
recommended: CMSC 203. Prerequisite:
MATH 142 or 152
and 221.

MATH 302
Introduction to
Mathematical Analysis II. 
Topics of this course include:
continuity, differentiation of
functions of several variables,
uniform convergence of
sequences of functions, multiple
integration, contraction mapping
principle, and implicit and
inverse function theorems.
Note: Credit will not be given for
both MATH 302 and 401. Prerequisites:
MATH 251 and 301.

MATH 306
Geometry. 
Topics of this course are to be
selected from foundations of
geometry, modern Euclidean
geometry, non-Euclidean geometry,
projective geometry and its
subgeometries. Prerequisite:
MATH 301.

MATH 341
Computational Methods. 

Basic computational methods
for interpolation, systems of linear
equations, least squares
numerical solution of
polynomial and transcendental
equations. Emphasis on the
methods and their computational
properties, rather than on
their analytic aspects. Prerequisites:
MATH 142 or 152, 221,
CMSC 201 or permission of
instructor.

MATH 380
Introduction to Operations
Research (MS). 
Linear programming, including
the simplex method. Transportation,
assignment and
trans-shipment problems. Network
problems. Not recommended
for mathematics/
statistics or computer science
majors. Note: Credit will not be
given for both MATH 380 and
381. Prerequisite: MATH 115
or 150.

MATH 381
Linear Methods in
Operations Research. 
Introduction to convex sets.
Theory of linear programming.
Applications to transportation
and assignment problems.
Introduction to graphs with
applications to network problems,
including shortest route
and maximum flow problems.
Introduction to game theory.
Note: Credit will not be given
for both MATH 380 and 381.
Prerequisite: MATH 221.

MATH 385
Introduction to
Mathematical Modeling. 
This is a project-oriented course
offering the opportunity to discover
how various real-world
problems can be described and
analyzed with the aid of simple
mathematical models and computer
simulations. Possible project
topics include operation of
a fuse, spread of pollutants in a
river, propagation of an infectious
disease, traffic flow on a
highway, oscillating chemical
reactions, etc. Specific selection
of problems will depend on
the background and interests of
the students enrolled in the
course. Students seeking elementary
teacher certification in
science or math are particularly
welcome. This course incorporates
constructivist principles
and has been designed as an
MCTP course for students in
the Maryland Collaborative for
Teacher Preparation Program.
Prerequisite: MATH 225.

MATH 390
Special Topics
in Mathematics. [1-4]