academic-catalog2011.. - LAU Publications - Lebanese American ...

Department of Computer Science and Mathematics
iterative solutions for finding roots (Newton’s
Method), curve fitting, function approximation,
numerical differentiation and integration, explicit
and implicit methods, differential equations
(Euler’s Method), and finite differences.
Prerequisite: MTH201 Calculus III.
MTH304 Differential Equations [3-0, 3 cr.]
This course covers the topics of first
order ordinary differential equations and
applications, linear higher order differential
equations and applications, systems of linear
differential equations, series solutions of
differential equations and solutions, and
Laplace transforms.
Prerequisite: MTH201 Calculus III.
MTH305 Probability and Statistics [3-0, 3 cr.]
This course covers essentially the distribution
theory, estimation and tests of statistical
hypotheses. More specifically, the topics
of this course include: Random variables,
discrete probability, conditional probability,
independence, expectation, standard discrete
and continuous distributions, regression and
correlation, point and interval estimation. Also
included are illustrations from various fields.
Prerequisite: MTH 201 - Calculus III.
MTH306 Non-Linear Dynamics and Chaos
[3-0, 3 cr.]
This course covers the topics of iteration,
fixed and periodic points, graphical analysis of
iteration, stable and unstable orbits, attracting
and repelling periodic points, iterations of a
quadratic family, Julia sets, Mandelbrot sets,
fractals, and chaos.
Prerequisite: MTH201 Calculus III.
MTH307 DISCRETE STRUCTURES II
This course covers computational complexity
and order analysis, recurrence relations
and their solutions, graphs and trees,
elementary computability, classes P and
NP problems, NP-completeness (Cook’s
theorem), NP-complete problems, reduction
techniques, automata theory including
deterministic and nondeterministic finite
automata, equivalence of DFAs and NFAs,
regular expressions, the pumping lemma for
regular expressions, context-free grammars,
Turing machines, nondeterministic Turing
machines, sets and languages, uncomputable
functions, the halting problem, implications of
uncomputability, Chomsky hierarchy, and the
Church-Turing thesis.
Prerequisites: MTH207: Discrete Structures I,
and MTH201: Calculus III.
MTH 308: Number Theory
Topics covered are: The history of number
representation systems, divisibility, greatest
common divisor and prime factorization, linear
Diophantine equations, congruences, and
condition congruences.
MTH309 Graph Theory [3-0, 3 cr.]
This course covers the fundamental
concepts and methods of graph theory,
and their applications in various areas of
computing. Topics include graphs as models,
representation of graphs, trees, distances,
matching, connectivity, and flows in networks,
graph colorings, Hamiltonian cycles, traveling
salesman problem, and planarity.
Prerequisite: MTH201 Calculus III.
MTH 310: Set Theory
Operations on sets and families of sets,
ordered sets, transfinite induction, axiom of
choice and equivalent forms, and ordinal and
cardinal numbers.
Prerequisite: MTH207
MTH311 Abstract Algebra [3-0, 3 cr.]
This course studies the algebra of sets, the
definition and basic properties of groups,
rings, and fields, and the divisibility theorems
for integers and polynomials.
Prerequisite: MTH207 Discrete Structures I,
and Junior Standing.
MTH 400: Advanced Linear Algebra
A thorough treatment of vector spaces and
linear transformations over an arbitrary field; the
Hamilton-Cayley Theorem, similarity, the Jordan
Normal form, the dual of a linear transformation,
direct sums, canonical forms, orthogonal and
unitary transformations, normal matrices, and
selected applications of linear algebra.
Prerequisite: MTH 301
MTH 401 Real Analysis I [3-0, 3 cr.]
Topics covered are: Metric spaces, basic topics
in topology, numerical sequences and series,
continuity and uniform continuity of functions,
differentiation, the mean-value theorem, Taylor’s
theorem, and the Riemann-Stieljes integral.
Prerequisite: MTH201Calculus III, MTH 207
Discrete Structures I, MTH 301 Linear Algebra
ACADEMIC CATALOG [ 2011-2012 ] SCHOOL OF ARTS AND SCIENCES
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