academic-catalog2011.. - LAU Publications - Lebanese American ...
academic-catalog2011.. - LAU Publications - Lebanese American ...
academic-catalog2011.. - LAU Publications - Lebanese American ...
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Department of Computer Science and Mathematics<br />
iterative solutions for finding roots (Newton’s<br />
Method), curve fitting, function approximation,<br />
numerical differentiation and integration, explicit<br />
and implicit methods, differential equations<br />
(Euler’s Method), and finite differences.<br />
Prerequisite: MTH201 Calculus III.<br />
MTH304 Differential Equations [3-0, 3 cr.]<br />
This course covers the topics of first<br />
order ordinary differential equations and<br />
applications, linear higher order differential<br />
equations and applications, systems of linear<br />
differential equations, series solutions of<br />
differential equations and solutions, and<br />
Laplace transforms.<br />
Prerequisite: MTH201 Calculus III.<br />
MTH305 Probability and Statistics [3-0, 3 cr.]<br />
This course covers essentially the distribution<br />
theory, estimation and tests of statistical<br />
hypotheses. More specifically, the topics<br />
of this course include: Random variables,<br />
discrete probability, conditional probability,<br />
independence, expectation, standard discrete<br />
and continuous distributions, regression and<br />
correlation, point and interval estimation. Also<br />
included are illustrations from various fields.<br />
Prerequisite: MTH 201 - Calculus III.<br />
MTH306 Non-Linear Dynamics and Chaos<br />
[3-0, 3 cr.]<br />
This course covers the topics of iteration,<br />
fixed and periodic points, graphical analysis of<br />
iteration, stable and unstable orbits, attracting<br />
and repelling periodic points, iterations of a<br />
quadratic family, Julia sets, Mandelbrot sets,<br />
fractals, and chaos.<br />
Prerequisite: MTH201 Calculus III.<br />
MTH307 DISCRETE STRUCTURES II<br />
This course covers computational complexity<br />
and order analysis, recurrence relations<br />
and their solutions, graphs and trees,<br />
elementary computability, classes P and<br />
NP problems, NP-completeness (Cook’s<br />
theorem), NP-complete problems, reduction<br />
techniques, automata theory including<br />
deterministic and nondeterministic finite<br />
automata, equivalence of DFAs and NFAs,<br />
regular expressions, the pumping lemma for<br />
regular expressions, context-free grammars,<br />
Turing machines, nondeterministic Turing<br />
machines, sets and languages, uncomputable<br />
functions, the halting problem, implications of<br />
uncomputability, Chomsky hierarchy, and the<br />
Church-Turing thesis.<br />
Prerequisites: MTH207: Discrete Structures I,<br />
and MTH201: Calculus III.<br />
MTH 308: Number Theory<br />
Topics covered are: The history of number<br />
representation systems, divisibility, greatest<br />
common divisor and prime factorization, linear<br />
Diophantine equations, congruences, and<br />
condition congruences.<br />
MTH309 Graph Theory [3-0, 3 cr.]<br />
This course covers the fundamental<br />
concepts and methods of graph theory,<br />
and their applications in various areas of<br />
computing. Topics include graphs as models,<br />
representation of graphs, trees, distances,<br />
matching, connectivity, and flows in networks,<br />
graph colorings, Hamiltonian cycles, traveling<br />
salesman problem, and planarity.<br />
Prerequisite: MTH201 Calculus III.<br />
MTH 310: Set Theory<br />
Operations on sets and families of sets,<br />
ordered sets, transfinite induction, axiom of<br />
choice and equivalent forms, and ordinal and<br />
cardinal numbers.<br />
Prerequisite: MTH207<br />
MTH311 Abstract Algebra [3-0, 3 cr.]<br />
This course studies the algebra of sets, the<br />
definition and basic properties of groups,<br />
rings, and fields, and the divisibility theorems<br />
for integers and polynomials.<br />
Prerequisite: MTH207 Discrete Structures I,<br />
and Junior Standing.<br />
MTH 400: Advanced Linear Algebra<br />
A thorough treatment of vector spaces and<br />
linear transformations over an arbitrary field; the<br />
Hamilton-Cayley Theorem, similarity, the Jordan<br />
Normal form, the dual of a linear transformation,<br />
direct sums, canonical forms, orthogonal and<br />
unitary transformations, normal matrices, and<br />
selected applications of linear algebra.<br />
Prerequisite: MTH 301<br />
MTH 401 Real Analysis I [3-0, 3 cr.]<br />
Topics covered are: Metric spaces, basic topics<br />
in topology, numerical sequences and series,<br />
continuity and uniform continuity of functions,<br />
differentiation, the mean-value theorem, Taylor’s<br />
theorem, and the Riemann-Stieljes integral.<br />
Prerequisite: MTH201Calculus III, MTH 207<br />
Discrete Structures I, MTH 301 Linear Algebra<br />
ACADEMIC CATALOG [ 2011-2012 ] SCHOOL OF ARTS AND SCIENCES<br />
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