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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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