Undergraduate Catalogue - UPRM

COLLEGE OF ARTS AND SCIENCES
MATE 3181. DISCRETE MATHEMATICS I.
Three credit hours. Three hours of lecture per
week. Prerequisite: MATE 3031.
Sets, relations, and notation; algorithms; logic;
graphs; trees.
MATE 3182. DISCRETE MATHEMATICS II.
Three credit hours. Three hours of lecture per
week. Prerequisite: MATE 3181.
Combinatorics, difference equations, relations,
Boolean algebra, computational models.
MATE 4000. ELEMENTS OF TOPOLOGY.
Three credit hours. Three hours of lecture per
week. Co-requisite: MATE 4008.
Introduction to topology including topological
spaces, continuous functions and homeomorphisms,
metric spaces, compact spaces, connected spaces,
separation axioms, and elements of homotopy.
MATE 4003-4004. MATHEMATICS PRACTICE
FOR COOP STUDENTS I-II. Three credit hours
per semester. Prerequisite: Authorization of the
Director of the Department.
Practical experience in mathematics in cooperation
with private industry or government, to be jointly
supervised by the academic department, the COOP
Program Coordinator, and an official from the
COOP organization. A report will be required of
the student and the official at the end of the
semester.
MATE 4007. HIGHER GEOMETRY. Three
credit hours. Three hours of lecture per week.
Prerequisite: MATE 3063 or MATE 3185.
Coordinate systems in Euclidean 3-space, basic
configurations, vectors and geometry of n-space,
transformations, introduction to projective
geometry, axioms of non-Euclidean geometries.
MATE 4008. INTRODUCTION TO
ALGEBRAIC STRUCTURES. Three credit hours.
Three hours of lecture per week. Prerequisite:
MATE 3020.
Introduction to algebraic systems; sets, semigroups,
groups, rings, fields.
MATE 4009. ORDINARY DIFFERENTIAL
EQUATIONS. Three credit hours. Three hours of
lecture per week. Prerequisite: MATE 3063 or
MATE 3185.
Ordinary differential equations with applications:
basic existence theorem, linear systems, the
Laplace transform, series solutions, introduction to
Fourier series and orthogonal functions.
MATE 4010. INTRODUCTION TO COMPLEX
VARIABLES WITH APPLICATIONS. Three
credit hours. Three hours of lecture per week.
Prerequisite: MATE 3063 or MATE 3185.
Course designed for students who desire a working
knowledge of complex variables. Topics to be
covered include analytic functions, singularities,
residues, complex integration, power series,
conformal mapping.
MATE 4020. PARTIAL DIFFERENTIAL
EQUATIONS AND FOURIER SERIES. Three
credit hours. Three hours of lecture per week.
Prerequisite: MATE 4009.
Separation of variables in the solution of partial
differential equations, orthogonal expansions,
Fourier series in certain function spaces, and an
introduction to boundary value problems.
MATE 4021. FUNDAMENTALS OF
MATHEMATICAL LOGIC. Three credit hours.
Three hours of lecture per week. Prerequisite:
MATE 3020 or authorization of the Director of the
Department.
An introductory course to the fundamental
problems of logic, such as variables, the sentencial
calculus, the theory of identity, the theory of
classes, the theory of relations, and the deductive
method.
MATE 4023. MATHEMATICS EDUCATION I.
Three credit hours. Three hours of lecture per
week. Prerequisite: MATE 3020.
Strategies for teaching mathematics at the
elementary and secondary levels; analysis of
innovative programs of instruction in mathematics;
the use of computers in the teaching of
mathematics.
MATE 4031. INTRODUCTION TO LINEAR
ALGEBRA. Three credit hours. Three hours of
lecture per week. Prerequisite: MATE 3032 or
MATE 3184.
Euclidean vector spaces, matrices and linear
equations, spectral decomposition of normal
operators.
Undergraduate Catalogue 2004-2005 189