OEO Office of Equal Opportunity - Department of Mathematics and ...

MATHEMATICS AND STATISTICS 249
**318. Graph Theory. (3)
Trees, connectivity, planarity, colorability, and digraphs; algorithms
and models involving these concepts.
Restriction: permission of instructor. {Spring}
**319. Theory of Numbers. (3)
Divisibility, congruences, primitive roots, quadratic residues,
diophantine equations, continued fractions, partitions, number
theoretic functions. {Spring}
**321. Linear Algebra. (3) 1
Linear transformations, matrices, eigenvalues and eigenvectors,
inner product spaces.
Prerequisite: 264. {Fall, Spring}
322. Modern Algebra I. (3)
Groups, rings, homomorphisms, permutation groups, quotient
structure, ideal theory, fields.
Prerequisite: 264. {Fall}
**327. Introduction to Mathematical Thinking and
Discrete Structures. [Discrete Structures.] (3)
Course will introduce students to the fundamentals of mathematical
proof in the context of discrete structures. Topics
include logic, sets and relations, functions, integers, induction
and recursion, counting, permutations and combinations and
algorithms. Students who do not have the prerequisite may
seek permission of the instructor.
Prerequisite: 162 and 163. (Fall)
**412. Nonlinesar Dynamics and Chaos. (3)
Qualitative study of linear and nonlinear ordinary differential
equations and discrete time maps including stability analysis,
bifucations, fractal structures and chaos; applications to biology,
chemistry, physics and engineering.
Prerequisites: 264 and 314 or 316.
**415. [*415.] History and Philosophy of Mathematics.
[Philosophy of Mathematics.] (3)
(Also offered as PHIL 415.) A historical survey of principal
issues and controversies on the nature of mathematics.
Emphasis varies from year to year. Student who does not
have prerequisite may seek permission of instructor.
Prerequisite: 356 or 456.
*421. Modern Algebra II. (3)
Theory of fields, algebraic field extensions and Galois theory
for fields of characteristic zero.
Prerequisite: 322 or 422. {Alternate Springs}
**422. Modern Algebra for Engineers. (3)
Groups, rings and fields. (This course will not be counted in
the hours necessary for a mathematics major.)
Prerequisite: 264. {Fall}
*431. Introduction to Topology. (3)
Metric spaces, topological spaces, continuity, algebraic topology.
Prerequisite: 401. {Alternate Falls}
ARTS AND
SCIENCES
**331. Survey of Geometry. (3)
Topics from affine, projective, Euclidean and hyperbolic
geometries.
Prerequisites: 163 and (314 or 321). {Offered upon demand}
**356. [*356.] Symbolic Logic. (4)
(Also offered as PHIL 356.) This is a first course in logical
theory. Its primary goal is to study the notion of logical
entailment and related concepts, such as consistency and
contingency. Formal systems are developed to analyze these
notions rigorously.
**375. Introduction to Numerical Computing. (3)
(Also offered as CS 375.) An introductory course covering
such topics as solution of linear and nonlinear equations;
interpolation and approximation of functions, including
splines; techniques for approximate differentiation and integration;
solution of differential equations; familiarization with
existing software. {Fall, Spring}
391. Advanced Undergraduate Honors Seminar. (1-3 to
a maximum of 8) ∆
Advanced problem solving. Especially recommended for
students wishing to participate in the Putnam Intercollegiate
Mathematical Competition.
Restriction: permission of instructor. {Offered upon demand}
393. Topics in Mathematics. (3, no limit) ∆
Selected topics from analysis, algebra, geometry, statistics,
model building, interdisciplinary studies and problem solving.
{Offered upon demand}
401./**501. Advanced Calculus I. (4)
Rigorous treatment of calculus in one variable. Definition and
topology of real numbers, sequences, limits, functions, continuity,
differentiation and integration. Students will learn how
to read, understand and construct mathematical proofs.
Prerequisite: 264 and two courses at the 300+ level. {Fall,
Spring}
434./534. Introduction to Differential Geometry. (3)
Elementary theory of surfaces, differential forms, integral
geometry and Riemannian geometry.
Prerequisite: 311 or 402. {Offered upon demand}
**439. [*439.] Topics in Mathematics. (1-3, no limit) ∆
{Offered upon demand}
441. [441./527.] Probability. (3)
(Also offered as STAT 461/561.) Mathematical models for
random experiments, random variables, expectation. The
common discrete and continuous distributions with application.
Joint distributions, conditional probability and expectation,
independence. Laws of large numbers and the central
limit theorem. Moment generating functions.
Prerequisite: 264. {Fall}
462./512. Introduction to Ordinary Differential
Equations. (3)
Linear systems. Existence and uniqueness theorems, flows,
linearized stability for critical points, stable manifold theorem.
Gradient and Hamiltonian systems. Limit sets, attractors,
periodic orbits, Floquet theory and the Poincare Map.
Introduction to perturbation theory.
Prerequisite: 314 or 321, 316, 401. {Fall}
463./513. Introduction to Partial Differential Equations. (3)
Classification of partial differential equations; properly posed
problems; separation of variables, eigenfunctions and
Green’s functions; brief survey of numerical methods and
variational principles.
Prerequisites: 312, 313, 314 or 321, one of 311 or 402.
{Spring}
464./514. Applied Matrix Theory. (3)
Determinants; theory of linear equations; matrix analysis of
differential equations; eigenvalues, eigenvectors and canonical
forms; variational principles; generalized inverses.
Prerequisite: 314 or 321. {Fall}
402./**502. Advanced Calculus II. (3)
Generalization of 401/501 to several variables and metric
spaces: sequences, limits, compactness and continuity on
metric spaces; interchange of limit operations; series, power
series; partial derivatives; fixed point, implicit and inverse
function theorems; multiple integrals.
Prerequisite: 401.
*466. Mathematical Methods in Science and
Engineering. (3)
Special functions and advanced mathematical methods
for solving differential equations, difference equations and
integral equations.
Prerequisites: 311, 312, 313, 316. {Spring}
*471. Introduction to Scientific Computing. (3)
(Also offered as CS 471.) Introduction to scientific computing
fundamentals, exposure to high performance programming
language and scientific computing tools, case studies of
scientific problem solving techniques.
UNM CATALOG 2006–2007 Symbols, page 611.