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Math 500  [ 3 ]  Computing in the Mathematics Curriculum
Description: Use of computers and graphing utilities in the mathematics classroom. Introduction to hardware and commercial software. Applications of selected programming languages to the teaching of mathematics.
Prerequisite: 162 or 181. Restriction: College of Education graduate students
Math 501  [ 4 ]  Advanced Calculus I
Description: 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. Restriction: College of Education graduate students.
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
  Math 501 001 TR  1230-1345      Cancelled, .
  AOA Math 401 W  1200-1250       
36407  Math 501 002 TR  1230-1345  DSH    Vassilev, J.
Math 502  [ 3 ]  Advanced Calculus II
Description: 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: 501. Restriction: College of Education graduate students.
Math 503  [ 3 ]  Calculus for Teachers
Description: A penetrating look at functions, derivatives, integrals, and the Fundamental Theorem of Calculus that makes explicit how topics in the secondary school curriculum come to fruition in this fundamental subject.
Prerequisite: Restriction: permission of instructor.
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
35604  Math 503 001 WEB        Ediger, C.
Math 504  [ 3 ]  Introductory Numerical Analysis: Numerical Linear Algebra
Description: (Also offered as CS 575.) Direct and iterative methods of the solution of linear systems of equations and least squares problems. Error analysis and numerical stability. The eigenvalue problem. Descent methods for function minimization, time permitting.
Prerequisite: 464, 514
Semesters offered:  Spring
Math 505  [ 3 ]  Introductory Numerical Analysis: Approx. & Diff. Equations
Description: (Also offered as CS 576.) Numerical approximation of functions. Interpolation by polynomials, splines and trigonometric functions. Numerical integration and solution of ordinary differential equations. An introduction to finite difference and finite element methods, time permitting.
Prerequisite: 316 or 401
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
  Math 505 001 TR  1800-1915  HUM    Cancelled, .
  AOA C S 576          
36390  Math 505 002 TR  1700-1815  HUM    Day, D.
Math 506  [ 3 ]  College Geometry
Description: An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry.
Prerequisite: Restriction: College of Education graduate students.
Semesters offered:  Spring
Math 507  [ 3 ]  Mathematics from a Historical Perspective
Description: A survey of mathematical developments prior to 1800; emphasis on problem solving techniques; comparison of older and more modern methods.
Prerequisite: 163. Restriction: College of Education graduate students.
Semesters offered:  Fall
Math 508  [ 3 ]  Theory and Practice of Problem Solving
Description: An experience in mathematical invention and discovery at the level of high school geometry and algebra that includes a deeper look at sequences, series, and recursions.
Prerequisite: 180 or 162. Corequisite: 306. Restriction: College of Education graduate students.
Semesters offered:  Offered upon demand
Math 509  [ 3 ]  Applications of Mathematics
Description: An experience in mathematical invention and discovery at the level of high school geometry and algebra that includes a deeper look at sequences, series, and recursions.
Prerequisite: 181 or 163. Restriction: College of Education graduate students.
Math 510  [ 3 ]  Introduction to Analysis I
Description: Real number fields, sets and mappings. Basic point set topology, sequences, series, convergence issues. Continuous functions, differentiation, Riemann integral. General topology and applications: Weierstrass and Stone-Weierstrass approximation theorems, elements of Founier Analysis (time permitting).
Prerequisite: 321, 401.
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18798  Math 510 001 TR  1100-1215  EDUC    Pereyra, M.
Math 511  [ 3 ]  Introduction to Analysis II
Description: Continuation of 510. Differentiation in R^n. Inverse and implicit function theorems, integration in R^n, differential forms and Stokes theorem.
Prerequisite: 510.
Semesters offered:  Spring
Math 512  [ 3 ]  Introduction to Ordinary Differential Equations
Description: 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: Math 314, or 321, 316, 401.
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18801  Math 512 001 TR  1400-1515  ORTG    Embid, P.
  AOA Math 462          
Math 513  [ 3 ]  Introduction to Partial Differential Equations
Description: Classification of partial differential equations; properly posed problems; separation of variables, eigenfunctions and Green's functions; brief survey of numerical methods and variational principles.
Prerequisite: Math 312, 313, 314 or 321, one of 311 or 402.
Semesters offered:  Spring
Math 514  [ 3 ]  Applied Matrix Theory
Description: Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors and canonical forms; variational principles; generalized inverses.
Prerequisite: 314 or 321.
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18806  Math 514 001 TR  1530-1645  DSH    Coutsias, E.
  AOA Math 464          
Math 519  [ (3, N ]  Selected Topics in Number Theory
Description: (Credit: 3, no limit.)
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
29538  Math 519 001 MWF  1100-1150  HUM    Buium, A.
  Analogies btw func & numbers          
Math 520  [ 3 ]  Abstract Algebra I
Description: Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains.
Prerequisite: Math 322.
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18814  Math 520 001 MWF  1000-1050  HUM    Buium, A.
Math 521  [ 3 ]  Abstract Algebra II
Description: Continuation of 520. Module theory, field theory, Galois theory.
Prerequisite: Math 321, 520
Semesters offered:  Spring
Math 527  [ 3 ]  Probability
Description: Mathematical models for random experiments, random variables, expectation. The common discrete and continuous distributions with application. Joint distributions, conditional probability and expectation and independence. Laws of large numbers and the central limit theorem. Moment generating functions.
Prerequisite: 264 or equivalent
Semesters offered:  Fall
Math 528  [ 3 ]  Intermediate Probability
Description: Multivariate distributions and densities, transformations of random vectors, special multivariate distributions including the normal and multinomial, limit thereoms for sequences of random variables and topics from stochastic processes including random walks, Markov chains, Poisson pocesses and Brownian motion.
Prerequisite: 527
Semesters offered:  Spring
Math 529  [ 3 ]  Selected Topics in Algebra
Description: May be repeated for credit, no limit.
Math 530  [ 3 ]  Algebraic Geometry I
Description: Basic theory of complex affine and projective varieties. Smooth and singular points, dimension, regular and rational mappings between varieties, Chow's Theorem.
Prerequisite: Math 431, 521, 561
Semesters offered:  Alternate Falls
Math 531  [ 3 ]  Algebraic Geometry II
Description: Continuation of 530. Degree of a variety and linear systems. Detailed study of curves and surfaces.
Prerequisite: Math 530.
Semesters offered:  Alternate Springs
Math 532  [ 3 ]  Algebraic Topology I
Description: Introduction to homology and cohomology theories. Homotopy theory, CW complexes.
Prerequisite: Math 431, 521.
Semesters offered:  Alternate Falls
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
  Math 532 001 TR  0930-1045  HUM    Cancelled, .
Math 533  [ 3 ]  Algebraic Topology II
Description: Continuation of 532. Duality theorems, universal coefficients, spectral sequence.
Prerequisite: Math 532
Semesters offered:  Alternate Springs
Math 534  [ 3 ]  Introduction to Differential Geometry
Description: Elementary theory of surfaces, differential forms, integral geometry, Riemannian geometry.
Prerequisite: 311 or 402.
Semesters offered:  Offered Upon Demand
Math 535  [ 3 ]  Foundations of Topology
Description: Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.
Prerequisite: 401
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
24909  Math 535 001 TR  0930-1045  HUM    Vassilev, D.
  AOA Math 431          
Math 536  [ 3 ]  Introduction to Differentiable Manifolds
Description: Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes' theorem.
Prerequisite: Math 511.
Semesters offered:  Alternate Springs
Math 537  [ 3 ]  Riemannian Geometry I
Description: Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theoreom, geodesics. Riemannian submanifolds.
Prerequisite: Math 536.
Semesters offered:  Alternate Falls
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
29541  Math 537 001 MWF  1500-1550  HUM    Boyer, C.
Math 538  [ 3 ]  Riemannian Geometry II
Description: Continuation of MATH 537 with emphasis on adding more structures. Riemannian submersions, Bochner theorems with relation to topology of manifolds, Riemannian Foliations, Complex and Kaehler geometry, Sasakian and contact geometry.
Prerequisite: Math 537.
Semesters offered:  Alternate Springs
Math 539  [ (3, n ]  Selected Topics in Geometry and Topology
Description: 
Math 540  [ 3 ]  Stochastic Processes with Applications
Description: Markov chains and processes with applications. Classification of states. Decompositions. Stationary distributions. Probability of absorption, the gambler's ruin and mean time problems. Queuing and branching processes. Introduction to continuous time Markov processes. Jump processes and Brownian motion.
Prerequisite: Math 527.
Semesters offered:  Offered Upon Demand
Math 541  [ 3 ]  Advanced Probability
Description: (Also offered as STAT 567.) A measure theoretic introduction to probability theory. Construction of probability measures. Distribution and characteristic functions, independence and zero-one laws. Sequences of independent random variables, strong law of large numbers and central limit theorem. Conditional expectation. Martingales.
Prerequisite: Math 563
Semesters offered:  Alternate Springs
Math 542  [ 3 ]  Mathematics for Secondary Teachers
Description: Topics from secondary mathematics presented from an advanced standpoint and designed to meet the needs of pre- and in-service teachers. Open only to prospective and in-service teachers of mathematics.
Prerequisite: 306 and 322 and 327. Restriction College of Education graduate students.
Semesters offered:  Fall
Math 543  [ (1-3, ]  Topics in Mathematics for Elementary and Middle School Teachers
Description: (Credit: 1-3, no limit.) Presents mathematical topics of concern to elementary and mid-school teachers. Open only to in-service and prospective teachers.
Prerequisite: Restriction: College of Education graduate students.
Semesters offered:  Offered upon demand
Math 549  [ (3, n ]  Selected Topics in Probability Theory
Description: (Credit: 3 no limit.) (Also offered as STAT 569.)
Math 550  [ (1-3, ]  Topics in Mathematics for Secondary Teachers
Description: (Credit: 1-3, no limit.) Presents mathematical topics of concern to secondary teachers. Open only to in-service and prospective teachers. May be repeated for credit by permission of instructor.
Prerequisite: Restriction: College of Education graduate students.
Semesters offered:  Offered upon demand
Math 551  [ (1-3, ]  Problems
Description: (Credit: 1-3, no limit.)
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18837  Math 551 001 ARR        Coutsias, E.
18840  Math 551 002 ARR        Buium, A.
18841  Math 551 003 ARR        Embid, P.
18844  Math 551 004 ARR        Umland, K.
33521  Math 551 006 ARR        Boyer, C.
33563  Math 551 007 ARR        Wearing, H.
33460  Math 551 008 ARR        Lorenz, J.
36623  Math 551 009 ARR        Loring, T.
Math 557  [ (3, n ]  Selected Topics in Numerical Analysis
Description: (Credit: 3, no limit.) (Also offered as CS 557.) Possible topics include approximation theory, two point boundary value problems, quadrature, integral equations and roots of nonlinear equations.
Math 561  [ 3 ]  Functions of a Complex Variable I
Description: Analyticity, Cauchy theorem and formulas, Taylor and Laurent series, singularities and residues, conformal mapping, selected topics.
Prerequisite: Math 311 or 402
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
  Math 561 001 TR  1230-1345  HUM    Cancelled, .
36033  Math 561 002 MWF  0900-0950  HUM    Lorenz, J.
Math 562  [ 3 ]  Functions of a Complex Variable II
Description: The Mittag-Leffler theorem, series and product expansions, introduction to asymptotics and the properties of the gamma and zeta functions. The Riemann mapping theorem, harmonic functions and Dirichlet's problem. Introduction to elliptic functions. Selected topics.
Prerequisite: Math 561
Semesters offered:  Fall
Math 563  [ 3 ]  Measure Theory
Description: Functions of one and several real variables, measure theory, starting with Lebesque measure and integration. Product measures. Measure on spaces of functions.
Prerequisite: Math 401 or 510
Semesters offered:  Fall
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18861  Math 563 001 MWF  1400-1450  HUM    Blair, M.
Math 565  [ 3 ]  Harmonic Analysis
Description: Fourier analysis on the circle, real line and on compact and locally compact groups.
Prerequisite: Math 563
Semesters offered:  Offered Upon Demand
Math 568  [ 3 ]  Stochastic Differential Equations
Description: Basic theory of stochastic differential equations with applications. The presentation will be at a level accessible to scientists, engineers, and applied mathematicians.
Prerequisite: Math 316, 441.
Semesters offered:  Offered Upon Demand
Math 569  [ (3, N ]  Selected Topics in Analysis
Description: (Credit: 3, no limit.)
Math 570  [ 3 ]  Singular Perturbations
Description: Singularly perturbed boundary value problems, layer type expansions and matching. Initial value problems and multi-scaling methods for ordinary and partial differential equations. Phase plane and qualitative ideas. Applications. Perturbations of Hamiltonian systems.
Prerequisite: 462, 463
Semesters offered:  Alternate Springs
Math 571  [ 3 ]  Ordinary Differential Equations
Description: Existence and uniqueness of solutions, linear systems, asymptotic behavior of solutions to nonlinear systems, integral manifolds and linearizations, perturbation theory, bifurcation theory, dichotomies for solutions of linear systems.
Prerequisite: Math 462
Semesters offered:  Alternate Springs
Math 572  [ 3 ]  Fourier Analysis and Wavelets
Description: Discrete Fourier and Wavelet Transform. Fourier series and integrals. Expansions in series of orthogond wavelets and other functions. Multiresolution and time/frequency analysis. Applications to signal processing and statistics.
Prerequisite: 314, 321 or 401
Semesters offered:  Offered Upon Demand
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
33945  Math 572 001 TR  0800-0915  HUM    Pereyra, M.
  AOA Math 472          
Math 573  [ 3 ]  Partial Differential Equations
Description: Equations of first order, classification of equations and systems, elliptic equations and introduction to potential theory, hyperbolic equations and systems, parabolic equations.
Prerequisite: Math 463
Semesters offered:  Alternate Falls
Math 576  [ 3 ]  Numerical Linear Algebra
Description: Selected advanced topics in numerical linear algebra.
Prerequisite: Math 504
Semesters offered:  Alternate Springs
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
  Math 576 001 TR  0930-1045      Cancelled, .
  Math 576 002 MWF  0900-0950  HUM    Cancelled, .
36032  Math 576 003 TR  1230-1345  HUM    Coutsias, E.
Math 577  [ 3 ]  Numerical Ordinary Differential Equations
Description: Numerical methods for initial value and/or boundary value problems.
Prerequisite: Math 462, 504, 505.
Semesters offered:  Offered Upon Demand
Math 578  [ 3 ]  Numerical Partial Differential Equations
Description: Introduction to the numerical analysis of partial differential equations.
Prerequisite: Math 463, 504, 505
Semesters offered:  Alternate Falls
Math 578  [ 3 ]  Numerical Partial Differential Equations
Description: Introduction to the numerical analysis of partial differential equations.
Prerequisite: Math 463, 504, 505.
Semesters offered:  Offered Upon Demand
Math 579  [ 3 ]  Selected Topics in Applied Math
Description: (Credit: 3, no limit.)
Grading:  Homework
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
35594  Math 579 001 MW  1800-1915  HUM    Romero, L.
  Calculus of Variations          
35860  Math 579 010 W  1500-1730  CAST    Brown, J.
Math 581  [ 3 ]  Functional Analysis I
Description: Normed vector spaces, including Hibert and Banach spaces. Linear operators on these spaces, with an emphasis on applications.
Prerequisite: Math 510
Semesters offered:  Offered Upon Demand
Math 582  [ 3 ]  Functional Analysis II
Description: Advanced topics in function spaces and linear operators.
Prerequisite: Math 581
Math 583  [ 3 ]  Methods of Applied Math I
Description: Approximation in Hilbert spaces, basic operator theory, integral equations, distribution theory, Green's functions, differential operators, boundary value problems and nonlinear problems
Prerequisite: Math 312, 314, 316, 401.
Semesters offered:  Alternate Falls
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
33947  Math 583 001 MWF  1100-1150  ECON    Lorenz, J.
Math 584  [ 3 ]  Methods of Applied Math II
Description: Eigenfunction expansions for ordinary and partial differential operators, Euler-Lagrange equations, Hamilton's principle, calculus of variations, brief complex variable theory, special functions, transform and spectral theory, asymptotic expansions.
Prerequisite: Math 312, 314, 316, and 401.
Preparation: Advanced work in applied mathematics and applied science, such as electricity and magnetism, wave propagation, heat transfer, and quantum mechanics.
Grading:  Homeworks
Semesters offered:  Alternate Springs
Math 598  [ (1-6 ]  Practicum
Description: (Credit: 1-6 to a maximum of 6.) Practicum involves a project of an applied nature which may be done in conjunction with an industrial laboratory, a research institution or another department of the University. It is expected the student will become acquainted with a field of application in science or engineering and complete a project of use and interest to workers in that field. A final written report is required.
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18869  Math 598 001 ARR        Faculty, .
Math 599  [ 1-6 ( ]  Master's Thesis
Description: Offered on a CR/NC basis only.
Fall 2009 Class Schedule
Call # Course Days Time Bldg. Room Instructor
18872  Math 599 001 ARR        Lorenz, J.
18873  Math 599 002 ARR        Steinberg, S.
18875  Math 599 003 ARR        Hagstrom, T.
18876  Math 599 004 ARR        Aceves, A.
18877  Math 599 005 ARR        Loring, T.
18879  Math 599 006 ARR        Nakamaye, M.
18880  Math 599 007 ARR        Umland, K.
18881  Math 599 008 ARR        Pereyra, M.
18882  Math 599 009 ARR        Stone, A.
18883  Math 599 010 ARR        Buium, A.
24164  Math 599 011 ARR        Embid, P.
24816  Math 599 012 ARR        Sulsky, D.
28837  Math 599 013 ARR        Nitsche, M.
33192  Math 599 014 ARR        Wearing, H.
33230  Math 599 015 ARR        Simanca, S.
Department of Mathematics and Statistics, MSC03 2150, 1 University of New Mexico, Albuquerque, New Mexico, 87131-0001