Mathematics
106.
Problems in Intermediate Algebra.
(1)
Study session for 120 with an emphasis on problem solving. (I)
Offered on a CR/NC basis only.
{Fall, Spring}
107.
Problems in College Algebra.
(1)
Study session for 121 with an emphasis on problem solving. (I)
Offered on a CR/NC basis only.
{Fall, Spring}
110.
Problems in Elements of Calculus.
(1)
Study session for 180 with an emphasis on problem-solving. (I)
Offered on a CR/NC basis only.
{Fall, Spring}
111.
Mathematics for Elementary and Middle School Teachers I.
(3)
Course offers an in-depth look at the representations of rational numbers, including base-ten and decimal numbers, integers, fractions, and arithmetic operations on these sets. Problem solving is emphasized throughout. (T)
Prerequisite: 120 or 121 or 123 or 150 or 162 or 180 or STAT 145 or ISM 100 or ACT=>19 or SAT=>450 or Compass Pre-Algebra >56 or Algebra >33
112.
Mathematics for Elementary and Middle School Teachers II.
(3)
This course develops basic geometric concepts including rigid transformations and congruence; dilations and similarity; length, area and volume; systems of measurement and unit conversions; connections to coordinate geometry. Problem solving is emphasized throughout. (T)
Prerequisite: 111
116.
Topics in Pre-calculus Mathematics.
(3)
Selected topics from algebra, geometry and trigonometry. (I)
Restriction: permission of the department.
Offered on a CR/NC basis only.
120.
Intermediate Algebra.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Preparation for MATH 121, 129 and STAT 145. Covers linear equations and inequalities, polynomials, factoring, exponents, radicals, fractional expressions and equations, quadratic equations, perimeters, areas of simple geometric shapes, and logarithms. Emphasis on problem solving skills. Acceptable as credit toward graduation, but not acceptable to satisfy UNM core or group requirements. (I)
Prerequisite: ACT=>19 or SAT=>450 or ISM 100 or Compass Pre-Algebra >56 or Algebra >33
121.
College Algebra.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Preparation for MATH 150 and 180. The study of equations, functions and graphs, especially linear and quadratic functions. Introduction to polynomial, rational, exponential and logarithmic functions. Applications involving simple geometric objects. Emphasizes algebraic problem solving skills. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1113). (I)
Prerequisite: ACT=>22 or SAT=>510 or (MATH 118 and MATH 119) or MATH 120 or Compass Algebra >54 or Compass College Algebra >33.
123.
Trigonometry.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Definition of the trigonometric functions, radian and degree measure, graphs, basic trigonometric identities, inverse trigonometric functions, complex numbers, polar coordinates and graphs, vectors in 2 dimensions. May be taken concurrently with MATH 150. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1113). (I)
Prerequisite: ACT=>25 or SAT=>570 or MATH 121 or Compass College Algebra >54.
129.
A Survey of Mathematics.
(3)
An introduction to some of the great ideas of mathematics, including logic, systems of numbers, sequences and series, geometry and probability. Emphasizes general problem-solving skills. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics. (I)
Prerequisite: ACT=>22 or SAT=>510 or (MATH 118 and MATH 119) or MATH 120 or 121 or 123 or 150 or 162 or 163 or 180 or 181 or 264.
150.
Pre-Calculus Mathematics.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
In-depth study of polynomial, rational, exponential and logarithmic functions and their graphs. Includes the fundamental theorem of algebra, systems of equations, conic sections, parametric equations and applications in geometry. Exploration of the graphing calculator. May be taken concurrently with MATH 123. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics. (I)
Prerequisite: ACT=>25 or SAT=>570 or MATH 121 or Compass College Algebra >54.
162.
Calculus I.
(4)
Note: See Restrictions earlier in Mathematics and Statistics.
Limits. Continuity. Derivative: definition, rules, geometric and rate-of-change interpretations, applications to graphing, linearization and optimization. Integral: definition, fundamental theorem of calculus, substitution, applications to areas, volumes, work, average. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1614). (I)
Prerequisite: (ACT=28-31 or SAT=640-700 or MATH 150 or Compass College Algebra >66) and (MATH 123 or Compass Trig >59) or (ACT=>32 or SAT=>700).
163.
Calculus II.
(4)
Note: See Restrictions earlier in Mathematics and Statistics.
Transcendental functions, techniques of integration, numerical integration, improper integrals, sequences and series, Taylor series with applications, complex variables, differential equations.
(I)
Prerequisite: MATH 162.
180.
Elements of Calculus I.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Limits of functions and continuity, intuitive concepts and basic properties; derivative as rate of change, basic differentiation techniques; application of differential calculus to graphing and minima-maxima problems; exponential and logarithmic functions with applications. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1613). (I)
Prerequisite: ACT=>26 or SAT=>600 or MATH 121 or MATH 150 or Compass College Algebra >66.
181.
Elements of Calculus II.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Includes the definite integral, multivariate calculus, simple differential equations, basic review of trigonometry and its relation to calculus. (I)
Prerequisite: 180
215.
Mathematics for Elementary and Middle School Teachers III.
(3)
Algebra from the viewpoint of the elementary curriculum with emphasis on proportional and linear relationships. Also included: topics from probability and statistics with connections to other topics in the elementary curriculum. Problem solving is emphasized throughout. (T)
Prerequisite: 111.
264.
Calculus III.
(4)
Vector operations, vector representation of planes and curves, functions of several variables, partial derivatives, gradient, tangent planes, optimization, multiple integrals in Cartesian cylindrical and spherical coordinates, vector fields, line integrals and Green’s theorem. (I)
Prerequisite: C (not C-) or better in 163.
275.
Honors Calculus.
(3)
Differential and integral calculus with an emphasis on conceptual understanding. (I)
Prerequisite: Grade of at least A- in 180 or 162
301 / 503.
Calculus for Teachers.
(3)
A penetrating look at functions, derivatives, intergrals, and the Fundamental Theorem of Calculus that makes explicit how topics in the secondary school curriculum come to fruition in this foundational subject. (T)
Prerequisite: 163
Restriction: permission of instructor
305 / 507.
Mathematics from a Historical Perspective.
(3)
A survey of mathematical developments prior to 1800; emphasis on problem solving techniques; comparison of older and more modern methods. (T)
Prerequisite: 163
{Fall}
306 / 506.
College Geometry.
(3)
An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. (T)
{Spring}
Prerequisite: 162 or 215.
308 / 508.
Theory and Practice of Problem Solving.
(3)
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. (T)
Prerequisite: 180 or 162. Corequisite: 306
{Offered upon demand}
311.
Vector Analysis.
(3)
Vector algebra, lines, planes; vector valued functions, curves, tangent lines, arc length, line integrals; directional derivative and gradient; divergence, curl, Gauss’ and Stokes’ theorems, geometric interpretations.
Prerequisite: 264
**312.
Partial Differential Equations for Engineering.
(3)
Solution methods for partial differential equations; science and engineering applications; heat and wave equations, Laplace’s equation; separation of variables; Fourier series and transforms; special functions.
Prerequisite: 264 and 316
**313.
Complex Variables.
(3)
Theory of functions of a complex variable with application to physical and engineering problems. Although not required, skill in vector analysis will be helpful in taking this course.
Prerequisite: 264
**314.
Linear Algebra with Applications.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Systems of linear equations, Gaussian elimination, matrix algebra, determinants. Vector spaces. Inner product spaces, orthogonality, least squares approximations. Eigenvalues, eigenvectors, diagonalization. Emphasis on concepts, computational methods, and applications.
Prerequisite: 163 or 181. Pre- or Corequisite: CS 151L or CS 152L or PHYC 290 or ECE 131.
**316.
Applied Ordinary Differential Equations.
(3)
Introduction to algorithmic theory of ordinary differential equations. Topics covered: elementary theory of ordinary differential equations, numerical methods, phase-plane analysis, and introduction to Laplace transformations. Third-level calculus is helpful for this class.
Prerequisite: 163. Pre- or Corequisite: CS 151L or CS 152L or PHYC 290 or ECE 131.
**317.
Elementary Combinatorics.
(3)
Basic enumeration including combinations, permutations, set and integer partitions, distributions, and rearrangements, binomial and multinomial theorems together with pigeon-hole and inclusion-exclusion principles and mathematical induction principles. Discrete probability, elementary ordinary generating functions, recurrence relations, and sorting algorithms.
Prerequisite: 163 or 181
{Fall}
**318.
Graph Theory.
(3)
Trees, connectivity, planarity, colorability, and digraphs; algorithms and models involving these concepts. Ability in linear algebra is helpful when taking this course.
{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)
Note: See Restrictions earlier in Mathematics and Statistics.
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.
(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.
Prerequisite: 162 and 163
(Fall)
338 / 542.
Mathematics for Secondary Teachers.
(3)
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. (T)
Prerequisite: 306 and 327
{Spring}
339 / 543.
Topics in Mathematics for Elementary and Middle School Teachers.
(1-3, no limit Δ)
Presents mathematical topics of concern to elementary and mid-school teachers. Open only to in-service and prospective teachers. (T)
{Offered upon demand}
350 / 550.
Topics in Mathematics for Secondary Teachers.
(1-3, no limit Δ)
Presents mathematical topics of concern to secondary teachers. Open only to in-service and prospective teachers. (T)
{Offered upon demand}
**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.
Prerequisite: (314 or 316 or 321) and (CS 151L or CS 152L or PHYC 290 or ECE 131).
391.
Advanced Undergraduate Honors Seminar.
(1-3 to a maximum of 8 Δ)
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 Δ)
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.
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
**412.
Nonlinear 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.
Prerequisite: 264 and (314 or 321) or 316
**415.
History and 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.
Prerequisite: 163 or 181 or 356
*421.
Modern Algebra II.
(3)
Theory of fields, algebraic field extensions and Galois theory for fields of characteristic zero.
Prerequisite: 322 or 422
{Spring}
**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 / 535.
Introduction to Topology.
(3)
Metric spaces, topological spaces, continuity, algebraic topology.
Prerequisite: 401
{Fall}
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.
Topics in Mathematics.
(1-3, no limit Δ)
441.
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: MATH 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) and 316 and 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.
Prerequisite: 312 and 313 and (314 or 321) and (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}
*466.
Mathematical Methods in Science and Engineering.
(3)
Special functions and advanced mathematical methods for solving differential equations, difference equations and integral equations.
Prerequisite: 311 and 312 and 313 and 316
{Spring}
*471.
Introduction to Scientific Computing.
(3)
(Also offered as CS 471)
Parallel programming, performance evaluation. Error analysis, convergence, stability of numerical methods. Applications such as N-body problem, heat transfer, wave propagation, signal processing, Monte-Carlo simulations. C, C++, or FORTRAN skills required.
Prerequisite: 314 or 316 or 321.
472 / 572.
Fourier Analysis and Wavelets.
(3)
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 or 321) or 401
{Offered upon demand}
499.
Individual Study.
(1-3 to a maximum of 6 Δ)
Guided study, under the supervision of a faculty member, of selected topics not covered in regular courses.
501 / 401.
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.
Restriction: College of Education graduate students.
502 / 402.
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: 501
Restriction: College of Education graduate students.
503 / 301.
Calculus for Teachers.
(3)
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 foundational subject.
Restriction: permission of instructor
504.
Introductory Numerical Analysis: Numerical Linear Algebra.
(3)
(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
{Spring}
505.
Introductory Numerical Analysis: Approximation and Differential Equations.
(3)
(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, 401
{Fall}
506 / 306.
College Geometry.
(3)
An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry.
Restriction: College of Education graduate students
{Spring}
507 / 305.
Mathematics from a Historical Perspective.
(3)
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
{Fall}
508 / 308.
Theory and Practice of Problem Solving.
(3)
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
{Offered upon demand}
510.
Introduction to Analysis I.
(3)
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
{Fall}
511.
Introduction to Analysis II.
(3)
Continuation of 510. Differentiation in Rn. Inverse and implicit function theorems, integration in Rn, differential forms and Stokes theorem.
Prerequisite: 510
{Spring}
512 / 462.
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}
513 / 463.
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.
Prerequisite: 312, 313, 314 or 321, one of 311 or 402
{Spring}
514 / 464.
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}
519.
Selected Topics in Number Theory.
(3, no limit Δ)
520.
Abstract Algebra I.
(3)
Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains.
Prerequisite: 322
{Fall}
521.
Abstract Algebra II.
(3)
Continuation of 520. Module theory, field theory, Galois theory.
Prerequisite: 321, 520
{Spring}
530.
Algebraic Geometry I.
(3)
Basic theory of complex affine and projective varieties. Smooth and singular points, dimension, regular and rational mappings between varieties, Chow’s theorem.
Prerequisite: 431, 521, 561
{Alternate Falls}
531.
Algebraic Geometry II.
(3)
Continuation of 530. Degree of a variety and linear systems. Detailed study of curves and surfaces.
Prerequisite: 530
{Alternate Springs}
532.
Algebraic Topology I.
(3)
Introduction to homology and cohomology theories. Homotopy theory, CW complexes.
Prerequisite: 431, 521
{Alternate Falls}
533.
Algebraic Topology II.
(3)
Continuation of 532. Duality theorems, universal coefficients, spectral sequence.
Prerequisite: 532
{Alternate Springs}
534 / 434.
Introduction to Differential Geometry.
(3)
Elementary theory of surfaces, differential forms, integral geometry and Riemannian geometry.
Prerequisite: 311 or 402
{Offered upon demand}
535 / 431.
Foundations of Topology.
(3)
Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.
Prerequisite: 401
{Fall}
536.
Introduction to Differentiable Manifolds.
(3)
Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes’ theorem.
Prerequisite: 511
{Spring}
537.
Riemannian Geometry I.
(3)
Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theorem, geodesics. Riemannian submanifolds.
Prerequisite: 536
{Alternate Falls}
538.
Riemannian Geometry II.
(3)
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: 537
{Alternate Springs}
539.
Selected Topics in Geometry and Topology.
(3, no limit Δ)
540.
Stochastic Processes with Applications.
(3)
(Also offered as STAT 565)
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: STAT 527
{Offered on demand}
541.
Advanced Probability.
(3)
(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: 563
{Alternate Springs}
542 / 338.
Mathematics for Secondary Teachers.
(3)
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.
Restriction: College of Education graduate students
Prerequisite: 306 and 322 and 327
{Fall}
543 / 339.
Topics in Mathematics for Elementary and Middle School Teachers.
(1-3, no limit Δ)
Presents mathematical topics of concern to elementary and mid-school teachers. Open only to in-service and prospective teachers. May be repeated for credit by permission of instructor.
Restriction: College of Education graduate students
{Offered upon demand}
549.
Selected Topics in Probability Theory.
(3, no limit Δ)
(Also offered as STAT 569)
350 / 550.
Topics in Mathematics for Secondary Teachers.
(1-3, no limit Δ)
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.
Restriction: College of Education graduate students
{Offered upon demand}
551.
Problems.
(1-3, no limit Δ)
557.
Selected Topics in Numerical Analysis.
(3, no limit Δ)
(Also offered as CS 557)
Possible topics include approximation theory, two point boundary value problems, quadrature, integral equations and roots of nonlinear equations.
561.
Functions of a Complex Variable I.
(3)
Analyticity, Cauchy theorem and formulas, Taylor and Laurent series, singularities and residues, conformal mapping, selected topics.
Prerequisite: 311 or 402
{Fall}
562.
Functions of a Complex Variable II.
(3)
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: 561
{Fall}
563.
Measure Theory.
(3)
Functions of one and several real variables, measure theory, starting with Lebesque measure and integration. Product measures. Measure on spaces of functions.
Prerequisite: 401 or 510
{Fall}
565.
Harmonic Analysis.
(3)
Fourier analysis on the circle, real line and on compact and locally compact groups.
Prerequisite: 563
{Offered upon demand}
568.
Stochastic Differential Equations.
(3)
Basic theory of stochastic differential equations with applications. The presentation will be at a level accessible to scientists, engineers and applied mathematicians.
Prerequisite: 316 and 441
{Offered upon demand}
569.
Selected Topics in Analysis.
(3, no limit Δ)
570.
Singular Perturbations.
(3)
Singularly perturbed boundary value problems, layer type expansions and matching. Initial value problems and multiscaling methods for ordinary and partial differential equations. Phase plane and qualitative ideas. Applications. Perturbations of Hamiltonian systems.
Prerequisite: 462, 463
{Alternate Springs}
571.
Ordinary Differential Equations.
(3)
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: 462
{Alternate Springs}
572 / 472.
Fourier Analysis and Wavelets.
(3)
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
{Offered upon demand}
573.
Partial Differential Equations.
(3)
Equations of first order, classification of equations and systems, elliptic equations and introduction to potential theory, hyperbolic equations and systems, parabolic equations.
Prerequisite: 463
{Alternate Falls}
576.
Numerical Linear Algebra.
(3)
Selected advanced topics in numerical linear algebra.
Prerequisite: 504
{Alternate Springs}
577.
Numerical Ordinary Differential Equations.
(3)
Numerical methods for initial value and/or boundary value problems.
Prerequisite: 462, 504, 505
{Offered upon demand}
578.
Numerical Partial Differential Equations.
(3)
Introduction to the numerical analysis of partial differential equations.
Prerequisite: 463, 504, 505
{Alternate Falls}
579.
Selected Topics in Applied Mathematics.
(3, no limit Δ)
581.
Functional Analysis I.
(3)
Normed vector spaces, including Hilbert and Banach spaces. Linear operators on these spaces, with an emphasis on applications.
Prerequisite: 510
{Offered upon demand}
582.
Functional Analysis II.
(3)
Advanced topics in function spaces and linear operators.
Prerequisite: 581
583.
Methods of Applied Mathematics I.
(3)
Approximation in Hilbert spaces, basic operator theory, integral equations, distribution theory, Green’s functions, differential operators, boundary value problems and nonlinear problems.
Prerequisite: 312, 314, 316, 401
{Alternate Falls}
584.
Methods of Applied Mathematics II.
(3)
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: 312 and 314 and 316 and 401
{Alternate Springs}
598.
Practicum.
(1-6 to a maximum of 6 Δ)
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.
599.
Master’s Thesis.
(1-6, no limit Δ)
Offered on a CR/NC basis only.
605.
Graduate Colloquium.
(1 to a maximum of 4 Δ)
Students present their current research.
639.
Seminar in Geometry and Topology.
(1-3, no limit Δ)
649.
Seminar in Probability and Statistics.
(1-3, no limit Δ)
(Also offered as STAT 649)
650.
Reading and Research.
(1-6 to a maximum of 12 Δ)
669.
Seminar in Analysis.
(1-3, no limit Δ)
679.
Seminar in Applied Mathematics.
(1-3, no limit Δ)
689.
Seminar in Functional Analysis.
(1-3)
699.
Dissertation.
(3-12, no limit Δ)
Offered on a CR/NC basis only.