A minimum of 26 credit hours; 23 credit hours must be in courses acceptable toward graduation.
A cumulative grade point average of at least 2.00 on all work.
Completion of Department of Mathematics and Statistics admission coursework with grades of "C" or better:
See separate listing under Statistics for additional degree concentrations.
MATH 264 and 12 credit hours in Mathematics and Statistics courses numbered above 300. At least 6 of the 12 credit hours must be in courses labeled Math. (Note that a separate statistics minor is available.) The pass/fail (CR/NC) option may not be used for minor study and the grades in all mathematics and statistics courses must be "C" (not "C-") or better. Courses required for a major may not be used to fulfill minor requirement.
MATH 264 and STAT 145, 345, 427, 428, and an additional 3 credit hours of Statistics in courses numbered 300 and above. All 12 credit hours in courses 300-level and above must be in courses labeled STAT. (Note that a separate Mathematics Minor for Statistics majors is available). The pass/fail (CR/NC) option may not be used for minor study and the grades in all statistics courses must be a "C" (not "C-") or better.
Requirements for departmental honors in Mathematics are 1) a 3.5 GPA in Mathematics and Statistics courses and a 3.2 overall GPA; 2) notification to the department coordinator of program advisement no later than two full semesters prior to graduation; 3) completion of a project based on 6 credit hours of MATH 499 (project outline to be presented to the Undergraduate Honors Committee [UHC] for approval); 4) final written report to be submitted to UHC for approval; and 5) seminar to be given at the end of the project. These requirements are in addition to the major requirements.
One year of calculus, MATH 162 and 163, or MATH 180 and 181, STAT 145, 345, 427, 428 and an additional 3 credit hours of mathematics or statistics in courses numbered 250 and above. The pass/fail (CR/NC) option may not be used for minor study and the grades in all mathematics and statistics courses must be "C" (not "C-") or better.
MATH 264 and 12 credit hours of Mathematics courses numbered above 300. All 12 credit hours must be in courses labeled MATH. (Note that a separate Statistics Minor for Mathematics majors is available.) The pas/fail (CR/NC) option may not be used for minor study and the grades in all mathematics courses must be "C" (not "C-") or better.
Requirements for departmental honors in Statistics are 1) a 3.5 GPA in major courses and a 3.2 overall GPA; 2) notification to the department coordinator of program advisement no later than two full semesters prior to graduation; 3) completion of a project based on 6 credit hours of STAT 495 (project outline to be presented to the Undergraduate Honors Committee (UHC) for approval) 4) final written report to be submitted to UHC for approval; and 5) seminar to be given at the end of the project. These requirements are in addition to the major requirements.
Courses
MATH 101. Intermediate Algebra Part 1. (1)
This course includes equations and inequalities, applications and problem solving with linear equations, linear functions and the graph of a line, percent, perimeters, areas of simple geometric shapes.
Prerequisite: 100 or ISM 100 or ACT Math => 19 or SAT Math => 450 or COMPASS Pre-Algebra => 57 or COMPASS Algebra => 34.
MATH 102. Intermediate Algebra Part 2. (1)
This course includes quadratic equations, properties of exponents and scientific notation, simplifying polynomial expressions, factoring and introduction to functions.
Pre- or corequisite: 101.
MATH 103. Intermediate Algebra Part 3. (1)
This course includes radical expressions and equations, rational expressions and equations, the exponential and logarithm functions.
Pre- or corequisite: 102.
MATH 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}
MATH 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}
MATH 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}
MATH 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: (MATH 101 and MATH 102) or 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 Compass Algebra >33.
MATH 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.
MATH 116. Topics in Pre-calculus Mathematics. (3)
Selected topics from algebra, geometry and trigonometry. (I)
Offered on a CR/NC basis only.
Restriction: permission of the department.
MATH 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 101 and MATH 102 and MATH 103) or MATH 120 or Compass Algebra >54 or Compass College Algebra >33.
MATH 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.
MATH 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 Compass Algebra >54 or Compass College Algebra >33 or (MATH 118 and MATH 119) or (MATH 101 and MATH 102) or 120 or 121 or 123 or 150 or 162 or 163 or 180 or 181 or 264.
MATH 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.
MATH 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).
MATH 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.
MATH 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 >54.
MATH 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.
MATH 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.
MATH 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.
MATH 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.
MATH 305 / 507. Mathematics from a Historical Perspective. (3)
A study of the historical development of topics in mathematics taken from geometry, algebra, trigonometry, number systems, probability, and/or statistics. Emphasis on connections to the high school curriculum. (T)
Prerequisite: 163.
{Fall}
MATH 306 / 506. College Geometry. (3)
An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. (T)
Prerequisite: 162 or 215.
{Spring}
MATH 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.
(Fall, Spring, occasional Summer)
MATH **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.
{Fall, Spring, Occasional Summer}
MATH **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.
{Fall, Spring}
MATH **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.
{Fall, Spring, Summer}
MATH **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.
{Fall, Spring, Summer}
MATH **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.
{Spring}
MATH **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.
{Offered upon demand}
MATH **319. Theory of Numbers. (3)
Divisibility, congruences, primitive roots, quadratic residues, diophantine equations, continued fractions, partitions, number theoretic functions.
{Spring}
MATH **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}
MATH 322. Modern Algebra I. (3)
Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields.
Prerequisite: 264.
{Fall}
MATH **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, Spring}
MATH 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}
MATH 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}
MATH 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}
MATH **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.
MATH **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).
MATH 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}
MATH 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}
MATH 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 MATH courses 300-level or above.
{Fall, Spring}
MATH 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.
{Spring}
MATH **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).
{Spring}
MATH **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.
MATH *421. Modern Algebra II. (3)
Theory of fields, algebraic field extensions and Galois theory for fields of characteristic zero.
Prerequisite: 322 or 422.
{Spring}
MATH **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}
MATH *431 / 535. Introduction to Topology. (3)
Metric spaces, topological spaces, continuity, algebraic topology.
Prerequisite: 401.
{Fall}
MATH **439. Topics in Mathematics. (1-3, no limit Δ)
MATH 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}
MATH 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}
MATH 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}
MATH 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}
MATH *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}
MATH *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.
{Fall}
MATH 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) and 401.
{Offered every other Spring}
MATH 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.
MATH 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 MATH courses 300-level or above.
Restriction: College of Education graduate students.
{Fall and Spring}
MATH 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.
{Spring}
MATH 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}
MATH 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}
MATH 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}
MATH 507 / 305. Mathematics from a Historical Perspective. (3)
A study of the historical development of topics in mathematics taken from geometry, algebra, trigonometry, number systems, probability, and/or statistics. Emphasis on connections to the high school curriculum.
Prerequisite: 163.
Restriction: College of Education graduate students.
{Fall}
MATH 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}
MATH 511. Introduction to Analysis II. (3)
Continuation of 510. Differentiation in R^{n}. Inverse and implicit function theorems, integration in R^{n}, differential forms and Stokes theorem.
Prerequisite: 510.
{Spring}
MATH 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) and 316 and 401.
{Fall}
MATH 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}
MATH 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}
MATH 519. Selected Topics in Algebra and Number Theory [Selected Topics in Number Theory]. (3, no limit Δ)
MATH 520. Abstract Algebra I. (3)
Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains.
Prerequisite: 322.
{Fall}
MATH 521. Abstract Algebra II. (3)
Continuation of 520. Module theory, field theory, Galois theory.
Prerequisite: 321, 520.
{Spring}
MATH 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}
MATH 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}
MATH 532. Algebraic Topology I. (3)
Introduction to homology and cohomology theories. Homotopy theory, CW complexes.
Prerequisite: 431, 521.
{Alternate Falls}
MATH 533. Algebraic Topology II. (3)
Continuation of 532. Duality theorems, universal coefficients, spectral sequence.
Prerequisite: 532.
{Alternate Springs}
MATH 535 / 431. Foundations of Topology. (3)
Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.
Prerequisite: 401.
{Fall}
MATH 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}
MATH 537. Riemannian Geometry I. (3)
Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theorem, geodesics. Riemannian submanifolds.
Prerequisite: 536.
{Alternate Falls}
MATH 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}
MATH 539. Selected Topics in Geometry and Topology. (3, no limit Δ)
MATH 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}
MATH 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}
MATH 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.
Prerequisite: 306 and 322 and 327.
Restriction: College of Education graduate students.
{Fall}
MATH 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}
MATH 549. Selected Topics in Probability Theory. (3, no limit Δ)
(Also offered as STAT 569)
MATH 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}
MATH 551. Problems. (1-3, no limit Δ)
MATH 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.
MATH 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}
MATH 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}
MATH 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}
MATH 565. Harmonic Analysis. (3)
Fourier analysis on the circle, real line and on compact and locally compact groups.
Prerequisite: 563.
{Offered upon demand}
MATH 569. Selected Topics in Analysis. (3, no limit Δ)
MATH 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}
MATH 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 or 321 or 401.
{Offered every other Spring}
MATH 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}
MATH 576. Numerical Linear Algebra. (3)
Selected advanced topics in numerical linear algebra.
Prerequisite: 504.
{Alternate Springs}
MATH 577. Numerical Ordinary Differential Equations. (3)
Numerical methods for initial value and/or boundary value problems.
Prerequisite: 462, 504, 505.
{Offered upon demand}
MATH 578. Numerical Partial Differential Equations. (3)
Introduction to the numerical analysis of partial differential equations.
Prerequisite: 463, 504, 505.
{Alternate Falls}
MATH 579. Selected Topics in Applied Mathematics. (3, no limit Δ)
MATH 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}
MATH 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}
MATH 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}
MATH 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.
MATH 599. Master's Thesis. (1-6, no limit Δ)
Offered on a CR/NC basis only.
MATH 605. Graduate Colloquium. (1 to a maximum of 4 Δ)
Students present their current research.
MATH 639. Seminar in Geometry and Topology. (1-3, no limit Δ)
MATH 649. Seminar in Probability and Statistics. (1-3, no limit Δ)
(Also offered as STAT 649)
MATH 650. Reading and Research. (1-6 to a maximum of 12 Δ)
MATH 669. Seminar in Analysis. (1-3, no limit Δ)
MATH 679. Seminar in Applied Mathematics. (1-3, no limit Δ)
MATH 689. Seminar in Functional Analysis. (1-3)
MATH 699. Dissertation. (3-12, no limit Δ)
Offered on a CR/NC basis only.
STAT 145. Introduction to Statistics. (3)
Techniques for the visual presentation of numerical data, descriptive statistics, introduction to probability and basic probability models used in statistics, introduction to sampling and statistical inference, illustrated by examples from a variety of fields. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics (NMCCN 1113). (I)
Prerequisite: ACT = >22 or SAT = >510 or Compass Algebra >33 or Compass College Algebra >54 or (MATH 118 and MATH 119) or (MATH 101 and MATH 102) or 120 or 121 or 123 or 150 or 162 or 163 or 180 or 181 or 264.
{Summer, Fall, Spring}
STAT 279. Topics in Introductory Statistics. (1 to 3 to a maximum of 3 Δ)
STAT **345. Elements of Mathematical Statistics and Probability Theory. (3)
An introduction to probability including combinatorics, Bayes’ theorem, probability densities, expectation, variance and correlation. An introduction to estimation, confidence intervals and hypothesis testing.
Prerequisite: MATH 163 or MATH 181.
STAT 427 / 527. Advanced Data Analysis I. (3)
Statistical tools for scientific research, including parametric and non-parametric methods for ANOVA and group comparisons, simple linear and multiple linear regression, and basic ideas of experimental design and analysis. Emphasis placed on the use of statistical packages such as Minitab® and SAS®.
Prerequisite: 145.
{Fall}
STAT 428 / 528. Advanced Data Analysis II. (3)
A continuation of 427 that focuses on methods for analyzing multivariate data and categorical data. Topics include MANOVA, principal components, discriminant analysis, classification, factor analysis, analysis of contingency tables including log-linear models for multidimensional tables and logistic regression.
Prerequisite: 427.
STAT 434 / 534. Contingency Tables and Dependence Structures. (3)
This course examines the use of log-linear models to analyze count data. It also uses graphical models to examine dependence structures for both count data and measurement data.
Prerequisite: 345 and 427.
STAT 440 / 540. Regression Analysis. (3)
Simple regression and multiple regression. Residual analysis and transformations. Matrix approach to general linear models. Model selection procedures, nonlinear least squares, logistic regression. Computer applications.
Prerequisite: 427.
{Fall}
STAT 445 / 545. Analysis of Variance and Experimental Design. (3)
A data-analytic course. Multifactor ANOVA. Principles of experimental design. Analysis of randomized blocks, Latin squares, split plots, etc. Random and mixed models. Extensive use of computer packages with interpretation, diagnostics.
Prerequisite: 440.
{Spring}
STAT 453 / 553. Statistical Inference with Applications. (3)
Transformations of univariate and multivariate distributions to obtain the special distributions important in statistics. Concepts of estimation and hypothesis testing in both large and small samples with emphasis on the statistical properties of the more commonly used procedures, including student’s t-tests, F-tests and chi-square tests. Confidence intervals. Performance of procedures under non-standard conditions (i.e., robustness).
Prerequisite: 461.
{Spring}
STAT 461 / 561. Probability. (3)
(Also offered as MATH 441)
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}
STAT 470 / 570. Industrial Statistics. (3)
Basic ideas of statistical quality control and improvement. Topics covered: Deming’s 14 points and deadly diseases, Pareto charts, histograms, cause and effect diagrams, control charts, sampling, prediction, reliability, experimental design, fractional factorials, Taguchi methods, response surfaces.
Prerequisite: 345.
STAT 472 / 572. Sampling Theory and Practice. (3)
Basic methods of survey sampling; simple random sampling, stratified sampling, cluster sampling, systematic sampling and general sampling schemes; estimation based on auxiliary information; design of complex samples and case studies.
Prerequisite: 345.
{Alternate Falls}
STAT 474 / 574. Biostatistical Methods: Survival Analysis and Logistic Regression. (3)
A detailed overview of methods commonly used to analyze medical and epidemiological data. Topics include the Kaplan-Meier estimate of the survivor function, models for censored survival data, the Cox proportional hazards model, methods for categorical response data including logistic regression and probit analysis, generalized linear models.
Prerequisite: 428 or 440.
STAT 476 / 576. Multivariate Analysis. (3)
Tools for multivariate analysis including multivariate ANOVA, principal components analysis, discriminant analysis, cluster analysis, factor analysis, structural equations modeling, canonical correlations and multidimensional scaling.
Prerequisite: 428 or 440.
{Offered upon demand}
STAT 477 / 577. Introduction to Bayesian Modeling. (3)
An introduction to Bayesian methodology and applications. Topics covered include: probability review, Bayes’ theorem, prior elicitation, Markov chain Monte Carlo techniques. The free software programs WinBUGS and R will be used for data analysis.
Prerequisite: 461 and (427 or 440).
{Alternate Springs}
STAT 479. Topics in Statistics. (3, no limit Δ)
Modern topics not covered in regular course offerings.
STAT 481 / 581. Introduction to Time Series Analysis. (3)
Introduction to time domain and frequency domain models of time series. Data analysis with emphasis on Box-Jenkins methods. Topics such as multivariate models; linear filters; linear prediction; forecasting and control.
Prerequisite: 461.
{Alternate Springs}
STAT 495. 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 course offerings.
STAT 520. Topics in Interdisciplinary Biological and Biomedical Sciences. (3, no limit Δ)
(Also offered as ANTH 620, BIOL 520, CS 520, ECE 620)
Varying interdisciplinary topics taught by collaborative scientists from UNM, SFI, and LANL.
STAT 527 / 427. Advanced Data Analysis I. (3)
Statistical tools for scientific research, including parametric and non-parametric methods for ANOVA and group comparisons, simple linear and multiple linear regression and basic ideas of experimental design and analysis. Emphasis placed on the use of statistical packages such as Minitab® and SAS®. Course cannot be counted in the hours needed for graduate degrees in Mathematics and Statistics.
Prerequisite: 145.
{Fall}
STAT 528 / 428. Advanced Data Analysis II. (3)
A continuation of 527 that focuses on methods for analyzing multivariate data and categorical data. Topics include MANOVA, principal components, discriminate analysis, classification, factor analysis, analysis of contingency tables including log-linear models for multidimensional tables and logistic regression.
Prerequisite: 527.
STAT 534 / 434. Contingency Tables and Dependence Structures. (3)
This course examines the use of log-linear models to analyze count data. It also uses graphical models to examine dependence structures for both count data and measurement data.
Prerequisite: 345, 427.
STAT 540 / 440. Regression Analysis. (3)
Simple regression and multiple regression. Residual analysis and transformations. Matrix approach to general linear models. Model selection procedures, nonlinear least squares, logistic regression. Computer applications.
Prerequisite: 527.
{Fall}
STAT 545 / 445. Analysis of Variance and Experimental Design. (3)
A data-analytic course. Multifactor ANOVA. Principles of experimental design. Analysis of randomized blocks, Latin squares, split plots, etc. Random and mixed models. Extensive use of computer packages with interpretation, diagnostics.
Prerequisite: 540.
{Spring}
STAT 546. Theory of Linear Models. (3)
Theory of the Linear Models discussed in 440/540 and 445/545. Linear spaces, matrices, projections, multivariate normal distribution and theory of quadratic forms. Non-full rank models and estimability. Gauss-Markov theorem. Distribution theory for normality assumptions. Hypothesis testing and confidence regions.
Prerequisite: 553, 545, linear algebra.
{Alternate Falls}
STAT 547. Multivariate Analysis and Advanced Linear Models. (3)
Hotelling T2, multivariate ANOVA and Regression, classification and discrimination, principal components and factor analysis, clustering, graphical and computational techniques, topics in linear models.
Prerequisite: 546.
{Alternate Springs}
STAT 553 / 453. Statistical Inference with Applications. (3)
Transformations of univariate and multivariate distributions to obtain the special distributions important in statistics. Concepts of estimation and hypothesis testing in both large and small samples with emphasis on the statistical properties of the more commonly used procedures, including student’s t-tests, F-tests and chi-square tests. Confidence intervals. Performance of procedures under non-standard conditions (i.e., robustness).
Prerequisite: 561.
{Spring}
STAT 556. Advanced Statistical Inference I. (3)
Theory and methods of point estimation, sufficiency and its applications.
Prerequisite: 553, 561 and MATH 510.
{Alternate Falls}
STAT 557. Advanced Statistical Inference II. (3)
Standard limit theorems, hypothesis testing, confidence intervals and decision theory.
Prerequisite: 556.
{Alternate Springs}
STAT 561 / 461. Probability. (3)
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}
STAT 565. Stochastic Processes with Applications. (3)
(Also offered as MATH 540)
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: 561.
{Offered on demand}
STAT 567. Advanced Probability. (3)
(Also offered as MATH 541)
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.
{Alternate Springs}
STAT 569. Selected Topics in Probability Theory. (3, no limit Δ)
(Also offered as MATH 549)
STAT 570 / 470. Industrial Statistics. (3)
Basic ideas of statistical quality control and improvement. Topics covered: Deming’s 14 points and deadly diseases, Pareto charts, histograms, cause and effect diagrams, control charts, sampling, prediction, reliability, experimental design, fractional factorials, Taguchi methods, response surfaces.
Prerequisite: 345.
STAT 572 / 472. Sampling Theory and Practice. (3)
Basic methods of survey sampling; simple random sampling, stratified sampling, cluster sampling, systematic sampling and general sampling schemes; estimation based on auxiliary information; design of complex samples and case studies.
Prerequisite: 345.
{Alternate Falls}
STAT 574 / 474. Biostatistical Methods: Survival Analysis and Logistic Regression. (3)
A detailed overview of methods commonly used to analyze medical and epidemiological data. Topics include the Kaplan-Meier estimate of the survivor function, models for censored survival data, the Cox proportional hazards model, methods for categorical response data including logistic regression and probit analysis, generalized linear models.
Prerequisite: 528 or 540.
STAT 576 / 476. Multivariate Analysis. (3)
Tools for multivariate analysis including multivariate ANOVA, principal components analysis, discriminant analysis, cluster analysis, factor analysis, structural equations modeling, canonical correlations and multidimensional scaling.
Prerequisite: 528 or 540.
{Offered upon demand}
STAT 577 / 477. Introduction to Bayesian Modeling. (3)
An introduction to Bayesian methodology and applications. Topics covered include: probability review, Bayes’ theorem, prior elicitation, Markov chain Monte Carlo techniques. The free software programs WinBUGS and R will be used for data analysis.
Prerequisite: 561 and (527 or 540).
{Alternate Springs}
STAT 579. Selected Topics in Statistics. (3, no limit Δ)
STAT 581 / 481. Introduction to Time Series Analysis. (3)
Introduction to time domain and frequency domain models of time series. Data analysis with emphasis on Box-Jenkins methods. Topics such as multivariate models; linear filters; linear prediction; forecasting and control.
Prerequisite: 561.
{Alternate Springs}
STAT 585. Nonparametric and Robust Methods. (3)
Statistical methods that are insensitive to the distribution of the data. Sign tests, Kolmogorov-Smirnov tests, rank tests including the Wilcoxon, Mann-Whitney, Kruskal-Wallis and Friedman tests. Robust estimation including M estimators, L estimators and R estimators.
Prerequisite: 561.
{Offered upon demand}
STAT 586. Nonparametric and Robust Methods. (3)
Nonparametric regression, density estimation, filtering, spectral density estimation, image reconstruction and pattern recognition. Tools include orthogonal series, kernels, splines, wavelets and neural networks. Applications to medicine, engineering, biostatistics and economics.
Prerequisite: 561.
{Offered upon demand}
STAT 590. Statistical Computing. (3)
A detailed examination of essential statistical computing skills needed for research and industrial work. Students will use S-Plus, Matlab and SAS® to develop algorithms for solving a variety of statistical problems using resampling and simulation techniques such as the bootstrap, Monte Carlo methods and Markov chain methods for approximating probability distributions. Applications to linear and non-linear models will be stressed.
Prerequisite: 528.
STAT 595. Problems. (1-3, no limit Δ)
STAT 599. Master's Thesis. (1-6, no limit Δ)
Offered on a CR/NC basis only.
STAT 605. Graduate Colloquium. (1 to a maximum of 4 Δ)
Students present their current research.
STAT 649. Seminar in Probability and Statistics. (1-3, no limit Δ)
(Also offered as MATH 649)
STAT 650. Reading and Research. (1-6 to a maximum of 12 Δ)
STAT 699. Dissertation. (3-12, no limit Δ)
Offered on a CR/NC basis only.