M. Cristina Pereyra, Chair
Department of Mathematics and Statistics
Science and Math Learning Center
MSC01 1115
1 University of New Mexico
Albuquerque, NM 87131-0001
(505) 277-4613
Mathematics is fundamental to the formulation and analysis of scientific theories, is a rich and independent field of inquiry, and its study is excellent preparation for life in our highly specialized society. Active research throughout the mathematical sub-disciplines, spurred on in part by advances in computing technology, leads to new perspectives and applications. The major in mathematics combines broad study of fundamental theories with in-depth investigation of particular subjects chosen from pure, applied and computational mathematics. A degree in mathematics, either alone or in combination with study in another field, is excellent preparation for careers in industry, academia, and research institutes.
Statistics is the science of collecting and analyzing data. Statisticians interact with researchers in all the various disciplines of science, engineering, medicine, social science and business to develop scientifically sound methods in those areas. Most course work in the department is devoted to understanding current methods and the reasoning behind them. A degree in statistics prepares students for careers in industry, government, academia, and research institutes, as well as being excellent preparation for professional programs in medicine, law, business administration and public policy and administration.
A beginning student who wishes to take MATH 1522 or a more advanced course must have College Board Advanced Placement scores as described in the Admissions section of this Catalog.
A student who wishes to enroll in a course requiring a prerequisite must earn a grade of "C" (not "C-") or better in the prerequisite course.
1. Content on specific courses overlaps enough to necessitate restricting credit of both courses toward a student’s degree. These courses are not considered equivalent and the completion of the second course in a pair will not affect a student’s earned hours on the transcript. Students should consult their advisor if they feel the incorrect course is applied for credit on their degree audit.
Students will be allowed to apply only one of the following courses in each pair for credit towards a degree:
2. Students who have credit for MATH 1220 College Algebra or higher may not then take MATH 1215X, 1215Y, and 1215Z Intermediate Algebra for credit.
Courses
MATH 107.
Problems in College Algebra.
(1)
Study session for 1220 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 1430 with an emphasis on problem-solving. (I)
Offered on a CR/NC basis only.
{Fall, Spring}
MATH 1118.
Mathematics for Elementary and Middle School Teachers I.
(3)
Course offers an in-depth look at rational numbers, arithmetic operations, and basic geometric concepts. Problem solving is emphasized throughout. (T)
Prerequisite: 1130 or 1215 or 1220 or 1230 or 1240 or 1350 or 1430 or 1512 or FYEX 1010 or ACT Math =>19 or SAT Math Section =>480 or ACCUPLACER Next-Generation Arithmetic =>276.
MATH 1130.
Survey of Mathematics.
(3)
This course will develop students’ ability to work with and interpret numerical data, to apply logical and symbolic analysis to a variety of problems, and/or to model phenomena with mathematical or logical reasoning. Topics include financial mathematics used in everyday life situations, statistics, and optional topics from a wide array of authentic contexts. (I)
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: (118 and 119) or 1215 or (1215X and 1215Y) or 1220 or 1230 or 1240 or 1350 or 1430 or 1440 or 1512 or 1522 or 2530 or ACT Math =>22 or SAT Math Section =>540 or ACCUPLACER Next-Generation Advanced Algebra and Functions =>218 or ACCUPLACER Next-Generation Quantitative Reasoning, Algebra, and Statistics =>253.
MATH 116.
Topics in Pre-Calculus Mathematics.
(1-6 to a maximum of 12 Δ)
Selected topics from algebra, geometry and trigonometry. (I)
Restriction: permission of department.
MATH 1215X.
Intermediate Algebra IA.
(1)
A study of linear and quadratic functions, and an introduction to polynomial, absolute value, rational, radical, exponential, and logarithmic functions. A development of strategies for solving single-variable equations and contextual problems.
This is the first course in a three-part sequence. In order to receive transfer credit for MATH 1215, all courses in this sequence (MATH 1215X, MATH 1215Y, MATH 1215Z) must be taken and passed.
Prerequisite: (MATH 021 and MATH 022) or MATH 100 or FYEX 1010 or ISM 100 or ACT Math =>17 or SAT Math Section =>460 or ACCUPLACER Next-Generation Advanced Algebra and Functions =218-238.
Corequisite: 1215Y.
MATH 1215Y.
Intermediate Algebra IB.
(1)
A study of linear and quadratic functions, and an introduction to polynomial, absolute value, rational, radical, exponential, and logarithmic functions. A development of strategies for solving single-variable equations and contextual problems.
This is the second course in a three-part sequence. In order to receive transfer credit for MATH 1215, all courses in this sequence (MATH 1215X, MATH 1215Y, MATH 1215Z) must be taken and passed.
Prerequisite: 1215X.
MATH 1215Z.
Intermediate Algebra IC.
(1)
A study of linear and quadratic functions, and an introduction to polynomial, absolute value, rational, radical, exponential, and logarithmic functions. A development of strategies for solving single-variable equations and contextual problems.
This is the third course in a three-part sequence. In order to receive transfer credit for MATH 1215, all courses in this sequence (MATH 1215X, MATH 1215Y, MATH 1215Z) must be taken and passed.
Pre- or corequisite: 1215Y.
MATH 1220.
College Algebra.
(3)
Note: See Restrictions earlier in Mathematics and Statistics.
Preparation for 1240 and 1430. The study of equations, functions and graphs, reviewing linear and quadratic functions, and concentrating on polynomial, rational, exponential and logarithmic functions. Emphasizes algebraic problem solving skills and graphical representation of functions. (I)
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: (118 and 119) or 1215 or (1215X and 1215Y and 1215Z) or ACT Math =>22 or SAT Math Section =>540 or ACCUPLACER Next-Generation Advanced Algebra and Functions =239-248.
MATH 1230.
Trigonometry.
(3)
A study of plane trigonometry including the definitions of the fundamental trig functions using right angle triangle and unit circle approaches. Trig functions of any real number will be evaluated and the functions graphed along with their transformations. Trigonometric identities will be developed and demonstrated including multiple angle identities and identities developed from them. Inverse trigonometric functions will be developed and used to solve trigonometric equations. Trigonometric applications will be solved using right angle trigonometry and the laws of sines and cosines. Trigonometric methods will be applied to complex numbers and the use of 2D vectors and vector dot products.May be taken concurrently with 1240. (I)
Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.
MATH 1240.
Pre-Calculus.
(3)
This course extends students’ knowledge of polynomial, rational, exponential and logarithmic functions to new contexts, including rates of change, limits, systems of equations, conic sections, and sequences and series. May be taken concurrently with 1230. (I)
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.
MATH 1250.
Trigonometry and Pre-Calculus.
(5)
Includes the study of functions in general with emphasis on the elementary functions: algebraic, exponential, logarithmic, trigonometric and inverse trigonometric functions. Topics include rates of change, limits, systems of equations, conic sections, sequences and series, trigonometric equations and identities, complex number, vectors, and applications.
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.
MATH 1350.
Introduction to Statistics.
(3)
This course discusses the fundamentals of descriptive and inferential statistics. Students will gain introductions to topics such as descriptive statistics, probability and basic probability models used in statistics, sampling and statistical inference, and techniques for the visual presentation of numerical data. These concepts will be illustrated by examples from a variety of fields. (I)
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: (118 and 119) or 1215 or (1215X and 1215Y) or 1220 or 1230 or 1240 or 1430 or 1440 or 1512 or 1522 or 2530 or ACT Math =>22 or SAT Math Section =>540 or ACCUPLACER Next-Generation Quantitative Reasoning, Algebra, and Statistics =>253.
{Summer, Fall, Spring}
MATH 1430.
Applications of Calculus I.
(3)
An algebraic and graphical study of derivatives and integrals, with an emphasis on applications to business, social science, economics and the sciences. (I)
Credit for both this course and MATH 1512 may not be applied toward a degree program.
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: 1220 or 1240 or 1250 or ACT Math =>26 or SAT Math Section =>620 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.
MATH 1440.
Applications of Calculus II.
(3)
Topics in this course include functions of several variables, techniques of integration, an introduction to basic differential equations, and other applications. (I)
Credit for both this course and MATH 1522 may not be applied toward a degree program.
Prerequisite: 1430.
MATH 1512.
Calculus I.
(4)
Limits. Continuity. Derivative: definition, rules, geometric interpretation and as rate-of-change, applications to graphing, linearization and optimization. Integral: definition, fundamental theorem of calculus, substitution, applications such as areas, volumes, work, averages. (I)
Credit for both this course and MATH 1430 may not be applied toward a degree program.
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: (1230 and 1240) or 1250 or ACT Math =>28 or SAT Math Section =>640 or ACCUPLACER Next-Generation Advanced Algebra and Functions =>284.
MATH 1522.
Calculus II.
(4)
Transcendental functions, techniques of integration, numerical integration, improper integrals, sequences and series, Taylor series with applications, complex variables, differential equations. (I)
Credit for both this course and MATH 1440 may not be applied toward a degree program.
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: 1512.
MATH 1996.
Topics.
(1-6, no limit Δ)
MATH 2115.
Math for Middle School Teachers.
(3)
Development of mathematical concepts from the viewpoint of the middle school curriculum. Topics include: in-depth development of algebraic thinking, connections between algebra and geometry, and applications. Problem solving is emphasized throughout.
Prerequisite: 2118.
MATH 2118.
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: data analysis and other topics with connections to the elementary curriculum. Problem solving is emphasized throughout. (T)
Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics.
Prerequisite: 1118 and (1215X or 1220 or 1230 or 1240 or 1350 or 1430 or 1512 or ACT Math =>19 or SAT Math Section =>480 or ACCUPLACER Next-Generation Quantitative Reasoning, Algebra, and Statistics =>262).
MATH 2530.
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: 1522.
MATH 2996.
Topics.
(1-6, no limit Δ)
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: 1522.
{Fall}
MATH 306.
College Geometry.
(3)
An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. (T)
Prerequisite: 1512 or 2118.
{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: 2530.
{Occasional Summer, Fall, Spring}
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: 2530 and **316.
{Occasional Summer, Fall, Spring}
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: 2530 and one MATH course 300-level or above.
{Fall, Spring}
MATH **314.
Linear Algebra with Applications.
(3)
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.
Credit for both this course and MATH **321 may not be applied toward a degree program.
Prerequisite: 1440 or 1522.
Pre- or corequisite: CS 151L or CS 152L or ECE 131L or PHYS 2415.
{Summer, Fall, Spring}
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: 1522.
Pre- or corequisite: CBE 253 or CS 151L or CS 152L or ECE 131L or PHYS 2415.
{Summer, Fall, Spring}
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: 1522 or STAT **345.
{Spring}
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)
Linear transformations, matrices, eigenvalues and eigenvectors, inner product spaces.
Credit for both this course and MATH **314 may not be applied toward a degree program.
Prerequisite: 2530.
{Fall, Spring}
MATH 322.
Modern Algebra I.
(3)
Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields.
Prerequisite: 2530 and (**321 or **327).
{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: 1522.
{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 **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 ECE 131L or PHYS 2415).
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: 2530 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: 2530 and (**314 or **316 or **321).
{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: 1440 or 1522 or **356 or PHIL 356.
MATH *421.
Modern Algebra II.
(3)
Theory of fields, algebraic field extensions and Galois theory for fields of characteristic zero.
Prerequisite: 322.
{Spring}
MATH *431.
Introduction to Topology.
(3)
Metric spaces, topological spaces, continuity, algebraic topology.
Prerequisite: **321.
Pre- or corequisite: 322.
{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: 2530.
{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: (311 or 402) and **312 and **313 and (**314 or **321).
{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 *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.
{Alternate Springs}
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: 2530 and two MATH courses 300-level or above.
Restriction: College of Education graduate students.
{Fall, 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 or 514.
{Spring}
MATH 505.
Introductory Numerical Analysis: Approximation and Differential Equations.
(3)
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.
{Fall}
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: 1522.
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 Rn. Inverse and implicit function theorems, integration in Rn, 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: (311 or 402), **312, **313, **314 or **321.
{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.
(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.
Commutative Algebra [Algebraic Geometry I].
(3)
Basic theory of Commutative Algebra including ideals, modules, localization, valuation rings, Integral extensions, dimension theory, Cohen-Macaulay, Gorenstein and regular rings.
Prerequisite: 521.
MATH 531.
Algebraic Geometry.
(3)
Basic theory of affine and projective varieties over an arbitrary algebraically closed field, with main emphasis on algebraic curves.
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.
Foundations of Topology.
(3)
Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.
Prerequisite: 501.
{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 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 upon demand}
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 549.
Selected Topics in Probability Theory.
(3, no limit Δ)
(Also offered as STAT 569)
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.
Analysis III [Measure Theory].
(3)
Lebesgue measure and integration, abstract measure spaces, differentiation. Fundamentals of functional analysis: Hilbert and Banach spaces, linear operators, L^p spaces, compact operators.
Prerequisite: 511.
{Alternate Falls}
MATH 565.
Analysis IV [Harmonic Analysis].
(3)
Further topics in functional analysis: spectral theory, unbounded operators. Fundamentals of Fourier analysis: Fourier series and transforms and their pointwise convergence. Introduction to distributions.
Prerequisite: 563.
{Alternate Springs}
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) and 401.
{Alternate Springs}
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: 504 and 505 and 512.
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, may be repeated three times Δ)
Students present their current research.
MATH 639.
Seminar in Algebra and Geometry [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 699.
Dissertation.
(3-12, no limit Δ)
Offered on a CR/NC basis only.
STAT 279.
Topics in Introductory Statistics.
(1-3 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 1440 or MATH 1522.
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: MATH 1350.
{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 2530.
{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: (427 or 440) and 461.
{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: MATH 1350.
{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 and 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)
(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 2530.
{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 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: (527 or 540) and 561.
{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 586.
Nonparametric Curve Estimation and Image Reconstruction.
(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, may be repeated three times 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.