Academic Calendar

Keys and Symbols Reference

Study session for 1220 with an emphasis on problem solving. (I)

Offered on a CR/NC basis only.

{Fall, Spring}

Study session for 1430 with an emphasis on problem-solving. (I)

Offered on a CR/NC basis only.

{Fall, Spring}

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 (1215X and 1215Y and 1215Z) 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 Arithmetic =>276.

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. (I)

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

Prerequisite: (118 and 119) or 1215 or (1215X and 1215Y and 1215Z) 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.

Selected topics from algebra, geometry and trigonometry. (I)

Restriction: permission of department.

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.

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.

This course includes quadratic equations, properties of exponents and scientific notation, simplifying polynomial expressions, factoring and introduction to functions.

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.

This course includes radical expressions and equations, rational expressions and equations, the exponential and logarithm functions.

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.

Note: See Restrictions earlier in Mathematics and Statistics.

Preparation for 1240 and 1430. 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. (I)

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

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.

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 1240. (I)

Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.

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 1230. (I)

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.

Algebraic expressions, algebraic equations, inequalities, functions, graphing. Exponential, logarithmic, and trigonometric functions. Complex numbers and vectors. Limits.

Prerequisite: 1220 or ACT Math =>25 or SAT Math Section =>590 or ACCUPLACER Next-Generation Advanced Algebra and Functions =249-283.

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. (I)

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

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}

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. (I)

Credit for both this course and MATH 1512 may not be applied toward a degree program.

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

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.

Includes the definite integral, multivariate calculus, simple differential equations, basic review of trigonometry and its relation to calculus. (I)

Credit for both this course and MATH 1522 may not be applied toward a degree program.

Prerequisite: 1430.

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. (I)

Credit for both this course and MATH 1430 may not be applied toward a degree program.

Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics.

Prerequisite: (1230 and 1240) or 1250 or ACT Math =>28 or SAT Math Section =>640 or ACCUPLACER Next-Generation Advanced Algebra and Functions =>284.

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.

Prerequisite: 1512.

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.

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 Lower-Division General Education Common Core Curriculum Area II: Mathematics.

Prerequisite: 1118.

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.

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}

An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. (T)

Prerequisite: 1512 or 2118.

{Spring}

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}

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}

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}

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}

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}

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}

Divisibility, congruences, primitive roots, quadratic residues, diophantine equations, continued fractions, partitions, number theoretic functions.

{Spring}

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}

Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields.

Prerequisite: 2530 and (**321 or **327).

{Fall}

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}

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}

(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.

(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).

Advanced problem solving. Especially recommended for students wishing to participate in the Putnam Intercollegiate Mathematical Competition.

Restriction: permission of instructor.

{Offered upon demand}

Selected topics from analysis, algebra, geometry, statistics, model building, interdisciplinary studies and problem solving.

{Offered upon demand}

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}

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}

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}

(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.

Theory of fields, algebraic field extensions and Galois theory for fields of characteristic zero.

Prerequisite: 322.

{Spring}

Metric spaces, topological spaces, continuity, algebraic topology.

Prerequisite: **321.

Pre- or corequisite: 322.

{Fall}

{Offered upon demand}

(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}

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}

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}

Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors and canonical forms; variational principles; generalized inverses.

Prerequisite: **314 or **321.

{Fall}

Special functions and advanced mathematical methods for solving differential equations, difference equations and integral equations.

Prerequisite: 311 and **312 and **313 and **316.

{Spring}

(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}

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}

Guided study, under the supervision of a faculty member, of selected topics not covered in regular courses.

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}

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}

(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}

(Also offered as CS 576)

Numerical approximation of functions. Interpolation by polynomials, splines and trigonometric functions. Numerical integration and solution of ordinary differential equations. An introduction to finite difference and finite element methods, time permitting.

Prerequisite: **316 or 401.

{Fall}

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}

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}

Continuation of 510. Differentiation in Rⁿ. Inverse and implicit function theorems, integration in Rⁿ, differential forms and Stokes theorem.

Prerequisite: 510.

{Spring}

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}

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}

Determinants; theory of linear equations; matrix analysis of differential equations; eigenvalues, eigenvectors and canonical forms; variational principles; generalized inverses.

Prerequisite: **314 or **321.

{Fall}

Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains.

Prerequisite: 322.

{Fall}

Continuation of 520. Module theory, field theory, Galois theory.

Prerequisite: **321, 520.

{Spring}

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}

Introduction to homology and cohomology theories. Homotopy theory, CW complexes.

Prerequisite: *431, 521.

{Alternate Falls}

Continuation of 532. Duality theorems, universal coefficients, spectral sequence.

Prerequisite: 532.

{Alternate Springs}

Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.

Prerequisite: 501.

{Fall}

Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes’ theorem.

Prerequisite: 511.

{Spring}

Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theorem, geodesics. Riemannian submanifolds.

Prerequisite: 536.

{Alternate Falls}

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}

(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}

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}

(Also offered as STAT 569)

(Also offered as CS 557)

Possible topics include approximation theory, two point boundary value problems, quadrature, integral equations and roots of nonlinear equations.

Analyticity, Cauchy theorem and formulas, Taylor and Laurent series, singularities and residues, conformal mapping, selected topics.

Prerequisite: 311 or 402.

{Fall}

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}

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}

Fourier analysis on the circle, real line and on compact and locally compact groups.

Prerequisite: 563.

{Offered upon demand}

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}

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}

Selected advanced topics in numerical linear algebra.

Prerequisite: 504.

{Alternate Springs}

Introduction to the numerical analysis of partial differential equations.

Prerequisite: 463, 504, 505.

{Alternate Falls}

Normed vector spaces, including Hilbert and Banach spaces. Linear operators on these spaces, with an emphasis on applications.

Prerequisite: 510.

{Offered upon demand}

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}

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}

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.

Offered on a CR/NC basis only.

Students present their current research.

(Also offered as STAT 649)

Offered on a CR/NC basis only.

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