MATH 101 - Intermediate Algebra Part I

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: (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: 102.

MATH 102 - Intermediate Algebra Part II

This course includes quadratic equations, properties of exponents and scientific notation, simplifying polynomial expressions, factoring and introduction to functions. Prerequisite: 101.

MATH 103 - Intermediate Algebra Part III

This course includes radical expressions and equations, rational expressions and equations, the exponential and logarithm functions. Pre- or corequisite: 102.

MATH 1110 - Mathematics for Teachers I

Course offers an in-depth look at rational numbers, arithmetic operations, and basic geometric concepts. Problem solving is emphasized throughout. Prerequisite: (101 and 102 and 103) or 1130 or 1215 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.

MATH 1130 - Survey of Mathematics

MATH 116 - T: Pre-Calculus Mathematics

Selected topics from algebra, geometry and trigonometry. Restriction: permission of department.

MATH 1220 - College Algebra

MATH 1230 - Trigonometry

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. 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

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. 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.

MATH 1250 - Trigonometry & Pre-Calculus

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.

MATH 1350 - Intro Statistics

MATH 1430 - Applications of Calculus I

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. 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.

MATH 1440 - Applications of Calculus II

Includes the definite integral, multivariate calculus, simple differential equations, basic review of trigonometry and its relation to calculus. Credit for both this course and MATH 1522 may not be applied toward a degree program. Prerequisite: 1430.

MATH 1512 - Calculus I

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. 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.

MATH 1522 - Calculus II

Transcendental functions, techniques of integration, numerical integration, improper integrals, sequences and series, Taylor series with applications, complex variables, differential equations. Credit for both this course and MATH 1440 may not be applied toward a degree program. Prerequisite: 1512.

MATH 215 - Math Elem-Mid School Teachers

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. Meets New Mexico Lower-Division General Education Common Core Curriculum Area II: Mathematics. Prerequisite: 1110.

MATH 216 - Math Middle School Teachers

MATH 2530 - Calculus III

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. Prerequisite: 1522.

MATH 305 - Math Historic Perspective

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.

MATH 311 - Vector Analysis

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.

MATH 312 - Part Differential Equats Engin

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.

MATH 313 - Complex Variables

Theory of functions of a complex variable with applications 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.

MATH 314 - Linear Algebra with Apps

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.

MATH 316 - Applied Ordinary Diff Equas

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.

MATH 321 - Linear Algebra

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.

MATH 322 - Modern Algebra I

Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields. Prerequisite: 2530 and (**321 or **327).

MATH 327 - Discrete Structures

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.

MATH 375 - Intro Numerical Computing

(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 401 - Advanced Calculus I

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.

MATH 415 - Hist & Phil of Mathemathics

(Also offered as PHIL *415) A historical survey of principal issues and controversies on the nature of mathematics. Emphasis varies from year to year. Student who does not have prerequisite may seek permission of instructor. Prerequisite: 1440 or 1522 or **356 or PHIL 356.

MATH 431 - Intro To Topology

Metric spaces, topological spaces, continuity, algebraic topology. Prerequisite: **321. Pre- or corequisite: 322. {Fall}

MATH 441 - Probability

(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.

MATH 462 - Intro to Ordinary Diff Equa

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 464 - Applied Matrix Theory

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 - Intro to Scientific Computing

(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. {Fall}

MATH 472 - Fourier Analysis & Wavelets

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

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

MATH 501 - Advanced Calculus I

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.

MATH 505 - Intro Numerical Approx & DE

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.

MATH 507 - Math Historic Perspective

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.

MATH 510 - Intro To Analysis

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 512 - Intro to Ordinary Diff Equa

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 514 - Applied Matrix Theory

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 520 - Abstract Algebra I

Theory of groups, permutation groups, Sylow theorems. Introduction to ring theory, polynomial rings. Principal ideal domains. Prerequisite: 322. {Fall}

MATH 530 - Algebraic Geometry I

MATH 535 - Foundations of Topology

Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces. Prerequisite: 501. {Fall}

MATH 537 - Riemannian Geometry I

Theory of connections, curvature, Riemannian metrics, Hopf-Rinow theorem, geodesics. Riemannian submanifolds. Prerequisite: 536. {Alternate Falls}

MATH 539 - Sel T: Geometry & Topology

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MATH 551 - Problems

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MATH 557 - Sel T: Numerical Analysis

(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 - Complex Variables I

Analyticity, Cauchy theorem and formulas, Taylor and Laurent series, singularities and residues, conformal mapping, selected topics. Prerequisite: 311 or 402. {Fall}

MATH 572 - Fourier Analysis & Wavelets

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 583 - Methods in Applied Math I

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 598 - Practicum

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 - Masters Thesis

Offered on a CR/NC basis only.

MATH 605 - Graduate Colloquium

Students present their current research.

MATH 639 - Sem: Geometry & Topology

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MATH 650 - Reading and Research

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MATH 669 - Sem: Analysis

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MATH 679 - Sem: Applied Mathematics

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MATH 699 - Dissertation

Offered on a CR/NC basis only.