MATH 1118 - Math Elem-Mid Sch Teachers I

Course offers an in-depth look at rational numbers, arithmetic operations, and basic geometric concepts. Problem solving is emphasized throughout. 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

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 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 2531 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 - T: Pre-Calculus Mathematics

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

MATH 1215X - Intermediate Algebra IA

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

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

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

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. 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

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. 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

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. 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 & Pre-Calculus

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 1300 - Statistical Literacy

Participants will study the social statistics encountered by consumers. Investigate the story behind the statistics. Study the influences on social statistics. Study the techniques used to control these influences. Strong focus on confounding. 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 or ACCUPLACER Next-Generation Advanced Algebra & Functions =>218.

MATH 1350 - Intro Statistics

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. 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 2531 or ACT Math =>22 or SAT Math Section =>540 or ACCUPLACER Next-Generation Quantitative Reasoning, Algebra, and Statistics =>253.

MATH 1430 - Applications of Calculus I

An algebraic and graphical study of derivatives and integrals, with an emphasis on applications to business, social science, economics and the sciences. 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

Topics in this course include functions of several variables, techniques of integration, an introduction to basic differential equations, and other applications. 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 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. 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

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. Meets New Mexico General Education Curriculum Area 2: Mathematics and Statistics. Prerequisite: 1512.

MATH 2115 - Math Middle School Teachers

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 - Math Elem-Mid Sch Teachers III

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 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 2531 - 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: 2531.

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: 2531 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

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: 2531.

MATH 322 - Modern Algebra I

Groups, rings, homomorphisms, permutation groups, quotient structure, ideal theory, fields. Prerequisite: 2531 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: 2531 and two MATH courses 300-level or above.

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: 2531.

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: 2531 and two MATH courses 300-level or above. Restriction: College of Education and Human Sciences 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 and Human Sciences 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 532 - Algebraic Topology I

Introduction to homology and cohomology theories. Homotopy theory, CW complexes. Prerequisite: *431, 521 or permission of instructor. {Alternate Falls}

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 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 579 - Sel T: Applied Math

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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: Algebra & Geometry

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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.