MATH 1118 - Math Elem-Mid Sch Teachers I

MATH 1130 - Survey of Mathematics

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

MATH 116 - T: Pre-Calculus Mathematics

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

MATH 1215X - Intermediate Algebra IA

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

MATH 1230 - Trigonometry

MATH 1240 - Pre-Calculus

MATH 1250 - Trigonometry & Pre-Calculus

MATH 1300 - Statistical Literacy

MATH 1350 - Intro Statistics

MATH 1430 - Applications of Calculus I

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

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 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 306 - College Geometry

An axiomatic approach to fundamentals of geometry, both Euclidean and non-Euclidean. Emphasis on historical development of geometry. Prerequisite: 1512 or 2118.

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 317 - Elementary Combinatorics

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.

MATH 319 - Theory of Numbers

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

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 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 338 - Math for Secondary Teachers

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 **327. {Spring}

MATH 375 - Intro Numerical Computing

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 402 - Advanced Calculus II

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

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: 2531 and (**314 or **316 or **321).

MATH 439 - T:

A course exploring a topic not covered by the standard curriculum but of interest to faculty and students in a particular semester.

MATH 463 - Intro to Partial Diff Equa

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).

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 502 - Advanced Calculus II

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 and Human Sciences graduate students.

MATH 504 - Intro to Numerical Linear Alg

(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.

MATH 511 - Intro To Analysis II

Continuation of 510. Differentiation in Rn. Inverse and implicit function theorems, integration in Rn, differential forms and Stokes theorem. Prerequisite: 510. {Spring}

MATH 513 - Intro to Partial Diff Equa

Classification of partial differential equations; properly posed problems; separation of variables, eigenfunctions and Green's functions; brief survey of numerical methods and variational principles. Prerequisite: **312, **313, **314 or **321, one of 311 or 402. {Spring}

MATH 519 - ST: Algebra & Number Theory

A course exploring a topic not covered by the standard curriculum but of interest to faculty and students in a particular semester.

MATH 521 - Abstract Algebra II

Continuation of 520. Module theory, field theory, Galois theory. Prerequisite: **321, 520. {Spring}

MATH 533 - Algebraic Topology II

Continuation of 532. Duality theorems, universal coefficients, spectral sequence. Prerequisite: 532. {Alternate Springs}

MATH 536 - Intro to Differential Manifold

Concept of a manifold, differential structures, vector bundles, tangent and cotangent bundles, embedding, immersions and submersions, transversality, Stokes' theorem. Prerequisite: 511. {Spring}

MATH 538 - Riemannian Geometry II

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.

MATH 540 - Stochastic Processes with Apps

(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 - Math for Secondary Teachers

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 and Human Sciences graduate students.

MATH 551 - Problems

Individual research into an area proposed by the student and conducted under the direction of a faculty member.

MATH 562 - Complex Variables II

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 578 - Numerical Partial Diff Equa

Introduction to the numerical analysis of partial differential equations. Prerequisite: 463, 504, 505. {Alternate Falls}

MATH 584 - Methods in Applied Math II

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 599 - Masters Thesis

Faculty-supervised investigative study that results in the development and writing of a master’s thesis. Offered on a CR/NC basis only.

MATH 639 - Sem: Algebra & Geometry

MATH 650 - Reading and Research

A faculty-supervised course culminating in a comprehensive paper or research proposal that integrates knowledge attained through coursework, research, and experience.

MATH 669 - Sem: Analysis

MATH 679 - Sem: Applied Mathematics

MATH 699 - Dissertation

Faculty-supervised investigative study that results in the development and writing of a doctoral dissertation. Offered on a CR/NC basis only.