MATH 1118 - Math Elem-Mid Sch Teachers I

MATH 1130 - Survey of Mathematics

MATH 116 - T: Pre-Calculus Mathematics

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

MATH 1215X - Intermediate Algebra IA

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.

MATH 1215Y - Intermediate Algebra IB

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.

MATH 1215Z - Intermediate Algebra IC

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.

MATH 1220 - College Algebra

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. 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.

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

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. 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.

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 2118 - Math Elem-Mid Sch Teachers III

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 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: 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 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: 2530.

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

(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 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: 2530 and (**314 or **316 or **321).

MATH 439 - Topics in Math

{Offered upon demand}

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 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 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 graduate students. {Spring}

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

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MATH 521 - Abstract Algebra II

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

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 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 graduate students. {Fall}

MATH 551 - Problems

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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 579 - Select Topics in Applied Math

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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

Offered on a CR/NC basis only.

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.