# MATH Courses

## Filter these Courses

MATH
100A

Prereqs: One year high school algebra and appropriate score on the Math Placement Exam.

Credit earned in MATH 100A will not count toward degree requirements.

Review of the topics in a second-year high school algebra course taught at the college level. Includes: real numbers, 1st and 2nd degree equations and inequalities, linear systems, polynomials and rational expressions, exponents and radicals. Heavy emphasis on problem solving strategies and techniques.

This course is a prerequisite for:
MATH 101

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
101

Prereqs: Appropriate placement exam score and either two years of high school algebra or a grade of P, C, or better in MATH 100A.

Real numbers, exponents, factoring, linear and quadratic equations, absolute value, inequalities, functions, graphing, polynominal and rational functions, exponential and logarithmic functions, systems of equations.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
102

Prereqs: One year high school geometry and either two years high school algebra, one semester high school precalculus, and a qualifying score on the Math Placement Exam; or a grade of C, P, or better in MATH 101.

Trigonometric functions, identities, trigonometric equations, solution of triangles, inverse trigonometric functions, and graphs.

Credit Hours: | 2 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
103

Prereqs: Appropriate placement exam score, one year high school geometry, and two years high school algebra.

For students with previous college math courses, permission is also required.

First and second degree equations and inequalities, absolute value, functions, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions and identities, laws of sines and cosines, applications, polar coordinates, systems of equations, graphing, conic sections.

Credit Hours: | 5 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
104

Prereqs: Appropriate placement exam score or a grade of P (pass), or C or better in MATH 101.

Rudiments of differential and integral calculus with applications to problems from business, economics, and social sciences.

Credit Hours: | 3 |

Course Delivery: | Classroom, Web |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
106

Prereqs: One year high school geometry; two years algebra and one year precalculus-trig in high school, or MATH 102 or MATH 103 or equivalent.

Functions of one variable, limits, differentiation, exponential, trigonometric and inverse trigonometric functions, maximum-minimum, and basic integration theory (Riemann sums) with some applications.

This course is a prerequisite for:
AECN 815, AGRO 479, AGRO 807, AGRO 966, BIOS 456, BLAW 372, BSEN 225, BSEN 355, CEEN 103, CHEM 109, CHEM 111, CHEM 113, CHEM 471, CHME 114, CIVE 221, CIVE 252, CNST 241, CNST 252, CNST 306, CSCE 156H, CSCE 235H, ECON 215, ECON 215H, FDST 363, FORS 411, GEOG 458, GEOL 372, GEOL 410, GEOL 472, GEOL 825, MATH 107, MATH 107H, MATH 238, MECH 220, METR 205, METR 415, METR 483, MRKT 341, NRES 408, NRES 453, NRES 469, NRES 488, NRES 880, PHYS 211, PHYS 211H

Credit Hours: | 5 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
106B

Prereqs: One year high school geometry; two years high school algebra and one year high school precalculus-trigonometry, or MATH 102 or 103 or equivalent.

Math Placement Policy applies. Credit toward the degree may be earned in only one of: MATH 104, 106, 106B, or 108H. MATH 106B serves as a prerequisite for other courses in place of MATH 106 or 108H.

Functions of one variable, limits, differentiation, integration theory, fundamental theorem of calculus, with applications in the life sciences.

Credit Hours: | 5 |

Course Format: | Lecture , Recitation |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
107

Prereqs: A grade of P, C or better in MATH 106.

Integration theory; techniques of integration; applications of definite integrals; series, Taylor series, vectors, cross and dot products, lines and planes, space curves.

Credit Hours: | 4 |

Course Format: | Lecture 5 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
107H

Prereqs: Good standing in the University Honors Program or by invitation; and a grade of "B" or better in MATH 106 or equivalent.

MATH
107R

Prereqs: A grade of P, C or better in Math 106.

Open only to students who previously completed the 5 credit hour Math 107 at UNL and wish to improve their grade.

Integration theory, techniques of integration, applications of definite integrals, series, Taylor series, vectors, cross and dot products, lines and planes, space curves.

Credit Hours: | 5 |

Course Format: | Lecture 5 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

MATH
108H

Prereqs: Good standing in the University Honors Program or by invitation.

Credit Hours: | 5 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
109H

MATH
189H

Prereqs: Good standing in the University Honors Program or by invitation; placement score on the Math Placement Examination (MPE) at the MATH 104-level or above.

A University Honors Seminar 189H is required of all students in the University Honors Program.

Topics vary.

Credit Hours: | 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
198

Pass/No Pass only.

This course has no description.

Credit Hours: | 1-3 |

Max credits per degree: | 6 |

Course Format: | Lecture |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

MATH
198H

Prereqs: Good standing in the University Honors Program or by invitation.

This course has no description.

Credit Hours: | 1-3 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

MATH
203

Applications of quantitative reasoning and methods to problems and decision making in the areas of management, statistics, and social choice. Includes networks, critical paths, linear programming, sampling, central tendency, inference, voting methods, power index, game theory, and fair division problems.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
203J

Prereqs: Must be admitted to the College of Journalism.

Applications of quantitative reasoning and methods to problems and decisions making in areas of particular relevance to College of Journalism and Mass Communication, such as governance, finance, statistics, social choice, and graphical presentation of data. Financial mathematics, statistics and probability (sampling, central tendency, and inference), voting methods, power index, and fair division problems.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

MATH
208

Prereqs: A grade of P, C or better in MATH 107.

Vectors and surfaces, parametric equations and motion, functions of several variables, partial differentiation, maximum-minimum, Lagrange multipliers, multiple integration, vector fields, path integrals, Green's Theorem, and applications.

This course is a prerequisite for:
ACTS 401, ACTS 440, ACTS 441, AGRO 908, AGRO 909, AGRO 958, AGRO 961, BSEN 244, CEEN 328, CHEM 481, CHME 332, CHME 832, ELEC 215, ELEC 935, GEOG 458, GEOL 889, GEOL 985, GEOL 986, GEOL 988, MATH 221, MATH 310, MATH 314, MATH 325, MATH 407, MATH 495, MATH 807, MATH 858, MATL 470, MECH 321, MECH 325, MECH 325H, MECH 373, MECH 373H, MECH 421, METR 311, METR 433, METR 811, MRKT 341, NRES 918, PHYS 213, PHYS 213H, STAT 462, STAT 880, STAT 882

Credit Hours: | 4 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

Prereqs: Good standing in the University Honors Program or by invitation.

MATH
221/821

Not open to MA or MS students in mathematics or statistics.

First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications.

This course is a prerequisite for:
BSEN 303, BSEN 311, BSEN 317, BSEN 344, BSEN 350, CEEN 213, CEEN 328, CHME 312, CHME 434, CHME 462, CIVE 310H, CIVE 326, CIVE 326H, CIVE 327, CIVE 401, CSCE 441, ELEC 216, ELEC 304, ELEC 306, ELEC 442, ELEC 935, IMSE 328, MATH 424, MATH 427, MATH 430, MATH 442, MATH 456, MATH 489, MATL 472, MECH 310, MECH 330, MECH 381, MECH 416, MECH 449, MECH 454, MECH 475, MECH 480, METR 312, METR 812, METR 880, METR 924, PHYS 311, PHYS 422, PHYS 451

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Advanced Mathematics Courses |

MATH
221H

Prereqs: Good standing in the University Honors Program or by invitation.

MATH
238/838

MATH 838 will not count toward a MA or MS degree in MATH or STAT. Some computation and visualizations in MATH 238/838 will be done with Matlab.

Mathematical modeling, discrete and continuous probability, parameter estimation, discrete and continuous dynamical systems, and Markov chains. Application of mathematical models in the life sciences. Methods include regression analysis, cobweb diagrams, the phase line, nullcline analysis, eigenvalue analysis, linearization, and likelihood analysis. Applications include fisheries, stage-structured populations, pharmacokinetics, epidemiology, and medical testing.

This course is a prerequisite for:
CHEM 471

Credit Hours: | 5 |

Course Format: | Lecture 5 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
300

Prereqs: Parallel TEAC 308; admission to the College of Education and Human Sciences; removal of any mathematics entrance deficiencies.

MATH
300M

Prereqs: Admission to the College of Education and Human Sciences.

MATH 300M is open only to a middle grades teaching endorsement program student. Credit towards degree may be earned in only one of: MATH 300, or MATH 300M. MATH 300M is designed to strengthen the mathematics knowledge of the middle-level mathematics teacher.

Develop a deeper understanding of "number and operations". The importance of careful reasoning, problem solving, and communicating mathematics, both orally and in writing. Connections with other areas of mathematics and the need for developing the "habits of mind of a mathematical thinker".

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
301

Prereqs: MATH 300, with a grade of C or Pass or better.

Credit towards the degree may be earned in only one of: MATH 301. Designed for elementary education majors with mathematics as an area of concentration.

Geometry and measurement. Develop an understanding of geometry as taught in the elementary school.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
302

Math 300 is a strongly recommended prerequisite. Math 302 is intended for middle grades teaching endorsement majors with a mathematics emphasis and/or to elementary education majors who want a mathematics concentration.

Using mathematics to model solutions or relationships for realistic problems taken from the middle school curriculum. The mathematics for these models are a mix of algebra, geometry, sequences (dynamical systems, queuing theory), functions (linear, exponential, logarithmic), and logic. Mathematical terminology, concepts and principles. Calculator based lab devices, graphing calculators, and computers as tools to collect data, to focus on concepts and ideas, and to made the mathematics more accessible.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

Prereqs: Admission to the College of Education and Human Sciences.

Open only to middle grades teaching endorsement majors with a mathematics emphasis and/or to elementary education majors who want a mathematics concentration.

How to express mathematical solutions and ideas logically and coherently in both written and oral forms in the context of problem solving. Inductive and deductive logical reasoning skills through problem solving. Present and critique logical arguments in verbal and written forms. Problem topics taken from topics nationally recommended for middle school mathematics.

Credit Hours: | 3 |

Course Format: | Lecture |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

Prereqs: Admission to the College of Education and Human Sciences.

MATH 306 is open only to a middle school or elementary grades teaching endorsement program student.

Basic number theory results which are needed to understand the number theoretic RSA cryptography algorithm. Primes, properties of congruences, divisibility tests, linear Diophantine equations, linear congruences, Chinese Remainder Theorem, Wilson's Theorem, Fermat's Little Theorem, Euler's Theorem, and Euler's phi function. Integers with connections to the middle school curriculum and mathematical reasoning.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
310

Prereqs: MATH 208.

Elementary number theory, including induction, the Fundamental Theorem of Arithmetic, and modular arithmetic. Introduction to rings and fields as natural extension of the integers. Particular emphasis on the study of polynomials with coefficients in the rational, real, or complex numbers.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Advanced Mathematics Courses |

MATH
310H

MATH
314/814

Prereqs: MATH 208.

Not open to MA or MS students in mathematics or statistics

Fundamental concepts of linear algebra, including properties of matrix arithmetic, systems of linearequations, vector spaces, inner products, determinants, eigenvalues and eigenvectors, and diagonalization.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Advanced Mathematics Courses |

MATH
314H

MATH
316

Case Studies in Theoretical Ecology
Crosslisted as BIOS 316, NRES 316

Prereqs: Permission.

Case studies are structured around preparation for subsequent independent research (BIOS 498 or MATH 496).

Introduction to biological literature, applied mathematics, computer programming, and/or statistical techniques relevant to particular questions in ecology, evolution, and behavior. Typical mathematical topics include discrete dynamics, systems of differential equations, matrix algebra, or statistical inference and probability.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
322/822

Not open to MA or MS students in mathematics or statistics

Uniform convergence of sequences and series of functions, Green's theorem, Stoke's theorem, divergence theorem, line integrals, implicit and inverse function theorems, and general coordinate transformations.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
325

Prereqs: MATH 208.

An introduction to mathematical reasoning, construction of proofs, and careful mathematical writing in the context of continuous mathematics and calculus. Topics may include the real number system, limits and continuity, the derivative, integration, and compactness in terms of the real number system.

Credit Hours: | 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Advanced Mathematics Courses |

MATH
350

Prereqs: MATH 310.

NOT open to MATH majors EXCEPT those under degree option "E" who are seeking a secondary mathematics teaching endorsement.

Modern elementary geometry, plane transformations and applications, the axiomatic approach, Euclidean constructions. Additional topics vary.

Credit Hours: | 3 |

Course Format: | Lecture |

Course Delivery: | Classroom |

Groups: | Introductory Mathematics Courses |

MATH
380

Statistics and Applications
Crosslisted as STAT 380

Credit toward the degree can not be earned in STAT 218 if taken after or taken in parallel with STAT/MATH 380.

Probability calculus; random variables, their probability distributions and expected values; t, F and chi-square sampling distributions; estimation; testing of hypothesis; and regression analysis with applications.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Advanced Mathematics Courses |

MATH
394

Prereqs: Sophomore standing and removal of all entrance deficiencies in mathematics.

MATH 394 is not intended for students who are required to take calculus. MATH 394 may be repeated if the subtitles differ. See the Schedule of Classes each term for the specific sections and subtitles offered.

Topics course for students in academic fields not requiring calculus. Emphasis on understanding and mathematical thinking rather than mechanical skills. Topic varies.

Credit Hours: | 3 |

Max credits per semester: | 6 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
398

Prereqs: Permission.

This course has no description.

Credit Hours: | 1-24 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

MATH
399

Prereqs: Prior arrangement with and permission of individual faculty member.

This course has no description.

Credit Hours: | 1-24 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

MATH
399H

Prereqs: For candidates for degrees with distinction, with high distinction, or with highest distinction in the College of Arts and Sciences.

This course has no description.

Credit Hours: | 1-4 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

Credit is not allowed for both CSCE 235 and MATH 405. NOT open to MATH majors EXCEPT those under degree option "E" who are seeking a secondary mathematics teaching endorsement.

Graphs and networks. Map coloring. Finite differences. Pascal's triangle. The Pigeonholed Principle. Markov chains. Linear programming. Game Theory.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

NOT open to MATH majors EXCEPT those under degree option "E" who are seeking a secondary mathematics teaching endorsement.

Analysis of the connections between college mathematics and high school algebra and precalculus.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

NOT open to MATH majors EXCEPT those under degree option "E" who are seeking a secondary mathematics teaching endorsement.

Analysis of the connections between college mathematics and high school algebra and geometry.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

Prereqs: Math 310, Math 314, Math 380/Stat 380

Not open to MA or MS students in Mathematics. This course is for students seeking a mathematics major under the Education Option and for students in CEHS who are seeking their secondary mathematics teaching certificate.

This course is designed around a series of projects in which students create mathematical models to examine the mathematics underlying several socially-relevant questions.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
415/815

Prereqs: Math 314/814 and either Math 325 or Math 310.

Topics fundamental to the study of linear transformations on finite and infinite dimensional vector spaces over the real and complex number fields including: subspaces, direct sums, quotient spaces, dual spaces, matrix of a transformation, adjoint map, invariant subspaces, triangularization and diagonalization. Additional topics may include: Riesz Representation theorem, projections, normal operators, spectral theorem, polar decomposition, singular value decomposition, determinant as an n-linear functional, Cayley-Hamilton theorem, nilpotent operators, and Jordan canonical form.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
417

Prereqs: MATH 310.

Elementary group theory, including cyclic, dihedral, and permutation groups; subgroups, cosets, normality, and quotient groups; fundamental isomorphism theorems; the theorems of Cayley, Lagrange, and Cauchy; and if time allows, Sylow's theorems.

Credit Hours: | 3 |

Course Format: | Lecture |

Course Delivery: | Classroom |

ACE Outcomes: | 10 |

Groups: | Advanced Mathematics Courses |

MATH
423/823

Prereqs: Math 208.

Complex numbers, functions of complex variables, analytic functions, complex integration, Cauchy's integral formulas, Taylor and Laurent series, calculus of residues and contour integration, conformal mappings, harmonic functions. Applications of these concepts in engineering, physical sciences, and mathematics

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
424/824

Prereqs: MATH 221.

Not open to MA or MS students in mathematics or statistics.

Derivation of the heat, wave, and potential equations; separation of variables method of solution; solutions of boundary value problems by use of Fourier series, Fourier transforms, eigenfunction expansions with emphasis on the Bessel and Legendre functions; interpretations of solutions in various physical settings.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
425

Prereqs: MATH 325 or permission.

Real number system, topology of Euclidean space and metric spaces, compactness, sequences, series, convergence and uniform convergence, and continuity and uniform continuity.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
427/827

Prereqs: MATH 221.

Not open to mathematics majors. Not open to MA or MS students in mathematics.

Matrix operations, transformations, inverses, orthogonal matrices, rotations in space. Eigenvalues and eigenvectors, diagonalization, applications of diagonalization. Curvilinear coordinate systems, differential operations in curvilinear coordinate systems, Jacobians, changes of variables in multiple integration. Scalar, vector and tensor fields, tensor operations, applications or tensors. Complex function theory, integration by residues, conformal mappings.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
428/828

Introduction to techniques and applications of operations research. Includes linear programming, queueing theory, decision analysis, network analysis, and simulation.

Credit Hours: | 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 10 |

Groups: | Advanced Mathematics Courses |

MATH
430

Qualitative behaviour of solutions of systems of differential equations, including existence and uniqueness, extendibility, and periodic solutions. The Putzer algorithm, Floquet theory, matrix norms, linearization,stability theory, and period-doubling and chaos.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
432/832

Mathematical theory of linear optimization, convex sets, simplex algorithm, duality, multiple objective linear programs, formulation of mathematical models.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
433/833

Mathematical theory of unconstrained and constrained optimization for nonlinear multivariate functions, particularly iterative methods, such as quasi-Newton methods, least squares optimization, and convex programming. Computer implementation of these methods.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
435

Prereqs: Math 208 and at least two of Math 221, Math 314, Math 380.

A research experience modeling problems of current interest to the local community, businesses, or government.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 10 |

MATH
439/839

Prereqs: MATH 107 or permission.

Discrete and continuous models in ecology: population models, predation, food webs, the spread of infectious diseases, and life histories. Elementary biochemical reaction kinetics; random processes in nature. Use of software for computation and graphics.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
440/840

Numerical Analysis I
Crosslisted as CSCE 840/440

Credit toward the degree may be earned in only one of the following: CSCE/MATH 440/840 and MECH 480/880.

Principles of numerical computing and error analysis covering numerical error, root finding, systems of equations, interpolation, numerical differentiation and integration, and differential equations. Modeling real-world engineering problems on digital computers. Effects of floating point arithmetic.

This course is a prerequisite for:
CSCE 942

Credit Hours: | 3 |

Max credits per degree: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
441/841

Approximation of Functions
Crosslisted as CSCE 441/841

Polynomial interpolation, uniform approximation, orthogonal polynomails, least-first-power approximation, polynomial and spline interpolation, approximation and interpolation by rational functions.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
442

Derivation, analysis, and interpretation of mathematical models for problems in the physical and applied sciences. Scaling and dimensional analysis. Asymptotics, including regular and singular perturbation methods and asymptotic expansion of integrals. Calculus of variations.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
445/845

Fundamentals of number theory, including congruences, primality tests, factoring methods. Diophantine equations, quadratic reciprocity, continued fractions, and elliptic curves.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
447/847

Numerical Linear Algebra
Crosslisted as CSCE 447/847

Prereqs: MATH 314

Mathematics and algorithms for numerically stable matrix and linear algebra computations, including solution of linear systems, computation of eigenvalues and eigenvectors, singular value decomposition, and QR decomposition.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
450

Theory of enumeration and/or existence of arrangements of objects: Pigeonhole principle, inclusion-exclusion, recurrence relations, generating functions, systems of distinct representatives, combinatorial designs and other applications.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
452

Selected applications.

Theory of directed and undirected graphs. Trees, circuits, subgraphs, matrix representations, coloring problems, and planar graphs. Methods which can be implemented by computer algorithms.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
456

Introduction to a selection of topics in modern differential manifolds, vector bundles, vector fields, tensors, differential forms, Stoke's theorem, Riemannian and semi-Riemannian metrics, Lie Groups, connections, singularities. Includes gauge field theory, catastrophe theory, general relativity, fluid flow.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
465/865

Semantical and syntactical developments of propositional logic, discussion of several propositional calculi, applications to Boolean algebra and related topics, semantics and syntax of first-order predicate logic including Godel's completeness theorem, the compactness theorem.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

MATH
471

Prereqs: Math 314 and either Math 325 or 310.

Elementary point-set and geometric topology. Point-set topics include topological spaces, continuous functions, homeomorphisms, connectedness, compactness, quotient spaces. Geometric topology topics include Euler characteristic, classification of surfaces, and other applications.

This course is a prerequisite for:
MATH 856

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
487/887

Prereqs: Math 314 and Math 325.

Probability, conditional probability, Bayes' theorem, independence, discrete and continuous random variables, density and distribution functions, multivariate distributions, probability and moment generating functions, the central limit theorem, convergence of sequences of random variables, random walks, Poisson processes. and applications.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Groups: | Advanced Mathematics Courses |

Properties of stochastic processes and solutions of stochastic differential equations as a means of understanding modern financial instruments. Derivation and modeling of financial instruments, advanced financial models, advanced stochastic processes, partial differential equations, and numerical methods from a probabilistic point of view.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

ACE Outcomes: | 10 |

Groups: | Advanced Mathematics Courses |

MATH
495

MATH
496/896

Prereqs: Permission.

This course has no description.

Credit Hours: | 1-3 |

Max credits per degree: | 6 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |

MATH
497

Prereqs: Senior standing and especially qualified Juniors; and permission.

This course has no description.

Credit Hours: | 1-4 |

Max credits per degree: | 4 |

Course Delivery: | Classroom |

Groups: | Seminars, Independent Study, Topics and Reading Courses |