# MATH 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, polynomial 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. Credit for both MATH 101 and 103 is not allowed; credit for both MATH 102 and MATH 103 is not allowed.

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 472, AGRO 807, BIOS 456, BSEN 225, BSEN 355, CHEM 109, CHEM 111, CHEM 113, CHEM 471, CHME 114, CIVE 221, CIVE 252, CNST 241, CNST 252, CNST 306, CSCE 156H, CSCE 235H, ECEN 103, ECON 215, ECON 215H, FDST 363, GEOG 458, GEOL 372, GEOL 410, GEOL 472, GEOL 825, MATH 107, MATH 107H, MATH 238, MECH 220, METR 205, METR 415, METR 483, 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
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
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, BSEN 244, CHEM 481, CHME 332, CHME 832, ECEN 215, ECEN 328, ECEN 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, 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 |

MATH
208H

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

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.

Credit Hours: | 4 |

Course Delivery: | Classroom |

ACE Outcomes: | 3 |

Groups: | Introductory Mathematics Courses |

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, CHME 312, CHME 434, CHME 462, CIVE 310H, CIVE 326, CIVE 326H, CIVE 327, CIVE 401, CSCE 441, ECEN 213, ECEN 216, ECEN 304, ECEN 306, ECEN 328, ECEN 442, ECEN 935, IMSE 328, MATH 424, MATH 427, MATH 430, MATH 442, MATH 456, 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 221 or Math 325.

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 polynomials, 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 |

MATH
489/889

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 |

Prereqs: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences

Number and operations. Place value and its role in arithmetic operations. Development of fractions and number systems. Develop the habits of mind of a mathematical thinker and to develop a depth of understanding of number and operations sufficient to enable the teacher to be a disciplinary resource for other K-3 teachers.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
800T

Prereqs: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences

MATH 800T is intended for mid-level mathematics teachers.

Numbers and operations. Careful reasoning, problem solving, and communicating mathematics both orally and in writing. Connections with other areas of mathematics. Development of mathematical thinking habits.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Prereqs: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences

Polygons, polyhedra, rigid motions, symmetry, congruence, similarity, measurement in one, two and three dimensions, functions, mathematical expressions, solving equations, sequences. Develop the habits of mind of a mathematical thinker and to develop a depth of understanding of geometry, measurement and algebraic thinking to enable the teacher to be a disciplinary resource for other K-3 teachers.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Prereqs: Admission to the MAT or MScT program in mathematics or to a graduate program in the College of Education and Human Sciences.

MATH *802P will not count toward the MA or MS degree in mathematics or statistics.

Number sense and operations in the context of rational numbers, geometry and algebra in grades 4-6 curriculum, and how the mathematical content in grades K-3 (e.g., Taylor-Cox, 2003) lays a foundation for abstract thinking beginning in grades 4 and beyond. Designed to develop a depth of understanding sufficient to enable the teacher to be a disciplinary resource to other K-3 teachers.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH *802T is intended for mid-level mathematics teachers.

Variables and functions. Use of functions in problem solving. Theory of measurement, especially length, area, and volume. Geometric modeling in algebra. Graphs, inverse functions, linear and quadratic functions, the fundamental theorem of arithmetic, modular arithmetic, congruence and similarity. Ways these concepts develop across the middle level curriculum.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Prereqs: A valid elementary or early childhood teaching certificate, or permission.

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

Course explores the mathematics supporting algebraic thinking in elementary mathematics. Develops a deeper understanding of algebraic properties and greater flexibility in mathematical reasoning. Case studies, video segments, and student work samples will be examined. Complex mathematical problems will be worked with connections made between participants' thinking and that of their students.

Credit Hours: | 3 |

Course Format: | Lecture |

Course Delivery: | Classroom |

Prereqs: A valid elementary or early childhood teaching certificate, or permission.

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

Course uses problem-solving experiences to develop teachers' critical-thinking skills in order to build a strong foundation for teaching and communicating mathematical concepts. Provides a guided opportunity for the implementation of problem-solving instruction is aligned with the Mathematics Standards in both the primary (K-2) and intermediate (3-5) elementary classroom.

Credit Hours: | 3 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH *804T is intended for middle-level mathematics teachers.

Problem solving, reasoning and proof, and communicating mathematics. Development of problem solving skills through the extensive resources of the American Mathematics Competitions. Concepts of logical reasoning in the context of geometry, number patterns, probability and statistics

Credit Hours: | 3 |

Course Delivery: | Classroom |

Prereqs: Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences

MATH *805T is intended for mid-level mathematics teachers.

Concepts of discrete mathematics, as opposed to continuous mathematics, which extend in directions beyond, but related to, topics covered in middle-level curricula. Problems which build upon middle-level mathematics experiences. Logic, mathematical reasoning, induction, recursion, combinatorics, matrices, and graph theory.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH *806T is intended for mid-level mathematics teachers.

Basic number theory results and the RSA cryptography algorithm. Primes, properties of congruences, divisibility tests, linear Diophantine equations, linear congruences, the Chinese Remainder Theorem, Wilson’s Theorem, Fermat’s Little Theorem, Euler’s Theorem, and Euler’s phi-function. Mathematical reasoning and integers’ connections to the middle school curriculum.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Prereqs: Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences

MATH *807T is intended for middle-level mathematics teachers.

The mathematics underlying several socially-relevant questions from a variety of academic disciplines. Construct mathematical models of the problems and study them using concepts developed from algebra, linear and exponential functions, statistics and probability. Original documentation, such as government data, reports and research papers, in order to provide a sense of the role mathematics plays in society, both past and present.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

Prereqs: Admission to the MAT-MScT program in MATH or to a graduate program in the College of Education and Human Sciences

MATH *808T is intended for middle-level mathematics teachers.

The processes of differentiation and integration, their applications and the relationship between the two processes. Rates of change, slopes of tangent lines, limits, derivatives, extrema, derivatives of products and quotients, anti-derivatives, areas, integrals, and the Fundamental Theorem of Calculus. Connections to concepts in the middle level curriculum.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
810T

The integers. The Euclidean algorithm, the Fundamental Theorem of Arithmetics, and the integers mod n. Polynomials with coefficients in a field. The division algorithm, the Euclidean algorithm, the unique factorization theorem, and its applications. Polynomials whose coefficients are rational, real or complex. Polynomial interpolation. The habits of mind of a mathematical thinker. The conceptual underpinnings of school algebra.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
811T

Prereqs: A valid secondary mathematics teaching certificate or by permission.

Course examines mathematics underlying pre-calculus material through problem solving. Connections to other topics in mathematics, including algebra, geometry and advanced mathematics are highlighted.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
812T

Prereqs: A valid secondary mathematics teaching certificate.

Course examines mathematics underlying high school geometry through problem solving. Topics include Spherical, Euclidean and Hyperbolic geometry, introduction to Neutral geometry, Platonic and Archimedean solids and projective geometry.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
814T

Prereqs: A valid secondary mathematics teaching certificate or by permission.

Emphasis on connections between linear equations, linear transformations and the geometry of lines and planes. Applications to production planning, encryption methods, and analyzing data. Topics include methods of solving linear systems with an emphasis on solution behavior, along with behaviors exhibited by explicit linear transformations.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom, Web |

MATH
816T

Prereqs: An undergraduate course in at least one of statistics, differential equations or matrix algebra; a valid secondary mathematics teaching certificate.

A modeling course run in collaboration with area businesses or organizations in which real world problems are studied. Course emphasizes how mathematics is used outside academia.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
817

Prereqs: MATH 417

Topics from elementary group theory and ring theory, including fundamental isomorphism theorems, ideals, quotient rings, domains. Euclidean or principal ideal rings, unique factorization, modules and vector spaces including direct sum decompositions, bases, and dual spaces.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
818

Prereqs: MATH 817

Topics from field theory including Galois theory and finite fields and from linear transformations including characteristic roots, matrices, canonical forms, trace and transpose, and determinants.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
820

Prereqs: Math 208 and evidence of adequate preparation.

A term paper and/or project is required for graduate credit. Not open to graduate students in Mathematics. Students in the sciences and Statistics cannot count MATH 820 toward a minor in Mathematics.

A mathematical introduction to elementary analysis (the calculus). Specifically, it is a demanding course that introduces concepts in abstraction: the axiomatic method, proofs, and mathematical thinking and writing in the context of elementary real analysis, or the theory underlying calculus. Specific topics include: logic, sets, functions; the real number system (field and order axioms, completeness axiom); mathematical induction; limits of sequences and functions, convergence, and continuity; the derivative and Riemann integral.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
825

Prereqs: MATH 325

Real number system, topology of Euclidean space and metric spaces, continuous functions, derivatives and the mean value theorem, the Riemann and Riemann-Stieltjes integral, convergence, the uniformity concept, implicit functions, line and surface integrals.

This course is a prerequisite for:
MATH 826

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
826

Prereqs: MATH 825

Real number system, topology of Euclidean space and metric spaces, continuous functions, derivatives and the mean value theorem, the Riemann and Riemann-Stieltjes integral, convergence, the uniformity concept, implicit functions, line and surface integrals.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
830

Prereqs: MATH 325.

Phase diagrams, bifurcation theory, linear systems, the matrix exponential function, Floquet theory, stability theory, existence (Poincare-Bendixson Theorem) and non-existence of periodic solutions for non-linear ordinary differential equations, self-adjoint equations, and Sturm-Liouville theory.

This course is a prerequisite for:
MATH 831

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
831

Prereqs: MATH 830.

Vector calculus, transport equations, Laplace's equation, the heat equation, the wave equation, maximum principles, mean-value formulae, finite speed of propagation, energy methods, solution representations.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
842

MATH
843

Prereqs: MATH 842 or permission

Application of partial differential equation models to problems in the physical and applied sciences. Includes derivation of partial differential equations, the theory of continuous media, linear and nonlinear wave propagation, diffusion, transform methods, and potential theory.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
850

Enumeration of standard combinatorial objects (subsets, partitions, permutations). Structure and existence theorems for graphs and sub-graphs. Selected classes of error-correcting codes. Extremal combinatorics of graphs, codes, finite sets and posets.

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
852

Prereqs: MATH *850

Credit Hours: | 3 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
856

MATH
858

Prereqs: MATH 208

Selected topics in some branch of geometry.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
871

MATH
872

MATH
874M

MATH *874M may be counted towards the MAT and MScT degrees in mathematics and statistics, not the MA, MS, or PhD.

This course has no description.

Credit Hours: | 2-3 |

Course Delivery: | Classroom |

MATH
897

This course has no description.

Credit Hours: | 1-4 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
899

Prereqs: Admission to masters degree program and permission of major adviser

This course has no description.

Credit Hours: | 6-10 |

Course Delivery: | Classroom |

MATH
901

MATH
902

MATH
905

Prereqs: MATH 818 or permission

Selected topics from classical ideal theory, Dedekind rings, completions, local rings, valvation theory.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
909

Prereqs: MATH 818 or permission

Selected topics from semigroups of transformations, ideal structure and homomorphisms, free semigroups, inverse semigroups, matrix representation, decompositions and extensions.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
911

Basic topics of infinite and finite group theory from among geometric, combinatorial, and algorithmic group theory, homology of groups, solvable and nilpotent groups and representation theory.

Credit Hours: | 3-6 |

Max credits per degree: | 18 |

Course Format: | Lecture 3 |

Course Delivery: | Classroom |

MATH
913

Prereqs: MATH 818

Elementary ring theory and examples of rings, the Jacobson radical and the structure of semi-simple rings, rings with minimum condition, Wedderburn’s theorem, structure of modules.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
915

Prereqs: MATH 902 or permission

Basic topics in homological algebra, including homology of complexes, extensions, tensor and torsion products and homological dimension, with application to rings and algebras.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
918

This course has no description.

Credit Hours: | 3 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
921

Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
922

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
923

This course has no description.

Credit Hours: | 3 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
924

Prereqs: MATH 826 or permission

Complex number field, elementary functions, analytic functions, conformal mapping, integration and calculus of residues, entire and meromorphic functions, higher transcendental functions, Riemann surfaces.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
925

Prereqs: MATH 826 or permission

Credit Hours: | 3 |

Course Delivery: | Classroom |

Methods for approximating the solutions of differential equations, including local analysis near singular points, singular perturbation methods, boundary layer theory, WKB Theory, and multiple-scale methods. Asymptotic expansion of Laplace and Fourier integrals. Illustration of the use of asymptotics from journals in mathematics, science, and engineering.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
928

MATH
929

Prereqs: MATH 826 or permission

Cauchy-Peano existence theorems, continuity and differentiability of solutions with respect to initial conditions, differential inequalities, uniqueness theorem, oscillation theory, Poincare-Bendixson theory, stability theory, almost periodic solutions.

Credit Hours: | 3 |

Course Delivery: | Classroom |

Prereqs: MATH 826 or permission

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
934

This course has no description.

Credit Hours: | 6 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

Prereqs: MATH 935 or permission

Distributions, Green’s functions and boundary value problems; integral transforms and spectral representations.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
938

Advanced course in mathematical modeling for students who desire experience in formulating and analyzing open-ended, real-world problems in the natural and applied sciences. Participation in a few group projects that require conceptualization and analytical, numerical, and graphical analysis with formal oral and written presentation of the results.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
939

This course has no description.

Credit Hours: | 3 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
941

MATH
942

Numerical Analysis III
Crosslisted as CSCE 942

MATH
953

Prereqs: MATH 901-902

Affine geometry, coordinate rings, the Zariski topology, function fields and birational geometry, the Nullstellensatz, Krull dimension and transcendence degree, smoothness, projective geometry, divisors, curves.

Credit Hours: | 3 |

Course Delivery: | Classroom |

MATH
958

This course has no description.

Credit Hours: | 3 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
990

This course has no description.

Credit Hours: | 3 |

Max credits per degree: | 18 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
995

This course has no description.

Credit Hours: | 1-3 |

Max credits per degree: | 6 |

Course Format: | Lecture |

Course Delivery: | Classroom |

MATH
996

Advanced topics in one or more branches of mathematics.

Credit Hours: | 1-3 |

Max credits per degree: | 6 |

Course Delivery: | Classroom |

MATH
997

This course has no description.

Credit Hours: | 1-24 |

Course Delivery: | Classroom |

MATH
999

Prereqs: Admission to doctoral degree program and permission of supervisory committee chair

This course has no description.

Credit Hours: | 1-24 |

Course Delivery: | Classroom |