MATH100A
Intermediate Algebra

Prerequisites: Appropriate score on the Math Placement Exam.

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

Description: 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 100A; MATH 101; MATH 103

Credit Hours: 3 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH101
College Algebra

Prerequisites: Appropriate score on the Math Placement Exam; or grade of P, C, or better in MATH 100A.

Credit for both MATH 101 and 103 is not allowed; students with previous credit in any calculus course (Math 104, 106, 107, or 208) may not earn credit for this course.

Description: Real numbers, exponents, factoring, linear and quadratic equations, absolute value, inequalities, functions, graphing, polynomial and rational functions, exponential and logarithmic functions, system of equations.

Credit Hours: 3 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH102
Trigonometry

Prerequisites: Appropriate score on the Math Placement Exam; or grade of P, C, or better in MATH 101.

Credit for both MATH 102 and 103 is not allowed; students with previous credit in any calculus course (Math 104, 106, 107, or 208) may not earn credit for this course.

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

Credit Hours: 2 2 2 LEC Introductory Mathematics

Credit Hours:2

ACE:

MATH103
College Algebra and Trigonometry

Prerequisites: Appropriate score on the Math Placement Exam; or grade of P, C, or better in MATH 100A.

Credit for both MATH 101 and 103 is not allowed; credit for both MATH 102 and MATH 103 is not allowed; students with previous credit in any calculus course (Math 104, 106, 107, or 208) may not earn credit for this course.

Description: 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 5 5 LEC Introductory Mathematics

Credit Hours:5

ACE:

MATH104
Applied Calculus

Prerequisites: Appropriate score on the Math Placement Exam; or grade of P, C, or better in MATH 101, MATH 102 or MATH 103.

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

Credit Hours: 3 3 3 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH106
Calculus I

Prerequisites: Appropriate score on the Math Placement Exam; or grade of P, C, or better in MATH 102 or MATH 103.

Credit for both MATH 104 and MATH 106 is not allowed.

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

Credit Hours: 5 5 5 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:5

ACE:ACE 3 Math/Stat/Reasoning

MATH107
Calculus II

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

Description: 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 4 4 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:4

ACE:ACE 3 Math/Stat/Reasoning

MATH107H
Honors: Calculus II

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

Description: For course description, see MATH 107.

Credit Hours: 4 4 4 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:4

ACE:ACE 3 Math/Stat/Reasoning

MATH107R
Analytic Geometry and Calculus II

Prerequisites: 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.

Description: 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 5 5 LEC

Credit Hours:5

ACE:

MATH189H
University Honors Seminar

Prerequisites: 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.

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

This course is a prerequisite for: METR 100; METR 140; PHYS 141; PHYS 260; PHYS 261

Credit Hours: 3 3 3 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH198
Freshman Seminar

This course is a prerequisite for: METR 100; METR 140; PHYS 141; PHYS 260; PHYS 261

Credit Hours: 1-3 3 24 LEC Seminars,Ind Study, Topics

Credit Hours:1-3

ACE:

MATH198H
Honors: Freshman Seminar

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

This course is a prerequisite for: METR 100; METR 140; PHYS 141; PHYS 260; PHYS 261

Credit Hours: 1-3 3 6 LEC Seminars,Ind Study, Topics

Credit Hours:1-3

ACE:

MATH203
Contemporary Mathematics

Not open to students with credit or concurrent enrollment in MATH 106 or MATH 203J.

Description: 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 3 3 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH203J
Contemporary Math

Prerequisites: Must be admitted to the College of Journalism

Not open to students with credit or concurrent enrollment in MATH 106 or MATH 203.

Description: 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 3 3 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH208
Calculus III

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

Description: 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 4 4 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:4

ACE:ACE 3 Math/Stat/Reasoning

MATH208H
Honors: Calculus III

Prerequisites: Good Standing in the University Honors Program and a grade of P, C, or better in MATH 107 or MATH 107H

Description: 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 4 4 LEC Introductory Mathematics ACE 3 Math/Stat/Reasoning

Credit Hours:4

ACE:ACE 3 Math/Stat/Reasoning

MATH221
Differential Equations

Prerequisites: A grade of P, C, or better in MATH 107 or MATH 107H

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

Credit Hours: 3 3 3 LEC ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH221H
Honors:Differential Equations

Prerequisites: Good Standing in the University Honors Program and a grade of P, C, or better in MATH 107 or MATH 107H

Description: For course description, see MATH 221/821.

Credit Hours: 3 3 3 LEC ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH300
Mathematics Matters

Prerequisites: TEAC 308 or TEAC 416D or parallel.

Credit toward the degree may be earned in only one of: MATH 300 or MATH 300M.

Description: Numbers and operations. Develop an understanding of mathematics taught in the elementary school.

This course is a prerequisite for: MATH 301; TEAC 297E; TEAC 308

Credit Hours: 3 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH300M
Mathematics as a Second Language

Prerequisites: Must be degree seeking in the College of Education & Human Sciences.

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.

Description: 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 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH301
Geometry Matters

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

Credit towards the degree may be earned in only one of: MATH 301.

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

Credit Hours: 3 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH302
Math Modeling

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

Description: 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 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH304
Experimentation, Conjecture, and Reasoning

Prerequisites: Must be degree seeking in the College of Education & 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.

Description: 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 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH306
Number Theory and Cryptology for Middle Level Teachers

Prerequisites: Must be degree seeking in the College of Education & Human Sciences.

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

Description: 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 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH309
Introduction to Mathematical Proofs

Prerequisites: A grade of P, C, or better in MATH 107 or MATH 107H

Description: Basic set theory; elements of logic and types of proofs; induction; study of relations and functions; and cardinality of sets.

Credit Hours: 3 3 3 LEC

Credit Hours:3

ACE:

MATH310
Introduction to Modern Algebra

Prerequisites: A grade of P, C, or better in MATH 208 or MATH 208H

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH310H
Honors: Introduction to Modern Algebra

Prerequisites: Good Standing in the University Honors Program and a grade of P, C, or better in MATH 208 or MATH 208H

Description: For course description, see MATH 310.

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH314
Linear Algebra

Prerequisites: A grade of P, C, or better in MATH 107 or MATH 107H

Description: 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 3 3 LEC ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH314H
Honors: Linear Algebra

Prerequisites: Good Standing in the University Honors Program and a grade of P, C, or better in MATH 107 or MATH 107H

Description: For course description, see MATH 314.

This course is a prerequisite for: MATH 405; MATH 435; MATH 442; MATH 456; MATH 471; MATH 809, MATH 409; MECH 350

Credit Hours: 3 3 3 LEC ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH316
Case Studies in Theoretical EcologyCrosslisted with BIOS 316, NRES 316

Prerequisites: MATH 106 or higher OR LIFE 121. Parallel registration in BIOS 316L.

Description: Introduction to biological literature, applied mathematics, computer programming, and/or statistical techniques relevant to field 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 3 3 LEC Advanced Mathematics Courses ACE 4 Science

Credit Hours:3

ACE:ACE 4 Science

MATH322

Description: 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.

This course is a prerequisite for: MATH 456; MECH 812; MECH 939; METR 965

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH325
Elementary Analysis

Prerequisites: A grade of P, C, or better in MATH 208 or MATH 208H

Description: 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.

This course is a prerequisite for: MATH 425; MATH 430; MATH 450; MATH 452; MATH 471

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH350
Geometry for High School Teaching

Prerequisites: A grade of P, C, or better in MATH 310 or MATH 310H

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

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

This course is a prerequisite for: MATH 408

Credit Hours: 3 3 3 LEC Introductory Mathematics

Credit Hours:3

ACE:

MATH398
Special Topics in Mathematics

Prerequisites: Permission.

Credit Hours: 1-24 24 24 LEC Seminars,Ind Study, Topics

Credit Hours:1-24

ACE:

MATH399
Independent Study in Mathematics

Prerequisites: Permission.

Credit Hours: 1-24 24 24 IND Seminars,Ind Study, Topics

Credit Hours:1-24

ACE:

MATH399H
Honors Course

Prerequisites: Permission.

Credit Hours: 1-4 4 4 IND Seminars,Ind Study, Topics

Credit Hours:1-4

ACE:

MATH405
Discrete and Finite Mathematics for High School Teaching

Prerequisites: A grade of P, C, or better in MATH 314 or MATH 314H

Credit is not allowed for both CSCE 235 and MATH 405.

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH407
Mathematics for High School Teaching I

Prerequisites: MATH 208 and 310

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

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH408
Mathematics for High School Teaching II

Prerequisites: MATH 310 and 350

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

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH409
Math for High School Teachers II, Using Math to Understand Our WorldCrosslisted with MATH 809

Prerequisites: 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.

Description: Designed around a series of projects in which students create mathematical models to examine the mathematics underlying several socially-relevant questions.

Credit Hours: 3 3 3 LEC

Credit Hours:3

ACE:

MATH415
Theory of Linear TransformationsCrosslisted with MATH 815

Prerequisites: MATH 314/814 and either MATH 325 or MATH 310

Description: 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 3 3 LEC

Credit Hours:3

ACE:

MATH417
Group Theory

Prerequisites: A grade of P, C, or better in MATH 310 or MATH 310H

Description: 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 3 3 LEC Advanced Mathematics Courses ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH423
Complex AnalysisCrosslisted with MATH 823

Prerequisites: A grade of P, C, or better in MATH 208 or MATH 208H

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH424
Introduction to Partial Differential EquationsCrosslisted with MATH 824

Prerequisites: A grade of P, C, or better in MATH 221 or MATH 221H

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

Description: 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.

This course is a prerequisite for: MECH 812

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH425
Mathematical Analysis

Prerequisites: A grade of P, C, or better in MATH 325

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH427
Mathematical Methods in the Physical SciencesCrosslisted with MATH 827

Prerequisites: A grade of P, C, or better in MATH 221 or MATH 221H

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

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH428
Principles of Operations ResearchCrosslisted with MATH 828

Prerequisites: MATH 314; STAT 380 or MECH 321.

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH430
Ordinary Differential Equations

Prerequisites: MATH 221 or 221H; MATH 310 or MATH 310H or MATH 325.

Description: Qualitative behavior 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH432
Linear OptimizationCrosslisted with MATH 832

Prerequisites: MATH 314 or 314H; MATH 310 or 310H or MATH 325

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH433
Nonlinear OptimizationCrosslisted with MATH 833

Prerequisites: MATH 314/814 and MATH 310 or MATH 325

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH435
Math in the City

Prerequisites: MATH 221 or 221H and MATH 314 or 314H; or MATH 221 or 221H and STAT 380; or MATH 314 or 314H and STAT 380.

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

Credit Hours: 3 3 3 LEC ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH439
Mathematical Models in BiologyCrosslisted with MATH 839

Prerequisites: A grade of P, C, or better in MATH 107 or MATH 107H

Has a small laboratory component.

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH440
Numerical Analysis ICrosslisted with CSCE 440, CSCE 840, MATH 840

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

Description: 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, MATH 942

Credit Hours: 3 3 3 LEC

Credit Hours:3

ACE:

MATH441
Approximation of FunctionsCrosslisted with CSCE 441, CSCE 841, MATH 841

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

This course is a prerequisite for: CSCE 942, MATH 942

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH442
Methods of Applied Mathematics I

Prerequisites: MATH 221 and 314, or their equivalents.

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH445
Number TheoryCrosslisted with MATH 845

Prerequisites: MATH 310 or 310H

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH447
Numerical Linear AlgebraCrosslisted with CSCE 447, CSCE 847, MATH 847

Prerequisites: MATH 314

Description: 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.

This course is a prerequisite for: CSCE 942, MATH 942

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH450
Combinatorics

Prerequisites: MATH 310 or 310H or 325.

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH452
Graph Theory

Prerequisites: MATH 310 or MATH 325

Selected applications.

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH456
Differential Geometry I

Prerequisites: MATH 221 or 221H; MATH 314 or 314H; and MATH 322.

Description: 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 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH465
Introduction to Mathematical LogicCrosslisted with MATH 865

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

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses

Credit Hours:3

ACE:

MATH471
Introduction to Topology

Prerequisites: MATH 314 and either MATH 325 or 310

Description: 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.

Credit Hours: 3 3 3 LEC

Credit Hours:3

ACE:

MATH487
Probability TheoryCrosslisted with MATH 887

Prerequisites: MATH 314 and one of MATH 309, MATH 310, or MATH 325

Description: 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 3 3 LEC

Credit Hours:3

ACE:

MATH489
Stochastic ProcessesCrosslisted with MATH 889

Prerequisites: MATH 314 and STAT 380 (or STAT 880)

Description: Markov chains, continuous-time Markov processes, the Poisson process, Brownian motion, introduction to stochastic calculus.

Credit Hours: 3 3 3 LEC Advanced Mathematics Courses ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH495
Seminar

Prerequisites: MATH 208 or 208H; and permission.

Credit Hours: 1-3 3 6 LEC Seminars,Ind Study, Topics

Credit Hours:1-3

ACE:

MATH496
Seminar in MathematicsCrosslisted with MATH 896

Prerequisites: Permission.

Description: Topics in one or more branches of mathematics.

Credit Hours: 4.00 4 13 LEC Seminars,Ind Study, Topics

Credit Hours:4.00

ACE:

MATH497