# Mathematics (MATH)

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 Graded with Option \$10

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 Graded with Option \$10

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, MATH 106, MATH 107, or MATH 208) may not earn credit for this course.

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

Credit Hours: 3 3 3 Graded with Option \$10

Credit Hours:3

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 Graded with Option \$10

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.

Credit for both MATH 104 and 106 is not allowed; students with previous credit in any version of MATH 106, MATH 107, or MATH 208 may not earn credit for this course.

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

Credit Hours: 3 3 3 Graded with Option \$10 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 Graded with Option \$10 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 Graded with Option \$10 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 Graded with Option 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 Graded with Option

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 260; PHYS 261

Credit Hours: 3 3 3 Graded with Option ACE 3 Math/Stat/Reasoning

Credit Hours:3

ACE:ACE 3 Math/Stat/Reasoning

MATH191
Special Topics in Mathematics

Description: Topics vary.

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

Credit Hours: 1-6 6 6 Graded with Option

Credit Hours:1-6

ACE:

MATH203
Contemporary Mathematics

Credit toward the degree cannot be earned in both MATH 203 and 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 Graded with Option 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

Credit toward the degree cannot be earned in both MATH 203 and MATH 203J.

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 Graded with Option 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 Graded with Option 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 Graded with Option 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 Graded with Option

Credit Hours:3

ACE:

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.

Credit Hours: 3 3 3 Graded

Credit Hours:3

ACE:

MATH300
Mathematics Matters

Prerequisites: TEAC 308 or TEAC 416D or parallel.

Admission to the College of Education & Human Sciences and removal of math entrance deficiencies is required. 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 Graded with Option Introductory Mathematics

Credit Hours:3

ACE:

MATH301
Geometry Matters

Prerequisites: MATH 300

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

Credit Hours: 3 3 3 Graded with Option

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 make the mathematics more accessible.

Credit Hours: 3 3 3 Graded with Option

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.

This course is a prerequisite for: MATH 325; MATH 412; MATH 430; MATH 450; MATH 452; MATH 460; MATH 471

Credit Hours: 3 3 3 Graded with Option

Credit Hours:3

ACE:

MATH310
Introduction to Modern Algebra

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

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.

This course is a prerequisite for: MATH 325; MATH 412; MATH 417; MATH 430; MATH 450; MATH 452; MATH 460; MATH 471

Credit Hours: 3 3 3 Graded with Option

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.

This course is a prerequisite for: CSCE 970; MATH 430; MATH 435; MECH 350; STAT 301; STAT 871

Credit Hours: 3 3 3 Graded with Option

Credit Hours:3

ACE:

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 430; MATH 435; MECH 350; STAT 871

Credit Hours: 3 3 3 Graded with Option

Credit Hours:3

ACE:

MATH315
Linear Algebra for Data Science

Prerequisites: A grade of P, C, or better in MATH 104 or MATH 107/107H

Credit cannot be earned for both MATH 314/314H and MATH 315. MATH 315 cannot be used toward a major in Mathematics.

Description: Fundamental concepts of linear algebra, including properties of matrix arithmetic, systems of linear equations, vector spaces, inner products, determinants, eigenvalues and eigenvectors, and diagonalization, with emphasis in data science applications.

Credit Hours: 3 3 3 Graded with Option

Credit Hours:3

ACE:

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 Graded with Option SUMMER ACE 4 Science

Credit Hours:3

ACE:ACE 4 Science

MATH325
Elementary Analysis

Prerequisites: A grade of P, C, or better in MATH 208/208H, MATH 309, or MATH 310.

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 412; MATH 425; MATH 430; MATH 450; MATH 452; MATH 460; MATH 471

Credit Hours: 3 3 3 Graded with Option

Credit Hours:3

ACE:

MATH391
Special Topics in Mathematics

Prerequisites: Permission.

Description: Topics vary.

Credit Hours: 1-3 3 6 Graded with Option

Credit Hours:1-3

ACE:

MATH394
Independent Study in Mathematics

Prerequisites: Permission

Description: Independent reading or research directed by a faculty member.

Credit Hours: 1-3 3 6 Graded with Option

Credit Hours:1-3

ACE:

MATH399

Prerequisites: Permission.

Credit Hours: 1-3 3 6 Graded with Option

Credit Hours:1-3

ACE:

MATH399H

Prerequisites: Permission.

Credit Hours: 1-3 3 6 Graded with Option

Credit Hours:1-3

ACE:

MATH407
Mathematics for High School Teaching ICrosslisted with MATH 807

Prerequisites: MATH 208/208H and MATH 309 or MATH 310.

Open only MATH majors with a declared Education option.

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

Credit Hours: 3 3 3 Graded with Option SPRING

Credit Hours:3

ACE:

MATH408
Mathematics for High School Teaching IICrosslisted with MATH 808

Prerequisites: MATH 412 and MATH 309 or MATH 310.

Open only MATH majors with a declared Education option.

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

Credit Hours: 3 3 3 Graded with Option FALL

Credit Hours:3

ACE:

MATH412
Modern Geometry

Prerequisites: MATH 309, MATH 310, or MATH 325

Description: Modern geometry from multiple points of view, such as axiomatic, transformational, or analytic. Applications of geometry. Additional topics vary, but can include projective geometry, hyperbolic geometry, or Euclidean constructions.

Credit Hours: 3 3 3 Graded with Option FALL

Credit Hours:3

ACE:

MATH415
Theory of Linear TransformationsCrosslisted with MATH 815

Prerequisites: MATH 314/814; and MATH 309, MATH 310, or MATH 325.

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 Graded with Option

Credit Hours:3

ACE:

MATH417
Group Theory

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

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 Graded with Option 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 Graded with Option

Credit Hours:3

ACE:

MATH424
Introduction to Partial Differential EquationsCrosslisted with MATH 824

Prerequisites: A grade of P, C, or better in MATH 208/208H and MATH 221/221H.

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 Graded with Option

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 Graded with Option

Credit Hours:3

ACE:

MATH428
Principles of Operations ResearchCrosslisted with MATH 828

Prerequisites: MATH 314 or MATH 314H; and RAIK 270H, 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 Graded with Option ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH430
Ordinary Differential Equations

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 Graded with Option

Credit Hours:3

ACE:

MATH433
Nonlinear OptimizationCrosslisted with MATH 833

Prerequisites: MATH 208/208H; MATH 314/314H; and MATH 309, 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 Graded with Option SPRING

Credit Hours:3

ACE:

MATH435
Math in the City

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

Credit Hours: 3 3 3 Graded with Option ACE 10 Integrated Product Project-Based Learning

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH439
Mathematical BiologyCrosslisted with MATH 839

Prerequisites: MATH 221/221H & MATH 314/314H.

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 Graded with Option

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 Graded with Option \$20

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 Graded with Option

Credit Hours:3

ACE:

MATH445
Number TheoryCrosslisted with MATH 845

Prerequisites: MATH 310.

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 Graded with Option

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 Graded with Option

Credit Hours:3

ACE:

MATH450
Combinatorics

Prerequisites: MATH 309, MATH 310, or MATH 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 Graded with Option

Credit Hours:3

ACE:

MATH452
Graph Theory

Prerequisites: MATH 309, MATH 310, or MATH 325.

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 Graded with Option FALL

Credit Hours:3

ACE:

MATH460
History of Mathematics

Prerequisites: MATH 309, MATH 310, or MATH 325

Description: An overview of the development of modern mathematics, particularly the development of algebra, geometry, and calculus. Case studies, such as solvability of polynomial equations, the role of the parallel postulate in geometry, the development of analytic geometry, or additional topics.

Credit Hours: 3 3 3 Graded with Option FALL

Credit Hours:3

ACE:

MATH471
Introduction to Topology

Prerequisites: MATH 309, MATH 310, or MATH 325.

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 Graded with Option

Credit Hours:3

ACE:

MATH487
Probability TheoryCrosslisted with MATH 887

Prerequisites: MATH 314 or MATH 314H; and 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 Graded with Option

Credit Hours:3

ACE:

MATH489
Stochastic ProcessesCrosslisted with MATH 889

Prerequisites: MATH 314 or MATH 314H; and STAT 380 or RAIK 270H.

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

Credit Hours: 3 3 3 Graded with Option ACE 10 Integrated Product

Credit Hours:3

ACE:ACE 10 Integrated Product

MATH493
Seminar in MathematicsCrosslisted with MATH 893

Prerequisites: Permission.

Description: Topics in one or more branches of mathematics.

Credit Hours: 1-4 4 8 Graded with Option

Credit Hours:1-4

ACE:

MATH494
Independent Study in Mathematics

Prerequisites: Permission.

Description: Directed reading or research with a faculty member.

Credit Hours: 1-4 4 4 Graded with Option

Credit Hours:1-4

ACE: