# Course Descriptions

## UNO Course Descriptions

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## Mathematics

This is the UNO real time up to date course descriptions for the Mathematics (UNO) Department.

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##### MATH 1000: Pre-Intermediate Algebra

An introductory level algebra course designed to prepare students to be successful in MATH 1310 (Intermediate Algebra). Topics include whole numbers, integers, fractions and mixed numbers, decimals, simplifying mathematical expressions, the properties of equality, solving linear equations in one variable, using linear equations to solve problems, ratios and proportions, graphing and the rectangular coordinate system. This course is worth two credit hours and will not satisfy the Math General Education requirement.

**Credits:**2**Prereq:**ACT Math sub score of 11-18, Math SAT at least 220 or Math SAT2016 at least 230 within the last 2 years; or Accuplacer score of 1 or COMPASS score of 1 or 2 within the last two years; or an F or better in MATH 1000 within the last 2 years

##### MATH 1200: Quantitative Literacy

Relevant mathematical skills for educated citizens in today's society. Topics include: personal finance; linear equations and inequalities in one and two variables; quadratic, exponential and logarithmic functions; probability and statistics; and systems of equations. This course is intended to satisfy the general education mathematics requirement. It does not serve as a prerequisite for any other mathematics course.

**Credits:**3**Prereq:**Math ACT score of 19 (or equivalent MPE) within the last two years.

##### MATH 1310: Intermediate Algebra

This course presents properties of real numbers, linear equations and graphing, systems of equations, linear inequalities, quadratic equations, polynomials, algebraic fractions, exponents and radicals, and logarithms.

**Credits:**3**General Education Area:**Fundamental Academic Skills - Mathematics**Prereq:**ACT Math at least 19, Math SAT at least 460, or Math SAT2016 at least 500 within the last 2 years; or Accuplacer or COMPASS score at least 3 within the last 2 years; or MATH 1000 with C- or better within the last 2 years; or MATH 1310 within last 2 years

##### MATH 1320: College Algebra

An advanced algebra course that teaches the following topics: algebraic operations, functions, graphs, linear and quadratic equations and inequalities, polynomial and rational functions, systems of equations, binomial theorem, complex numbers, exponentials, logarithms, sequences, series, and combinatorics.

**Credits:**3**Prereq:**ACT Math at least 23, Math SAT at least 540, or Math SAT2016 at least 570 within the last 2 years; or Accuplacer or COMPASS score at least 4 within the last 2 years; or MATH 1310 with at least C- within the last 2 years; or MATH 1320 within last 2 years

##### MATH 1330: Trigonometry

This course introduces elements of plane trigonometry, including trigonometric and circular functions, inverse trigonometric functions, solutions of triangles, identities and conditional equations, vectors, complex numbers, and conic sections.

**Credits:**3**Prereq:**ACT Math at least 23, Math SAT at least 540, or Math SAT2016 at least 570 within last 2 years; or Accuplacer at least 5 or COMPASS at least 4 within last 2 years; or MATH 1320 with at least C- within last 2 years; or MATH 1330 within last 2 years

##### MATH 1340: Algebra and Trigonometry for Calculus

A combined algebra and trigonometry course for science and engineering students planning to enroll in Calculus I (MATH 1950). Topics include: systems of equations, polynomials and rational functions, exponential and logarithmic functions, trigonometric functions and their inverses, trigonometric identities and applications, conic sections, and complex numbers. Credit for both MATH 1320/1324 and MATH 1340, or both MATH 1330 and MATH 1340 will not be given.

**Credits:**5**Prereq:**ACT Math at least 23, Math SAT at least 540, or Math SAT2016 at least 570 within last 2 years; or Accuplacer at least 5 or COMPASS at least 4 within last 2 years; or MATH 1310 with at least C- within last 2 years; or MATH 1340 within last 2 years

##### MATH 1360: Applied Algebra with Data Analysis

This is an applied algebra course teaching the following topics with an emphasis on data analysis and application: algebraic, exponential, and logarithmic functions; probability and statistics. The course will emphasize data analysis and applications of covered topics in order to demonstrate the relevance of mathematics to solving real-world problems.

**Credits:**3**Prereq:**Students must have an ACT Math sub score of at least 23 within the last 2 years, a COMPASS Test score of at least 4 within the last 2 years, or MATH 1310 within the last 2 years with a grade of C- or better.

##### MATH 1370: Applied Algebra and Optimization with Data Analysis

This is an applied algebra course with optimization, teaching the following topics with an emphasis on data analysis and application: algebraic, exponential, and logarithmic functions; derivatives and applications thereof; and statistics. The course will emphasize data analysis and applications of covered topics in order to demonstrate the relevance of mathematics to solving real-world problems.

**Credits:**4**Prereq:**ACT Math sub score at least 23, Math SAT at least 540, or Math SAT2016 at least 570 within last 2 years; or Accuplacer or COMPASS score at least 4 within last 2 years; or MATH 1310 with C- or better with in last 2 years

##### MATH 1530: Introduction to Applied Probability and Statistics

An elementary introduction to the basic concepts of probability, descriptive statistics, and statistical inference, including point estimation, confidence intervals, and hypotheses testing.

**Credits:**3**Prereq:**ACT Math sub score at least 19, Math SAT at least 460, or Math SAT2016 at least 500 within last 2 years; Accuplacer or COMPASS score at least 3 within last 2 years; or MATH 1000 with C- or better within last 2 years; or MATH 1530 within last 2 years

##### MATH 1600: Computer Algebra

An introductory course to computer algebra systems such as MAPLE or MATHEMATICA. The course will discuss files and their management, the package interface, and the basic package commands. Emphasis will be placed on solving equations, systems of equations, sets, lists, tables, and matrices. The graphing capabilities of the package will be explored.

**Credits:**1**Prereq:**MATH 1320 or equivalent.

##### MATH 1930: Calculus for the Managerial, Life, and Social Sciences

Topics covered include functions, limits, derivatives, integrals, and applications. Trigonometry is not required. May not be used as a prerequisite for MATH 1960. Credit will not be granted for both MATH 1930 and 1950.

**Credits:**3**Prereq:**ACT Math sub score at least 25, Math SAT at least 570, or Math SAT2016 at least 590 within last 2 years; or Accuplacer or COMPASS score at least 6 within last 2 years; or MATH 1320 with at least C- within last 2 years; or MATH 1930 within last 2 years

##### MATH 1940: Calculus for Biomedicine

Introductory calculus with an emphasis on dynamical systems analysis applied to biological systems. Topics include differential and integral calculus, elementary chaos theory, discrete modeling, neural networks, and elementary differential equations, population dynamics, and biochemical signal transduction.

**Credits:**5**Prereq:**ACT Math sub score at least 25, Math SAT at least 570, or Math SAT2016 at least 590 within last 2 years; or Accuplacer or COMPASS score at least 6 within last 2 years; or MATH 1320 with at least C- within last 2 years; or permission of instructor

##### MATH 1950: Calculus I

This is a course in plane analytic geometry emphasizing the study of functions, limits, derivatives and applications, and an introduction to integration.

**Credits:**5**Prereq:**ACT Math sub score at least 26, Math SAT at least 590 or Math SAT2016 at least 610 within last 2 years; or Accuplacer or COMPASS score of 7 within last 2 years; or MATH 1320 and MATH 1330 or MATH 1340 with C- or better within last 2 years

##### MATH 1960: Calculus II

This course introduces applications of integration, techniques of integration, infinite sequences and series, vectors in the plane, and polar functions. A mathematical software package is introduced, with required assignments.

**Credits:**5**Prereq:**MATH 1950 with a grade of C- or better, or MATH 1960 with a grade of F or better, or permission of instructor.

##### MATH 1970: Calculus III

This course presents vector functions, parametric equations, solid analytic geometry, partial differentiation, multiple integration, and an introduction to vector calculus. A mathematical software package is introduced with required assignments.

**Credits:**4**Prereq:**MATH 1960 with a grade of C- or better, or MATH 1970 with a grade of F or better, or permission of instructor.

##### MATH 2030: Discrete Mathematics

A foundations course in discrete mathematics for applied disciplines, including computer science and computer engineering. Topics include: logic, sets, relations, functions, complexity functions and big congruences, induction and recursive definitions, elementary combinatorics, discrete probability, graphs and trees.

**Credits:**3**Prereq:**MATH 1950 or MATH 1930.

##### MATH 2040: Finite Discrete Mathematics for Information Science and Engineering

A foundations course in discrete mathematics for applied disciplines including information science and computer engineering. Topics include: logic, sets, relations, functions, complexity functions and big congruences, induction and recursive definitions, elementary combinatorics, discrete probability, graphs, trees, vectors, matrices, linear equations, eigenvalues, Markov chains, and linear programming.

**Credits:**3**Prereq:**MATH 1950 or MATH 1930.

##### MATH 2050: Applied Linear Algebra

This course presents Matrix algebra, simultaneous equations, vector spaces, with applications of linear algebra and computational considerations. Mathematical software is utilized, with required assignments.

**Credits:**3**Prereq:**MATH 1950 with a grade of C- or better

##### MATH 2200: Mathematical Computing 1

This is a first course in mathematical computing. It covers the basic elements of scientific programming in both a computer algebra system and a high-level programming language. Explored are implementation issues, problem description, model building, method development, and solution assessment.

**Credits:**3**Prereq:**MATH 1950

##### MATH 2230: Introduction to Abstract Mathematics

This course provides a transition from the calculus to more abstract mathematics. Topics include logic, sets and functions, an introduction to mathematical proof, mathematical induction, relations. Important prerequisite material for a number of more advanced mathematics courses is studied. Credit will not be given for both MATH 2030 (or MATH 2040) and MATH 2230.

**Credits:**3**Prereq:**MATH 1960 or permission.

##### MATH 2350: Differential Equations

Topics include solutions of linear and first-order nonlinear differential equations with applications, higher-order linear differential equations with applications, power series solutions, and Laplace transform methods.

**Credits:**3**Prereq:**MATH 1960 with a grade of C- or better

##### MATH 3100: Applied Combinatorics

Basic counting methods, generating functions, recurrence relations, principle of inclusion-exclusion. Polya's formula. Elements of graph theory, trees and searching network algorithms.

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**CSCI-3100

##### MATH 3100: Applied Combinatorics

Basic counting methods, generating functions, recurrence relations, principle of inclusion-exclusion. Polya's formula. Elements of graph theory, trees and searching network algorithms.

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**MATH-8105

##### MATH 3100: Applied Combinatorics

Basic counting methods, generating functions, recurrence relations, principle of inclusion-exclusion. Polya's formula. Elements of graph theory, trees and searching network algorithms.

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**CSCI-8105

##### MATH 3200: Mathematical Computing II

This course is a second course in mathematical computing. It covers the design and development of algorithms and more advanced elements of programming in a mathematical context. The computer algebra system Maple will be used. The programming assignments are primarily based on calculus concepts and are designed to reinforce and deepen the understanding of these concepts.

**Credits:**3**Prereq:**CIST 1400 OR MATH 2200, and MATH 1970 (the latter may be taked concurrently)

##### MATH 3230: Introduction to Analysis

Provides a theoretical foundation for the concepts of elementary calculus. Topics include real number system, topology of the real line, limits, functions of one variable, continuity, differentiation, integration.

**Credits:**3**Prereq:**MATH 1960 and MATH 2230**Cross List:**MATH-8235

##### MATH 3300: Numerical Methods

This course involves solving nonlinear algebraic equations and systems of equations, interpolation and polynomial approximation, numerical differentiation and integration, numerical solutions to ordinary differential equations, analysis of algorithms and errors, and computational efficiency.

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**CSCI-3300

##### MATH 3300: Numerical Methods

This course involves solving nonlinear algebraic equations and systems of equations, interpolation and polynomial approximation, numerical differentiation and integration, numerical solutions to ordinary differential equations, analysis of algorithms and errors, and computational efficiency.

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**MATH-8305

##### MATH 3300: Numerical Methods

This course involves solving nonlinear algebraic equations and systems of equations, interpolation and polynomial approximation, numerical differentiation and integration, numerical solutions to ordinary differential equations, analysis of algorithms and errors, and computational efficiency.

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**CSCI-8305

##### MATH 3400: Theory of Interest

A study of the measurement of interest, annuities, amortization schedules and other miscellaneous topics.

**Credits:**3**Prereq:**MATH 1970.

##### MATH 3500: Selected Topics in Mathematics

This is a variable content course with selected topics in the mathematical sciences which may be of interest to students in other disciplines such as mathematics education, psychology and business. The course may be taken more than once for credit provided topics differ, with a maximum of nine hours. Mathematics majors may apply no more than three hours of MATH 3500 toward the minimum major requirements.

**Credits:**1-6**Prereq:**Permission of instructor.**Cross List:**MATH-8505

##### MATH 3640: Modern Geometry

Axiomatic systems, finite geometries, modern foundations of Euclidean geometry, hyperbolic and other non-Euclidean geometrics, projective geometry.

**Credits:**3**Prereq:**MATH 2230 or MATH 2030, or equivalent mathematical maturity.**Cross List:**MATH-8645

##### MATH 3850: History of Mathematics

An overview of the historical development of mathematical concepts and methods. Brief biographies of major mathematicians, descriptions of the cultural context of selected major advances and examples of the solution of problems using the knowledge and methods appropriate for each time period will be included.

**Credits:**3**Prereq:**Students who enroll in this course should have completed MATH 1970 and MATH 2230 in order to have the minimum amount of mathematical background needed to appreciate the mathematical content of the course.**Cross List:**MATH-8855

##### MATH 4010: Introduction to the Theory of Recursive Functions

This is a proof-oriented course presenting the foundations of Recursion Theory. We present the definition and properties of the class of primitive recursive functions, study the formal models of computation, and investigate partially computable functions, universal programs. We prove Rice's Theorem, the Recursion Theorem, develop the arithmetic hierarchy, demonstrate Post's theorem. Introduction to the formal theories of computability and complexity is also given.

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**CSCI-4010

##### MATH 4010: Introduction to the Theory of Recursive Functions

This is a proof-oriented course presenting the foundations of Recursion Theory. We present the definition and properties of the class of primitive recursive functions, study the formal models of computation, and investigate partially computable functions, universal programs. We prove Rice's Theorem, the Recursion Theorem, develop the arithmetic hierarchy, demonstrate Post's theorem. Introduction to the formal theories of computability and complexity is also given.

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**MATH-8016

##### MATH 4010: Introduction to the Theory of Recursive Functions

This is a proof-oriented course presenting the foundations of Recursion Theory. We present the definition and properties of the class of primitive recursive functions, study the formal models of computation, and investigate partially computable functions, universal programs. We prove Rice's Theorem, the Recursion Theorem, develop the arithmetic hierarchy, demonstrate Post's theorem. Introduction to the formal theories of computability and complexity is also given.

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**CSCI-8016

##### MATH 4030: Modern Algebra

Algebra is the study of mathematical manipulations that preserve something (like equality -when solving equations). The areas in which Algebra finds application are quite diverse, from Ancient Greek Geometry through to Modern Information Protection and Security (error correcting codes, data compression, and cryptography). This course begins with topics that should be familiar (such as ruler-and-compass constructions, and modular arithmetic) and builds upon this foundation through polynomial rings up to finite fields and basic group theory.

**Credits:**3**Prereq:**Math 2230 with a C- or better or Math 2030 with a C- or better**Cross List:**MATH-8036

##### MATH 4050: Linear Algebra

The theory of vectors, vector spaces, inner product spaces, linear transformations, eigenvalues, canonical forms, complex vectors and matrices and orthogonality. Unlike MATH 2050, this course emphasizes the theoretical aspects of linear algebra.

**Credits:**3**Prereq:**MATH 2050; MATH 2030 or MATH 2230 or equivalent; or permission.**Cross List:**MATH-8056

##### MATH 4110: Abstract Algebra I

An introduction to group theory. Various classes of group are studied: symmetric groups, abelian, cyclic, and permutation groups. Basic tools are developed and used: subgroups, normal subgroups, cosets, the Lagrange theorem, group homomorphisms, quotient groups, direct products, and group actions on a set. The course culminates with the Sylow theorems in finite group theory. The theory is illustrated with examples from geometry, linear algebra, number theory, crystallography, and combinatorics.

**Credits:**3**Prereq:**Undergraduate and Graduate: MATH 4050/8056 with a C- or better or MATH 4560/8566 with a C- or better or permission of instructor**Cross List:**MATH-8116

##### MATH 4120: Abstract Algebra II

An introduction to ring and field theory. Various classes of commutative rings are considered including polynomial rings, and the Gaussian integers. Examples of fields include finite fields and various extensions of the rational numbers. Concepts such as that of an ideal, integral domain, characteristic and extension field are studied. The course culminates with an introduction to Galois theory. Applications include the resolution of two classical problems: the impossibility of angle-trisection and the general insolvability of polynomial equations of degree 5 or higher.

**Credits:**3**Prereq:**Undergraduate and Graduate: MATH 4110/8116 with a C- or better or permission of instructor**Cross List:**MATH-8126

##### MATH 4150: Graph Theory & Applications

Introduction to graph theory. Representations of graphs and graph isomorphism. Trees as a special case of graphs. Connectivity, covering, matching and coloring in graphs. Directed graphs and planar graphs. Applications of graph theory in several fields such as networks, social sciences, VLSI, chemistry, and parallel processing.

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**CSCI-4150

##### MATH 4150: Graph Theory & Applications

Introduction to graph theory. Representations of graphs and graph isomorphism. Trees as a special case of graphs. Connectivity, covering, matching and coloring in graphs. Directed graphs and planar graphs. Applications of graph theory in several fields such as networks, social sciences, VLSI, chemistry, and parallel processing.

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**MATH-8156

##### MATH 4150: Graph Theory & Applications

Introduction to graph theory. Representations of graphs and graph isomorphism. Trees as a special case of graphs. Connectivity, covering, matching and coloring in graphs. Directed graphs and planar graphs. Applications of graph theory in several fields such as networks, social sciences, VLSI, chemistry, and parallel processing.

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**CSCI-8156

##### MATH 4230: Mathematical Analysis I

Provides a theoretical foundation for the concepts of elementary calculus. Topics include ordered fields and the real number system, basic properties of complex numbers, metric space topology, sequences and series in Rk, limits and continuity in a metric space, monotonic functions.

**Credits:**3**Prereq:**MATH 3230/8235 or equivalent.**Cross List:**MATH-8236

##### MATH 4240: Mathematical Analysis II

Provides a theoretical foundation for the concepts of elementary calculus. Topics include differentiation and Riemann-Stieltjes Integration, sequences and series of functions, uniform convergence, power series, functions of several variables, Implicit Function Theorem.

**Credits:**3**Prereq:**MATH 4230**Cross List:**MATH-8246

##### MATH 4270: Complex Variables

Differentiation, integration and power series expansions of analytic functions, conformal mapping, residue calculus and applications.

**Credits:**3**Prereq:**MATH 3230/8235 or equivalent.**Cross List:**MATH-8276

##### MATH 4300: Deterministic Operations Research Models

This is a survey course of deterministic operations research models and algorithms. Topics include linear programming, network programming, and integer programming.

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**CSCI-4300

##### MATH 4300: Deterministic Operations Research Models

This is a survey course of deterministic operations research models and algorithms. Topics include linear programming, network programming, and integer programming.

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**MATH-8306

##### MATH 4300: Deterministic Operations Research Models

This is a survey course of deterministic operations research models and algorithms. Topics include linear programming, network programming, and integer programming.

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**CSCI-8306

##### MATH 4310: Probabilistic Operations Research Models

This is a survey course of probabilistic operations, research models and algorithms. Topics include Markov chains, queueing theory, inventory models, forecasting, and simulation.

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**CSCI-4310

##### MATH 4310: Probabilistic Operations Research Models

This is a survey course of probabilistic operations, research models and algorithms. Topics include Markov chains, queueing theory, inventory models, forecasting, and simulation.

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**MATH-8316

##### MATH 4310: Probabilistic Operations Research Models

This is a survey course of probabilistic operations, research models and algorithms. Topics include Markov chains, queueing theory, inventory models, forecasting, and simulation.

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**CSCI-8316

##### MATH 4320: Computational Operations Research

Survey of computational methods used in the solution of operations research problems. Topics include scripting to guide optimization software, metaheuristics for optimization, and basic machine learning algorithms.

**Credits:**3**Prereq:**MATH 3200 and MATH 4300 each with a grade of C- or better or permission of instructor.**Cross List:**MATH-8326

##### MATH 4330: Introduction to Partial Differential Equations

This course introduces the basic methods of PDEs guided by applications in physics and engineering. The main topics to be covered include The Linear First order PDEs, Transport equations, Characteristics, Classification of PDEs, Separation of variables, Heat conduction, vibrating membranes, boundary value problems, Maximum principle, Sturm-Liouville problems, Fourier series, Fourier integrals, Harmonic functions, Legendre polynomials, Distributions, Green's functions.

**Credits:**3**Prereq:**MATH 1970 with a C- or better and MATH 2350 with a C- or better, or permission of instructor; MATH 2050 recommended, not required.**Cross List:**MATH-8336

##### MATH 4350: Ordinary Differential Equations

Ordinary Differential Equations develops the theory of initial-, boundary-, and eigenvalue problems, existence theorems, real and complex linear systems of differential equations, and stability theory. There will be a strong emphasis on methods for finding solutions of initial and boundary value problems and analyzing properties of these solutions for various differential equations.

**Credits:**3**Prereq:**Undergraduate and Graduate: Math 2050 with a C- or better and Math 2350 with a C- or better or instructor's permission. It is recommended, but not required, that students take Math 3230, which would require a C- or better.**Cross List:**MATH-8356

##### MATH 4400: Finite Element Methods for Solving Ordinary and Partial Differential Equations

Introduction to finite elements methods for solving ordinary and partial differential equations. Theoretical foundations of finite element methods for boundary value problems, approximation by piecewise polynomial functions, variation formulation of partial differential equations, basic error estimates. The Rayleigh-Ritz-Galerkin method, convergence of approximations, time-dependent problems, error analysis, discretization and computer implementation, applications to problems in elasticity, heat transfer, and fluid mechanics.

**Credits:**3**Prereq:**Math 1970 with a C- or better, Math 2050 with a C- or better, and Math 2350 with a C- or better, or instructor's permission. MATH 3300/8305 and MATH 4330/8336 are recommended, but not required. Familiarity with MATLAB programming is assumed.**Cross List:**MATH-8406

##### MATH 4560: Number Theory & Cryptography

An overview of one of the many beautiful areas of mathematics and its modern application to secure communication. The course is ideal for any student who wants a taste of mathematics outside of, or in addition to, the calculus sequence. Topics to be covered include: prime numbers, congruences, perfect numbers, primitive roots, quadratic reciprocity, sums of squares, and Diophantine equations. Applications include error-correcting codes, symmetric and public key cryptography, secret sharing, and zero knowledge proofs.

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**CSCI-4560

##### MATH 4560: Number Theory & Cryptography

An overview of one of the many beautiful areas of mathematics and its modern application to secure communication. The course is ideal for any student who wants a taste of mathematics outside of, or in addition to, the calculus sequence. Topics to be covered include: prime numbers, congruences, perfect numbers, primitive roots, quadratic reciprocity, sums of squares, and Diophantine equations. Applications include error-correcting codes, symmetric and public key cryptography, secret sharing, and zero knowledge proofs.

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**MATH-8566

##### MATH 4560: Number Theory & Cryptography

An overview of one of the many beautiful areas of mathematics and its modern application to secure communication. The course is ideal for any student who wants a taste of mathematics outside of, or in addition to, the calculus sequence. Topics to be covered include: prime numbers, congruences, perfect numbers, primitive roots, quadratic reciprocity, sums of squares, and Diophantine equations. Applications include error-correcting codes, symmetric and public key cryptography, secret sharing, and zero knowledge proofs.

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**CSCI-8566

##### MATH 4580: Tensor Analysis

Review of vector spaces and matrix theory, tensor algebra, the metric tensor and Riemannian curvature, geodesics, applications to geometry, mechanics, relativity, and continuous media.

**Credits:**3**Prereq:**MATH 1970, 2050, 3350.**Cross List:**MATH-8586

##### MATH 4600: Differential Geometry

Curvature, torsion, Frenet frames, Fundamental theorem of curve theory, Frenchel's theorem, tangent spaces, first and second fundamental forms, shape operator, Fundamental theorem of surfaces theory, covariant derivative, parallel transport, geodesics.

**Credits:**3**Prereq:**MATH 1970 with a C- or better, MATH 2050 with a C- or better, and MATH 2350 with a C- or better, or permission of instructor.**Cross List:**MATH-8606

##### MATH 4610: Elementary Topology

This course covers topological spaces, connectedness, compactness, homotopy of paths, covering spaces, and fundamental groups.

**Credits:**3**Prereq:**MATH 1960 with a C- or better and MATH 3230 with a C- or better or permission of instructor.**Cross List:**MATH-8616

##### MATH 4650: Transform Methods and Applications

Laplace transform and the inversion integral. Fourier transform. Other transforms and special techniques. Applications to differential equations, boundary value problems of mathematical physics and signal analysis.

**Credits:**3**Prereq:**MATH 3350/8355 and MATH 4270/8276.**Cross List:**MATH-8656

##### MATH 4660: Automata, Computability and Formal Languages

This course presents a sampling of several important areas of theoretical computer science. Definition of formal models of computation, and important properties of such models, including finite automata and Turing machines. Definition and important properties of formal grammars and their languages. Introduction to the formal theories of computability and complexity.

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**CSCI-4660

##### MATH 4660: Automata, Computability and Formal Languages

This course presents a sampling of several important areas of theoretical computer science. Definition of formal models of computation, and important properties of such models, including finite automata and Turing machines. Definition and important properties of formal grammars and their languages. Introduction to the formal theories of computability and complexity.

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**MATH-8666

##### MATH 4660: Automata, Computability and Formal Languages

This course presents a sampling of several important areas of theoretical computer science. Definition of formal models of computation, and important properties of such models, including finite automata and Turing machines. Definition and important properties of formal grammars and their languages. Introduction to the formal theories of computability and complexity.

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**CSCI-8666

##### MATH 4740: Introduction to Probability and Statistics I

A mathematical introduction to probability theory including the properties of probability; probability distributions; expected values and moments; specific discrete and continuous distributions; and transformations of random variables.

**Credits:**3**Prereq:**MATH 1970 and either MATH 2230 or MATH 2030.**Cross List:**MATH-8746

##### MATH 4750: Introduction to Probability and Statistics II

Theory and methods of statistical inference including estimators, statistical hypotheses, multivariate estimation, chi-square tests, analysis of variance and statistical software.

**Credits:**3**Prereq:**MATH 4740/8746.**Cross List:**MATH-8756

##### MATH 4760: Topics in Modeling

Selection of such topics as formulation and analysis of various models involving Markov chains, Markov processes (including birth and death processes), queues, cellular automata, difference and differential equations, chaotic systems, and fractal geometries.

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**CSCI-4760

##### MATH 4760: Topics in Modeling

Selection of such topics as formulation and analysis of various models involving Markov chains, Markov processes (including birth and death processes), queues, cellular automata, difference and differential equations, chaotic systems, and fractal geometries.

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**MATH-8766

##### MATH 4760: Topics in Modeling

Selection of such topics as formulation and analysis of various models involving Markov chains, Markov processes (including birth and death processes), queues, cellular automata, difference and differential equations, chaotic systems, and fractal geometries.

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**CSCI-8766

##### MATH 4900: Independent Studies

A variable credit course for the junior or senior who will benefit from independent reading assignments and research-type problems. Independent study makes available courses of study not available in scheduled course offerings. The student wishing to take an independent study course should find a faculty member willing to supervise the course and then submit, for approval, a written proposal (including amount of credit) to the MATH/STAT Undergraduate Curriculum Committee at least one week prior to registration.

**Credits:**1-3**Prereq:**Junior and permission of the chair.

##### MATH 4980: Seminar

A seminar in mathematics.

**Credits:**1-3**Prereq:**At least one math course numbered 3000 or above (not including MATH 3500) and permission.

##### MATH 8016: Introduction to the Theory of Recursive Functions

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**MATH-4010

##### MATH 8016: Introduction to the Theory of Recursive Functions

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**CSCI-4010

##### MATH 8016: Introduction to the Theory of Recursive Functions

**Credits:**3**Prereq:**Undergraduate and graduate: MATH 2230 or CSCI 3660 or instructor's permission**Cross List:**CSCI-8016

##### MATH 8036: Modern Algebra

Algebra is the study of mathematical manipulations that preserve something (like equality -when solving equations). The areas in which Algebra finds application are quite diverse, from Ancient Greek Geometry through to Modern Information Protection and Security (error correcting codes, data compression, and cryptography). This course begins with topics that should be familiar (such as ruler-and-compass constructions, and modular arithmetic) and builds upon this foundation through polynomial rings up to finite fields and basic group theory.

**Credits:**3**Prereq:**Math 2230 with a C- or better or Math 2030 with a C- or better**Cross List:**MATH-4030

##### MATH 8050: Algorithm Graph Theory

Review of the basic concepts of graphy theory. Introduction to perfect graphs and their characterizations. Main classes of perfect graphs and their properties. Algorithms for main problems of perfect graphs. Applications of perfect graphs in several fields such as scheduling, VLSI and communication networks.

**Credits:**3**Prereq:**CSCI 3320 or CSCI 8325 and MATH 4150 or MATH 8156 or permission of instructor.- Not open to nondegree students.
**Cross List:**CSCI-8050

##### MATH 8056: Linear Algebra

The theory of vectors, vectorspaces, inner product spaces, linear transformations, eigenvalues, canonical forms, complex vectors and matrices and orthogonality. Unlike MATH 2050, this course emphasizes the theoretical aspects of linear algebra.

**Credits:**3**Prereq:**MATH 2050; MATH 2030 or 2230 or equivalent; or permission.**Cross List:**MATH-4050

##### MATH 8060: Algorithmic Combinatorics

This course includes classical combinatorial analysis graph theory, trees, network flow, matching theory, external problems, and block designs.

**Credits:**3**Prereq:**MATH 3100, CSCI 3100, MATH 8105 or CSCI 8105 or instructor's permission.**Cross List:**CSCI-8060

##### MATH 8080: Design and Analysis of Algorithms

The study of algorithms important in computer programming. Principles and underlying concepts of algorithm design, fundamental techniques of algorithm analysis, typical types of algorithms and computer architecture.

**Credits:**3**Prereq:**CSCI 3320 or CSCI 8325 or equivalent.- Not open to nondegree students.
**Cross List:**CSCI-8080

##### MATH 8105: Applied Combinatorics

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**MATH-3100

##### MATH 8105: Applied Combinatorics

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**CSCI-3100

##### MATH 8105: Applied Combinatorics

**Credits:**3**Prereq:**MATH 2030 with a C- or better or MATH 2040 with a C- or better or MATH 2230 with a C- or better. Mathematical logic; Set theory; Relations; Functions; Congruences; Inductive and recursive definitions; Discrete probability; Basic knowledge of sets, graphs, trees, and matrices; Ability to develop algorithmic solutions and express those solutions in a high-level programming language.**Cross List:**CSCI-8105

##### MATH 8116: Abstract Algebra I

An introduction to group theory. Various classes of group are studied: symmetric groups, abelian, cyclic, and permutation groups. Basic tools are developed and used: subgroups, normal subgroups, cosets, the Lagrange theorem, group homomorphisms, quotient groups, direct products, and group actions on a set. The course culminates with the Sylow theorems in finite group theory. The theory is illustrated with examples from geometry, linear algebra, number theory, crystallography, and combinatorics.

**Credits:**3**Prereq:**Undergraduate and Graduate: MATH 4050/8056 with a C- or better or MATH 4560/8566 with a C- or better or permission of instructor**Cross List:**MATH-4110

##### MATH 8126: Abstract Algebra II

An introduction to ring and field theory. Various classes of commutative rings are considered including polynomial rings, and the Gaussian integers. Examples of fields include finite fields and various extensions of the rational numbers. Concepts such as that of an ideal, integral domain, characteristic and extension field are studied. The course culminates with an introduction to Galois theory. Applications include the resolution of two classical problems: the impossibility of angle-trisection and the general insolvability of polynomial equations of degree 5 or higher.

**Credits:**3**Prereq:**Undergraduate and Graduate: MATH 4110/8116 with a C- or better or permission of instructor**Cross List:**MATH-4120

##### MATH 8156: Graph Theory & Applications

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**MATH-4150

##### MATH 8156: Graph Theory & Applications

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**CSCI-4150

##### MATH 8156: Graph Theory & Applications

**Credits:**3**Prereq:**MATH 2030 or permission of instructor.**Cross List:**CSCI-8156

##### MATH 8235: Introduction to Analysis

Provides a theoretical foundation for the concepts of elementary calculus. Topics include the real number system, topology of the real line, limits, functions of one variable, continuity, differentiation, integration.

**Credits:**3**Prereq:**MATH 1970, and MATH 2030 or MATH 2230 or equivalent.**Cross List:**MATH-3230

##### MATH 8236: Mathematical Analysis I

Provides a theoretical foundation for the concepts of elementary calculus. Topics include ordered fields and the real number system, basic properties of complex numbers, metric space topology, sequences and series in Rk, limits and continuity in a metric space, monotonic functions.

**Credits:**3**Prereq:**MATH 3230/8235 or equivalent.**Cross List:**MATH-4230

##### MATH 8246: Mathematical Analysis II

Provides a theoretical foundation for the concepts of elementary calculus. Topics include differentiation and Riemann-Stieltjes Integration, sequences and series of functions, uniform convergence, power series, functions of several variables, Implicit Function Theorem.

**Credits:**3**Prereq:**MATH 4230/8236.**Cross List:**MATH-4240

##### MATH 8250: Partial Differential Equations

Partial differential equations (PDEs) are fundamental in the application of mathematics to science and engineering. Topics to be covered will include: Linear and nonlinear first-order equations, classification of second-order linear equations, elliptic, hyperbolic and parabolic equations and boundary value problems, and Green's functions.

**Credits:**3**Prereq:**MATH 1970, MATH 2350, or instructor's permission. MATH 4330/8336 is recommended, but not required.

##### MATH 8276: Complex Variables

Differentiation, integration and power series expansions of analytic functions, conformal mapping, residue calculus, and applications.

**Credits:**3**Prereq:**MATH 3230/8235 or equivalent.**Cross List:**MATH-4270

##### MATH 8305: Numerical Methods

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**MATH-3300

##### MATH 8305: Numerical Methods

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**CSCI-3300

##### MATH 8305: Numerical Methods

**Credits:**3**Prereq:**MATH 1960 with a C- or better or permission of instructor**Cross List:**CSCI-8305

##### MATH 8306: Deterministic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**MATH-4300

##### MATH 8306: Deterministic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**CSCI-4300

##### MATH 8306: Deterministic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 with a C- or better or permission of instructor.**Cross List:**CSCI-8306

##### MATH 8316: Probabilistic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**MATH-4310

##### MATH 8316: Probabilistic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**CSCI-4310

##### MATH 8316: Probabilistic Operations Research Models

**Credits:**3**Prereq:**MATH 2050 and either MATH 4740 or MATH 8746 or STAT 3800 or STAT 8805 all with a C- or better or permission of instructor.**Cross List:**CSCI-8316

##### MATH 8326: Computational Operations Research

Survey of computational methods used in the solution of operations research problems. Topics include scripting to guide optimization software, metaheuristics for optimization, and basic machine learning algorithms.

**Credits:**3**Prereq:**MATH 3200 and MATH 4300 each with a grade of C- or better or permission of instructor.**Cross List:**MATH-4320

##### MATH 8336: Introduction to Partial Differential Equations

This course introduces the basic methods of PDEs guided by applications in physics and engineering. The main topics to be covered include The Linear First order PDEs, Transport equations, Characteristics, Classification of PDEs, Separation of variables, Heat conduction, vibrating membranes, boundary value problems, Maximum principle, Sturm-Liouville problems, Fourier series, Fourier integrals, Harmonic functions, Legendre polynomials, Distributions, Green's functions.

**Credits:**3**Prereq:**MATH 1970 with a C- or better and MATH 2350 with a C- or better, or permission of instructor; MATH 2050 recommended, not required.**Cross List:**MATH-4330

##### MATH 8356: Ordinary Differential Equations

Ordinary Differential Equations develops the theory of initial-, boundary-, and eigenvalue problems, existence theorems, real and complex linear systems of differential equations, and stability theory. There will be a strong emphasis on methods for finding solutions of initial and boundary value problems and analyzing properties of these solutions for various differential equations.

**Credits:**3**Prereq:**Undergraduate and Graduate: Math 2050 with a C- or better and Math 2350 with a C- or better or instructor's permission. It is recommended, but not required, that students take Math 3230, which would require a C- or better.**Cross List:**MATH-4350

##### MATH 8370: Fuzzy Set Theory and its Applications

The course is focused on the fundamental theory of fuzzy sets and its applications to data mining and decision making.

**Credits:**3**Prereq:**MATH 2030, MATH 2230, MATH 3230/8235, or permission of instructor.

##### MATH 8400: Dynamical Systems and Chaos

Review of difference equations and differential equations, stability theory, periodic orbits, lyapunov exponents, fractals, chaos, state reconstruction from time series data.

**Credits:**3**Prereq:**Permission from Instructor.

##### MATH 8406: Finite Element Methods for Solving Ordinary and Partial Differential Equations

Introduction to finite elements methods for solving ordinary and partial differential equations. Theoretical foundations of finite element methods for boundary value problems, approximation by piecewise polynomial functions, variation formulation of partial differential equations, basic error estimates. The Rayleigh-Ritz-Galerkin method, convergence of approximations, time-dependent problems, error analysis, discretization and computer implementation, applications to problems in elasticity, heat transfer, and fluid mechanics.

**Credits:**3**Prereq:**Math 1970 with a C- or better, Math 2050 with a C- or better, and Math 2350 with a C- or better, or instructor's permission. MATH 3300/8305 and MATH 4330/8336 are recommended, but not required. Familiarity with MATLAB programming is assumed.**Cross List:**MATH-4400

##### MATH 8410: Topics in Discrete Dynamical Networks: Boolean Networks

This course is focused on introduction to discrete dynamical networks, in particular logical networks, and their applications.

**Credits:**3**Prereq:**MATH 1960 (Calculus II), MATH 2230 (proof writing skills), MATH4740 or equivalent (basic probability theory), basic computer skills; or permission of the instructor.

##### MATH 8430: Linear Programming

This course includes a complete development of theoretical and computational aspects of linear programming. Basic theoretical foundations covered include polyhedra, convexity, linear inequalities and duality. Advanced topics such as decomposition and column generation are covered. Both simplex methods and interior point methods are included.

**Credits:**3**Prereq:**MATH 4300/8306

##### MATH 8440: Network Programming

A presentation of network flow models and optimization algorithms. Topics include pure, generalized, integer, and constrained network problems, plus special cases of each, including transportation, assignment, shortest-path, transshipment, and multicommodity.

**Credits:**3**Prereq:**MATH 4300/8306

##### MATH 8450: Calculus of Variations

Functionals, the Euler-Lagrange Equation, the Brachistochrone, minimum surface of revolution, isoperimetric problem, Fermat's Principle, Hamilton's Principle, least action, the vibrating string and membrane, max-min characterization of eigenvalues, further applications.

**Credits:**3**Prereq:**MATH 3230/8235 and 3350/8355.

##### MATH 8460: Integer Programming

Advanced study in mathematical programming with integer or mixed integer variables. Topics include integer programming, model creation, developing solution algorithms, and applications of integer programming.

**Credits:**3**Prereq:**MATH 2030 or MATH 2230- Not open to nondegree students.

##### MATH 8480: Multi-agent Systems and Game Theory

This course covers advanced topics in the area of coordination of distributed agent-based systems with a focus on computational aspects of game theory. The main topics covered in this course include distributed constraint satisfaction, distributed constraint optimization, and competitive and cooperative game theory.

**Credits:**3**Prereq:**CSCI 4450 or CSCI 8456. Suggested background courses: CSCI 4480 or CSCI 8486; CSCI 8080.- Not open to nondegree students.
**Cross List:**CSCI-8480

##### MATH 8490: Applied Complex Variables

Applications of complex variables to potential theory, Fourier and Laplace transforms, ordinary and partial differential equations, number theory, chaotic dynamical systems, etc.

**Credits:**3**Prereq:**MATH 4270/8276.

##### MATH 8500: Numerical Analysis I

Topics covered in this course include error propagation, solutions of nonlinear equations, solutions of linear and nonlinear systems by various schemes, matrix norms and conditioning, and computation of eigenvalues and eigenvectors.

**Credits:**3**Prereq:**MATH 1960 and MATH 2050, or permission of instructor. Familiarity with computer programming is assumed.**Cross List:**CSCI-8500

##### MATH 8505: Selected Topics in Mathematics

This is a variable content course with selected topics in the mathematical sciences which may be of interest to students in other disciplines such as mathematics education, psychology and business. The course may be taken more than once for credit provided topics differ, with a maximum of nine hours. Mathematics majors may apply no more than three hours of MATH 3500 toward the minimum major requirements.

**Credits:**1-6**Prereq:**Permission of instructor.**Cross List:**MATH-3500

##### MATH 8510: Numerical Analysis II

Topics covered in this course include interpolation and approximations, numerical differentiation, numerical integration, and numerical solutions of ordinary and partial differential equations.

**Credits:**3**Prereq:**MATH 1970, MATH 2350, or permission of instructor. Familiarity with computer programming is assumed.**Cross List:**CSCI-8510

##### MATH 8520: Advanced Topics in Operations Research

Advanced treatment of a specific topic in the area of operations research not available in the regular curriculum. Topics, developed by individual faculty members, will reflect their special interests and expertise. The course may be repeated for credit as topics differ.

**Credits:**3**Prereq:**MATH 4300 or MATH 8306 or CSCI 4300 or CSCI 8306 or permission of the instructor.**Cross List:**CSCI-8520

##### MATH 8530: Nonlinear Optimization with Nonlinear Integrals

The course is focused on using a new mathematical aggregation tool, the nonlinear integral, in nonlinear optimizations and on its applications in information fusion and data mining, where a soft computing technique (genetic algorithms and/or neural networks) is adopted to search numerical optimal solutions approximately.

**Credits:**3**Prereq:**MATH 1960 and MATH 4740. Preferred MATH 4300 and CIST 1400 or equivalent.

##### MATH 8566: Number Theory & Cryptography

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**MATH-4560

##### MATH 8566: Number Theory & Cryptography

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**CSCI-4560

##### MATH 8566: Number Theory & Cryptography

**Credits:**3**Prereq:**Undergraduates and Graduates: MATH 2230 with a C- or better or MATH 2030 with a C- or better or CSCI 2030 with a C- or better or permission of instructor**Cross List:**CSCI-8566

##### MATH 8586: Tensor Analysis

Vector and Tensors: Review of Vector algebra and Vector calculus. The integral theorems of Green, Gauss and Stokes. Applications to geometry and physics. Tensor algebra. The metric tensor and Riemannian curvature. Christoffel symbols and the Roicci tensor. Tensor in Euclidean geometry. Geodesics, applications to geometry and mechanics.

**Credits:**3**Prereq:**MATH 1970,2050, and 3350.**Cross List:**MATH-4580

##### MATH 8606: Differential Geometry

Curvature, torsion, Frenet frames, Fundamental theorem of curve theory, Frenchel's theorem, tangent spaces, first and second fundamental forms, shape operator, Fundamental theorem of surfaces theory, covariant derivative, parallel transport, geodesics.

**Credits:**3**Prereq:**MATH 1970 with a C- or better, MATH 2050 with a C- or better, and MATH 2350 with a C- or better, or permission of instructor.**Cross List:**MATH-4600

##### MATH 8616: Elementary Topology

This course covers topological spaces, connectedness, compactness, homotopy of paths, covering spaces, and fundamental groups.

**Credits:**3**Prereq:**MATH 1960 with a C- or better and MATH 3230 with a C- or better or permission of instructor.**Cross List:**MATH-4610

##### MATH 8620: General Topology

The concepts of MATH 4610/8616 are studied at an advanced level in conjunction with ordinal and cardinal numbers, open and closed maps, separation axioms and countable compactness.

**Credits:**3**Prereq:**MATH 4610/8616 or permission of instructor.

##### MATH 8645: Modern Geometry

Axiomatic systems, finite geometries, modern foundations of Euclidean geometry, hyperbolic and other non-Euclidean geometrics, projective geometry.

**Credits:**3**Prereq:**MATH 2230 or MATH 2030, or equivalent mathematical maturity.**Cross List:**MATH-3640

##### MATH 8650: Introduction to Probability Models

This is an introduction to probability modeling including Poisson Processes, Markov chains, birth-death processes, queueing models and renewal theory. Applications will be an important part of the course.

**Credits:**3**Prereq:**MATH 4740/8746, MATH/CSCI 4760/8766, STAT 3800/8805, or permission of instructor.

##### MATH 8656: Transform Methods and Applications

Laplace transform and the inversion integral. Fourier transform. Other transforms and special techniques. Applications to differential equations, boundary value problems of mathematical physics, and signal analysis.

**Credits:**3**Prereq:**MATH 3350/8355 and MATH 4270/8276.**Cross List:**MATH-4650

##### MATH 8666: Automata, Computability and Formal Languages

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**MATH-4660

##### MATH 8666: Automata, Computability and Formal Languages

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**CSCI-4660

##### MATH 8666: Automata, Computability and Formal Languages

**Credits:**3**Prereq:**MATH 2030. Recommended: CSCI 3320/8325.**Cross List:**CSCI-8666

##### MATH 8670: Topics in Probability and Statistics

A variable topics course in probability and or statistics. Topics covered will include one or more of the following: reliability theory and applications in engineering and science, advanced probability and statistical models, theory of parametric estimation and applications, and advanced probability theory and application.

**Credits:**3**Prereq:**MATH 4740/8740 or STAT 3800/8800 or permission from instructor.

##### MATH 8746: Introduction to Probability and Statistics I

A mathematical introduction to probability theory including the properties of probability; probability distributions; expected values and moments; specific discrete and continuous distributions; and transformations of random variables.

**Credits:**3**Prereq:**MATH 1970 and MATH 2030 or MATH 2230.**Cross List:**MATH-4740

##### MATH 8756: Introduction to Probability and Statistics II

Theory and methods of statistical inference including estimators, statistical hypotheses, multivariate estimation, chi-square tests, analysis of variance, and statistical software.

**Credits:**3**Prereq:**MATH 4740/8746.**Cross List:**MATH-4750

##### MATH 8766: Topics in Modeling

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**MATH-4760

##### MATH 8766: Topics in Modeling

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**CSCI-4760

##### MATH 8766: Topics in Modeling

**Credits:**3**Prereq:**MATH 2350 and MATH 4740 or MATH 8746.**Cross List:**CSCI-8766

##### MATH 8850: Advanced Automata and Formal Languages

A continuation of MATH/CSCI 4660/8666. The course will be an introduction to Computational Complexity. Topics that will be covered include space and time complexities of Turing Machines, deterministic versus non-deterministic machines, NP-Complete problems, alternating Turing machines, and concepts of reducibility.

**Credits:**3- Not open to nondegree students.
**Cross List:**CSCI-8850

##### MATH 8855: History of Mathematics

An overview of the historical development of mathematical concepts and methods. Brief biographies of major mathematicians, descriptions of the cultural context of selected major advances, and examples of the solution of problems using the knowledge and methods appropriate for each time period will be included.

**Credits:**3**Prereq:**Students who enroll in this course should have completed MATH 1970 and MATH 2230 in order to have the minimum amount of mathematical background needed to appreciate the mathematical content of the course.**Cross List:**MATH-3850

##### MATH 8880: Advance Placement Institute: Calculus

A workshop for teachers planning to offer an advanced placement course in calculus. Objectives include increasing teacher competencies in single-variable calculus, discussion and study of AP calculus exams, implementations of AP courses in calculus, and development and presentation of projects for graduate credit. (This course will not count toward the M.A. or M.S. degrees in Mathematics.)

**Credits:**3**Prereq:**Graduate in mathematics or mathematics education.

##### MATH 8960: Master's Project

An applied project, designed and executed under the supervision of both a faculty and industry advisor. In the project the student will apply their mathematical and/or statistical skills to an applied problem. The student will present their results via a written report and oral presentation.

**Credits:**1-6**Prereq:**Permission of faculty advisor and graduate program chair.- Not open to nondegree students.
**Cross List:**STAT-8960

##### MATH 8970: Independent Graduate Studies

Under this number a graduate student may pursue studies in an area that is not normally available to him/her in a formal course. The topics studied will be a graduate area in mathematics to be determined by the instructor.

**Credits:**1-3**Prereq:**Permission of instructor and graduate classification.

##### MATH 8980: Graduate Seminar

A graduate seminar in mathematics.

**Credits:**1-3

##### MATH 8990: Thesis

**Credits:**1-6

##### MATH 9110: Advanced Topics in Applied Mathematics

**Credits:**3

##### MATH 9230: Theory of Function of Real Variables

Real number system, convergence, continuity, bounded variation, differentiation, Lebesque-Stieltjes integration, abstract measure theory, the Lp spaces.

**Credits:**3**Prereq:**MATH 4230/8236 and MATH 8240 or equivalent.

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