# Mathematics Catalog

Admission to all courses at the 1000-level will be based on performance on the ACT or departmental placement exams.

**MATH 1002 - Mathematics Freshman Learning Community - 1 cr.**

Prerequisites: Open to Freshmen only. An introduction to applications of mathematics in sciences and engineering. Practical real world mathematical applications from various disciplines will be used to emphasize quantitative and analytical skills. Selected topics will vary each semester. May be repeated once for a total of two credit hours maximum.

**MATH 1003- Applied Algebra Supplemental Support - 1 cr.**

Prerequisites: Open for Pathway students only and concurrent enrollment in Math 1115 required. Factoring, graphing and applications of mathematics to real-world problems, functions and equations, mathematical notation, and critical thinking.

**MATH 1006- Survey of Mathematical Thought Supplemental Support- 1 cr.**

Prerequisites: Open for Pathway students only and concurrent enrollment in Math 1031 required. Inductive and deductive reasoning, set theory, logic, basic concepts of number theory, solving linear equations in one variable, applications of linear equations in one variable, and basic concepts of geometry.

**MATH 1021 - Problem Soving and Number Relations for Elementary Teachers - 3 cr.**

A problem solving approach to the number systems of arithmetic emphasizing the use of logic and sets as the language of mathematics. This course may be used for degree credit only in the College of Education and Human Development.

**MATH 1023 - Problem Solving and Geometry for Elementary Teachers - 3 cr.**

A problem solving and constructive approach to Euclidean Geometry and three dimensions. This course can be used for degree credit only in the College of Education and Human Development.

**MATH 1031 - A Survey of Mathematical Thought I - 3 cr.**

Non-technical survey of major branches of mathematics with examples of problems and methods in each. Topics include inductive and deductive reasoning, set theory, logic, basic concepts of number theory, solving linear equations in one variable, applications of linear equations in one variable, and basic concepts of geometry. Not offered for degree credit for students enrolled in the College of Sciences or Dr. Robert A. Savoie College of Engineering.

**MATH 1032- A Survey of Mathematical Thought II - 3 cr.**

Non-technical survey of major branches of mathematics with examples of problems and methods in each. Topics include personal loans, simple and compound interest, finance charge on a loan or credit card, and the monthly payment on a mortgage, distinguishing between different types of annuities and retirement investments, empirical and theoretical probabilities on events occurring, elementary rules of probability, counting techniques, applying probability concepts, descriptive and inferential statistics including graphs, calculating and interpreting descriptive statistics, applying the empirical rule to normal distributions, and correlation and linear regression. Not offered for degree credit for students enrolled in the College of Sciences or Dr. Robert A. Savoie College of Engineering.

**MATH 1115 - Applied Algebra- 3 cr.**

Real numbers and equations, functions, polynomial functions and graphs, exponential and logarithmic functions. A strong component of this course will be applications taken from different areas of concentration.

**MATH 1116 - College Trigonometry - 3 cr.**

Prerequisite: MATH 1115 or higher with a grade of C or better. Introduction to trigonometric functions, graphs of trigonometric functions, trigonometric identities, applications of trigonometry, linear and nonlinear systems, binomial theorem. Designed for students who are not required to take calculus. A strong component of this course will be applications taken from different areas of concentration. Credit for both MATH 1116 and 1126 will not be allowed.

**MATH 1125 - Precalculus Algebra - 3 cr.**

Prerequisites: MATH 1115 or higher with a grade of C or better. Fundamentals, functions, polynomials and rational functions, exponential and logarithmic functions.

**MATH 1126 - Precalculus Trigonometry - 3 cr.**

Prerequisites: MATH 1125 with a grade of C or better. Trigonometric functions of real numbers, trigonometric functions of angles, analytic trigonometry, systems of equations and inequalities, the binomial theorem. Credit for both MATH 1116 and 1126 will not be allowed.

**MATH 2114 - Calculus I - 4 cr.**

Prerequisites: Math 1126 with a grade of C or better. Limits and continuity of functions; introduction of the derivative; techniques of differentiation; Chain rule; implicit differentiation; differentiation of transcendental and inverse functions; applications of differentiation: concavity; relative extrema; maximum and minimum values of a function; optimization; anti-differentiation; definite integrals; Fundamental Theorem of Calculus; areas. This course requires an additional recitation hour.

**MATH 2124 - Calculus II - 4 cr.**

Prerequisites: Math 2114 with a grade of C or better.

Applications of integrals and definite integrals; volume; techniques of integration; parametric equations; sequences and infinite series; vectors, dot and cross products. This course requires an additional recitation hour.

**MATH 2134 - Calculus III - 4 cr.**

Prerequisites: Math 2124 with a grade of C or better. Work; functions of several variables; partial differentiation and applications; polar coordinates and change of variables; multiple integrals and applications; Green's Theorem; Gauss's Divergence Theorem; Stokes' Theorem. This course requires an additional recitation hour.

**MATH 2221 - Elementary Differential Equations - 3 cr.**

Prerequisite: MATH 2124 with a grade of C or better. Differential equations of first and higher order; constant coefficient equations with and without forcing terms and applications; series solutions; Laplace transforms and systems of differential equations.

**MATH 2314 - Elementary Statistical Methods - 3 cr.**

Prerequisite: MATH 1115 or higher or six hours of mathematics courses numbered at least 1000. Introduction to statistical methods. Topics include data analysis, frequency distributions, probability, inference, estimation, hypothesis testing, regression and correlation. Technology is required to explore and solve problems. Credit will not be allowed in both MATH 2314 and MATH 2785.

**MATH 2785 - Elementary Statistics for Business and Economics - 3 cr.**

Prerequisites: MATH 1115 or higher or six hours of MATH courses numbered at least 1000. This course may be used for degree credit only in the College of Business Administration. Tabular and graphical presentation of data, descriptive measures including measures of location and dispersion, introduction to probability theory including Baye's Theorem, discrete distributions including Binomial and Poisson distributions, continuous distributions including Uniform, Normal and Exponential distributions, statistical inference including sampling, point and interval estimation and hypothesis testing. Credit will not be allowed in both MATH 2314 and MATH 2785.

**MATH 2998 - Independent Study: Readings - 1 min. cr. - 3 max. cr.**

Prerequisite: consent of department. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. May be taken multiple times for a maximum of six (6) credit hours.

**MATH 3099 - Senior Honor Thesis - 1 min. cr. - 6 max. cr.**

Prerequisite: consent of department and the director of the Honors Program. Honors thesis research in mathematics under the direction of a faculty member. May be taken multiple times until thesis is accepted, for a maximum of six (6) credit hours.

**MATH 3221 - Methods in Differential Equations - 3 cr.**

Prerequisites: MATH 2221 and Math 2134. The major emphasis of this course will be on techniques and examples. Power series solutions, linear systems, matrix methods, eigenvalues, eigenvectors, partial differential equations, Fourier series, heat equation, wave equation, Laplace's equation.

**MATH 3400 - Geometry - 3 cr.**

Prerequisite: MATH 1115 or higher or six hours of mathematics courses numbered at least 1000. Absolute geometry, introduction to non-Euclidean geometries, Euclidean geometries, metric approach.

**MATH 3511 - Introduction to Linear Algebra - 3 cr.**

Prerequisite: MATH 2124 or PHYS 1061 or Math 2109 or 2112 or consent of department. Matrices, systems of linear equations, vector spaces, linear transformations, determinants, inner products and norms, eigenvalues and eigenvectors, diagonalization. Offered each semester.

**MATH 3512 - Introduction to Abstract Algebra - 3 cr.**

Prerequisite: MATH 2511; MATH 3721 is recommended. An introduction to modern algebraic structures: relations, mappings, semigroups, groups, rings and fields.

**MATH 3721 - Introduction to Discrete Structures - 3 cr.**

Prerequisite: MATH 1115 or higher, or six hours of mathematics courses numbered at least 1000. An introduction to the discrete structures that serve as a foundation for mathematics and computer science: set theory and mathematical logic; binary relations; counting and algorithm analysis; induction and strings.

**MATH 3900 - Undergraduate Oral Examination - 0 cr.**

Prerequisite: Junior standing required. Required for graduation of all Mathematics majors; independent study required. This is a Pass/Fail course. Students will demonstrate that they have acquired mastery over the material in undergraduate mathematics by creating an oral presentation, writing an essay and taking a standardized test on mathematics knowledge.

**MATH 4101 - Advanced Calculus - 3 cr.**

Prerequisite: MATH 2124 with a grade of C or better. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.

**MATH 4102 - Advanced Calculus - - 3 cr.**

Prerequisite: MATH 2134 and 4101 with a grade of C or better. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.

**MATH 4221 - Intermediate Ordinary Differential Equations3 cr.**

Prerequisite: MATH 2221 and 3511 or consent of department. Topics to be selected from the following: introduction to qualitative theory, phase plane analysis of autonomous systems, classification of equilibria, stability theory, Liapunov methods, limit cycles, Poincar Bendixson theorem, introduction to bifurcation theory and chaotic oscillations, Froebenius method for series solutions, special functions, Sturm comparison and separation theorems.

**MATH 4224 - Partial Differential Equations I - 3 cr.**

Prerequisite: MATH 2134 and 2221 or consent of department. Basic techniques for solving linear partial differential equations, separation of variables, eigenfunction expansions, integral transforms, Sturm-Liouville boundary value problems, initial value problems and boundary value problems for hyperbolic, parabolic, and elliptic equations, fundamental solutions, maximum principle, classical and modern applications.

**MATH 4230 - Finite Element Analysis - 3 cr.**

Prerequisites: MATH 2134 or 2221. Variational principle, weighted residual methods, finite element analysis of one and two dimensional steady state and transient boundary value problems involving partial differential equations, software development and implementations.

**MATH 4251 - Numerical Analysis - 3 cr.**

Prerequisite: MATH 2134 or 2221, or consent of department. Numerical solution of systems of linear and nonlinear equations; interpolation, approximation, and minimization of functions; numerical integration.

**MATH 4270 - Introduction to Optimization - 3 cr.**

Prerequisites: MATH 2134 and 3511 or consent of department. Methods for optimization of physical, economic, and business systems. Convex sets; methods for solving linear programming problems; review of classical methods of optimization; network flow analysis.

**MATH 4280 - Mathematical Modeling for Continuous Systems - 3 cr.**

Prerequisite: MATH 2134 and 2221, or consent of department. General principles in mathematical modeling, derivation and analysis of specific models using ordinary and partial differential equations; examples drawn from the applied sciences may include traffic flow, biological systems, mechanical systems, discussion of stability and dependence on parameters.

**MATH 4301 - Analysis of Variance and Experimental Design - 3 cr.**

Prerequisite: MATH 2314 or MATH 2785 or PSYC 1310 or SOC 2707. An introduction to the SAS statistical computer package. Basic analysis of variance with fixed and random effects models, multifactor analysis of variance, analysis of covariance. Experimental designs including completely randomized designs, randomized block designs, nested designs, and Latin squares. Only one of MATH 5301 or 6301 may be counted toward a master's degree in Mathematics.

**MATH 4304 - Introduction to Regression Analysis - 3 cr.**

Prerequisite: MATH 2314 or MATH 2785 or PSYC 1310 or SOC 2707. Linear regression, inferences in regression analysis, aptness of model and remedial measures, matrices, multiple and polynomial regression, indicator variables, multi-collinearity, selection of independent variables, nonlinear regression. SAS will be used for data analysis. Only one of MATH 5304 or 6304 may be counted toward a master's degree in Mathematics.

**MATH 4311 - Introduction to Mathematical Statistics - 3 cr.**

Prerequisite: MATH 2124. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics. Only one of MATH 5311 or 6311 may be counted toward a master's degree in Mathematics.

**MATH 4312 - Introduction to Mathematical Statistics - 3 cr.**

Prerequisite: MATH 4311. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics. Only one of MATH 5312 or 6312 may be counted toward a master's degree in Mathematics.

**MATH 4373 - Data Analytics - 3 cr.**

Prerequisite: Math 2314. Introduction to data analytics, data collection, date preparation, and data cleaning, date visualization, data management, data mining. Fundamental concepts from statistics: Uncertainty, probability, variance, sampling, randomness, describing and displaying data, correlation,joint probability distribution, conditional probability distribution, Bayes theorem, prior and posterior probability distribution, verification and testing, significance testing, confidence intervals, sensitivity, specificity, ROC curves, calibration, supervised and unsupervised learning, generalization, over-fitting, over-fitting avoidance, cross-validation. The focus of the lass will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 4587 and CSCI 4588.

**MATH 4385 - Statistical Learning - 3 cr.**

Prerequisite: MATH 2314. This course covers major statistical learning methods and application to modern problems in science, industry and society. Major topics include multiple linear regression, classification, resampling methods, model selection and regularization, non-linear models, tree methods, support vector machines, and unsupervised machine learning. The focus of the class will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 4587 and CSCI 4588.

**MATH 4411 - Introduction to Complex Analysis - 3 cr.**

Prerequisite: MATH 2134 or consent of department. Complex plane, analytic functions, Cauchy-Riemann equations, mappings by elementary functions, complex integration, Cauchy's theorem, Cauchy integral formula and applications, Taylor series, Laurent series, isolated singularities, residue theorem and applications.

**MATH 4511 - Linear Algebra - 3 cr.**

Prerequisite: MATH 3511 or 3512. Vector spaces (including infinite dimensional ones), linear maps, detenninants, polynomials, eigenvalues and eigenvectors, inner product spaces, operators on inner product spaces, and the spectral theorem. There is a focus on both rigor and proof as well as applications.

**MATH 4530 - Introduction to Cryptography - 3 cr.**

(MATH 4530 & CSCI 4130 are cross-listed) Prerequisites: MATH 3721. Elementary ciphers, Data Encryption Standard, Advanced Encryption Standard (Rijndael), Rivest-Adleman-Shamir (RSA) Encryption, and other topics in modern cryptography (subject to change as progress in field changes). This course is aimed at both CSCI and MATH majors, with both programming assignments and proofs as problem options.

**MATH 4611 - Topology - 3 cr.**

Prerequisite: MATH 4101 or consent of department. Topological spaces, continuous maps and homeomorphisms, product spaces, connectedness, separation axioms, compactness, and metric spaces.

**MATH 4801 - Actuarial Probability I - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2114. General probability, random variables and probability distributions, moments of a random variable, applications of each of the above topics to actuarial problems, exam P practice. This is the first part of the material covered on Exam P (Probability) and Exam 1 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively.

**MATH 4802 - Actuarial Probability II - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785 and MATH 2124. Multivariate distributions, risk and insurance, moments of several random variables, some discrete random variables and applications, some continuous random variables, normal approximations, and applications of each of the above topics to actuarial problems, exam P practice. This is the second part of the material covered on Exam P (Probability) and Exam 1 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively.

**MATH 4803 - Financial Math I - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2114. The Measurement of Interest, problems in interest, elementary annuities, yield rates, amortization schedules and sinking funds, bond and other securities, practical applications, more advanced financial analysis, a stochastic approach to interest. This is the material covered on Exam FM (Financial Mathematics) and Exam 2 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively. This course requires the use of a financial calculator.

**MATH 4804 - Financial Mathematics II - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2124. Forward price, no-arbitrage, pricing and risk-neutrality, options and their properties, the binomial model, stochastic models, options Greeks, exotic options, interest rate models. This is the material covered on Exam MFE administered by the Society of Actuaries.

**MATH 4990 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 4991 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 4992 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 4998 - Selected Readings in Mathematics - 1 min. cr. - 3 max. cr.**

Prerequisite: consent of department. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. May be taken multiple times for a maximum of six (6) credit hours.

**MATH 5101 - Advanced Calculus - 3 cr.**

Prerequisite: MATH 2124 with a grade of C or better. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.

**MATH 5102 - Advanced Calculus - 3 cr.**

Prerequisite: MATH 2134 and 4101 with a grade of C or better. These courses emphasize a balance between proofs and techniques in intermediate analysis involving one and several variables. Limits, continuity, differentiation, integration and convergence. Series of functions, functional dependence, Jacobian, vector analysis or other techniques of use in applications.

**MATH 5221 - Intermediate Ordinary Differential Equations - 3 cr.**

Prerequisite: MATH 2221 and 3511 or consent of department. Topics to be selected from the following: introduction to qualitative theory, phase plane analysis of autonomous systems, classification of equilibria, stability theory, Liapunov methods, limit cycles, Poincar Bendixson theorem, introduction to bifurcation theory and chaotic oscillations, Froebenius method for series solutions, special functions, Sturm comparison and separation theorems.

**MATH 5224 - Partial Differential Equations I - 3 cr.**

Prerequisite: MATH 2134 and 2221 or consent of department. Basic techniques for solving linear partial differential equations, separation of variables, eigenfunction expansions, integral transforms, Sturm-Liouville boundary value problems, initial value problems and boundary value problems for hyperbolic, parabolic, and elliptic equations, fundamental solutions, maximum principle, classical and modern applications.

**MATH 5230 - Finite Element Analysis - 3 cr.**

Prerequisites: MATH 2134 or 2221. Variational principle, weighted residual methods, finite element analysis of one and two dimensional steady state and transient boundary value problems involving partial differential equations, software development and implementations.

**MATH 5251 - Numerical Analysis - 3 cr.**

Prerequisite: MATH 2134 or 2221, or consent of department. Numerical solution of systems of linear and nonlinear equations; interpolation, approximation, and minimization of functions; numerical integration.

**MATH 5270 - Introduction to Optimization - 3 cr.**

Prerequisites: MATH 2134 and 3511 or consent of department. Methods for optimization of physical, economic, and business systems. Convex sets; methods for solving linear programming problems; review of classical methods of optimization; network flow analysis.

**MATH 5280 - Mathematical Modeling for Continuous Systems - 3 cr.**

Prerequisite: MATH 2134 and 2221, or consent of department. General principles in mathematical modeling, derivation and analysis of specific models using ordinary and partial differential equations; examples drawn from the applied sciences may include traffic flow, biological systems, mechanical systems, discussion of stability and dependence on parameters.

**MATH 5301 - Analysis of Variance and Experimental Design - 3 cr.**

Prerequisite: MATH 2314 or MATH 2785 or PSYC 1310 or SOC 2707. An introduction to the SAS statistical computer package. Basic analysis of variance with fixed and random effects models, multifactor analysis of variance, analysis of covariance. Experimental designs including completely randomized designs, randomized block designs, nested designs, and Latin squares. Only one of MATH 5301 or 6301 may be counted toward a master's degree in Mathematics.

**MATH 5304 - Introduction to Regression Analysis - 3 cr.**

Prerequisite: MATH 2314 or MATH 2785 or PSYC 1310 or SOC 2707. Linear regression, inferences in regression analysis, aptness of model and remedial measures, matrices, multiple and polynomial regression, indicator variables, multi-collinearity, selection of independent variables, nonlinear regression. SAS will be used for data analysis. Only one of MATH 5304 or 6304 may be counted toward a master's degree in Mathematics.

**MATH 5311 - Introduction to Mathematical Statistics - 3 cr.**

Prerequisite: MATH 2124. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics. Only one of MATH 5311 or 6311 may be counted toward a master's degree in Mathematics.

**MATH 5312 - Introduction to Mathematical Statistics - 3 cr.**

Prerequisite: MATH 4311. Axiomatic probability, discrete and continuous distributions, expectation, estimation, central limit theorem, confidence intervals and tests of hypotheses, regression, Bayesian statistics, other topics. Only one of MATH 5312 or 6312 may be counted toward a master's degree in Mathematics.

**MATH 5373 - Data Analytics - 3 cr.**

Prerequisite: Math 2314. Introduction to data analytics, data collection, date preparation, and data cleaning, date visualization, data management, data mining. Fundamental concepts from statistics: Uncertainty, probability, variance, sampling, randomness, describing and displaying data, correlation,joint probability distribution, conditional probability distribution, Bayes theorem, prior and posterior probability distribution, verification and testing, significance testing, confidence intervals, sensitivity, specificity, ROC curves, calibration, supervised and unsupervised learning, generalization, over-fitting, over-fitting avoidance, cross-validation. The focus of the lass will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 4587 and CSCI 4588.

**MATH 5385 - Statistical Learning - 3 cr.**

Prerequisite: MATH 2314. This course covers major statistical learning methods and application to modern problems in science, industry and society. Major topics include multiple linear regression, classification, resampling methods, model selection and regularization, non-linear models, tree methods, support vector machines, and unsupervised machine learning. The focus of the class will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 4587 and CSCI 4588.

**MATH 5411 - Introduction to Complex Analysis - 3 cr.**

Prerequisite: MATH 2134 or consent of department. Complex plane, analytic functions, Cauchy-Riemann equations, mappings by elementary functions, complex integration, Cauchy's theorem, Cauchy integral formula and applications, Taylor series, Laurent series, isolated singularities, residue theorem and applications.

**MATH 5511 - Linear Algebra - 3 cr.**

Prerequisite: MATH 3511 or 3512. Vector spaces (including infinite dimensional ones), linear maps, detenninants, polynomials, eigenvalues and eigenvectors, inner product spaces, operators on inner product spaces, and the spectral theorem. There is a focus on both rigor and proof as well as applications.

**MATH 5530 - Introduction to Cryptography - 3 cr.**

(MATH 4530 & CSCI 4130 are cross-listed) Prerequisites: MATH 3721. Elementary ciphers, Data Encryption Standard, Advanced Encryption Standard (Rijndael), Rivest-Adleman-Shamir (RSA) Encryption, and other topics in modern cryptography (subject to change as progress in field changes). This course is aimed at both CSCI and MATH majors, with both programming assignments and proofs as problem options.

**MATH 5611 - Topology - 3 cr.**

Prerequisite: MATH 4101 or consent of department. Topological spaces, continuous maps and homeomorphisms, product spaces, connectedness, separation axioms, compactness, and metric spaces.

**MATH 5801 - Actuarial Probability I - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2114. General probability, random variables and probability distributions, moments of a random variable, applications of each of the above topics to actuarial problems, exam P practice. This is the first part of the material covered on Exam P (Probability) and Exam 1 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively.

**MATH 5802 - Actuarial Probability II - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785 and MATH 2124. Multivariate distributions, risk and insurance, moments of several random variables, some discrete random variables and applications, some continuous random variables, normal approximations, and applications of each of the above topics to actuarial problems, exam P practice. This is the second part of the material covered on Exam P (Probability) and Exam 1 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively.

**MATH 5803 - Financial Math I - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2114. The Measurement of Interest, problems in interest, elementary annuities, yield rates, amortization schedules and sinking funds, bond and other securities, practical applications, more advanced financial analysis, a stochastic approach to interest. This is the material covered on Exam FM (Financial Mathematics) and Exam 2 administered by the Society of Actuaries and the Casualty Actuarial Society, respectively. This course requires the use of a financial calculator.

**MATH 5804 - Financial Mathematics II - 3 cr.**

Prerequisites: MATH 2314 or MATH 2785, and MATH 2124. Forward price, no-arbitrage, pricing and risk-neutrality, options and their properties, the binomial model, stochastic models, options Greeks, exotic options, interest rate models. This is the material covered on Exam MFE administered by the Society of Actuaries.

**MATH 5990 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 5991 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 5992 - Special Topics - 3 cr.**

Prerequisite: consent of department. May be taken two (2) times for a maximum of six (6) credit hours.

**MATH 5998 - Selected Readings in Mathematics - 1 min. cr. - 3 max. cr.**

Prerequisite: consent of department. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. May be taken multiple times for a maximum of six (6) credit hours.

**MATH 6201 - Introduction to Applied Mathematics - 3 cr.**

Prerequisites: Credit for or concurrent enrollment in MATH 4101. System of linear ordinary differential equations, fundamental matrices, nonlinear systems of ODE's, stability, limit cycles, separation of variables, heat equation, wave equation, Laplace's equation, Sturm-Liouville boundary value problems, Green's functions, integral transforms, conformal mapping, complex integration.

**MATH 6202 - Introduction to Applied Mathematics - 3 cr.**

Prerequisites: Credit or concurrent enrollment in MATH 4101. Dynamical systems, elementary bifurcations, chaos, nonlinear POE, characteristics, shocks, calculus of variations, Euler-Lagrange equation, normed linear spaces, linear operators, convex analysis, optimization.

**MATH 6221 - Advanced Differential Equations - 3 cr.**

Prerequisites: MATH 4101 or 4221. Ordinary differential equations in the real and complex domains, existence and uniqueness theorems, linear systems with constant and periodic coefficients. Linear differential equations or order n, self-adjoint eigenvalue problems, nonlinear equations, and stability theory.

**MATH 6224 - Partial Differential Equations II - 3 cr.**

Prerequisite: Math 4224 or Math 6201 or Math 6202. Topics in modern linear and nonlinear partial differential equations, distributions and weak solutions, method of characteristics, shock waves, Green functions, fixed point theorems, reaction diffusion equations.

**MATH 6230 - Advanced Finite Element Analysis - 3 cr.**

Prerequisites: MATH 3221 and Math 4101, or Math 4224, or Math 4230. Some knowledge of computer programming is required. Galerkin method, linear triangular elements, bilinear rectangular elements, axisymmetric elements, isoparametric elements, heat transfer by conduction and convection, torsion of noncircular sections, ground water with sources and sinks, biharmonic equation, vibration of membrane, iterative methods, software maintenance and development.

**MATH 6242 - Functional Analysis - - 3 cr.**

Prerequisite: MATH 4101 or equivalent. Topics will be selected from the following: metric spaces, normed spaces, Banach spaces, functionals, dual spaces and weak topology, inner product spaces, Hilbert spaces, compact operators, spectral analysis, fixed point theorems, implicit function theorem, Fredholm theory.

**MATH 6270 - Advanced Optimization - 3 cr.**

Prerequisite: MATH 4101 or consent of department; Mathematics 4270 is recommended. Theory and application of advanced computational methods for extremizing linear and nonlinear functions of many variables including constrained and unconstrained problems. Particular topics include a review of the simplex method an introduction to interior point methods for linear programming problems, descent methods, Newton-like methods, conjugate direction methods, and quadratic and nonlinear programming.

**MATH 6300 - Statistical Programming with SAS - 3 cr.**

Prerequisites: Previous experience using the SAS statistical package or consent of department. Proc IML, SAS macros and applications, Monte Carlo methods, resampling methods including bootstrap and jackknife, selected SAS procedures, statistical report writing with SAS.

**MATH 6301 - Applied Statistics - 3 cr.**

Prerequisite: Consent of department. Data analysis, analysis of variance, regression analysis, nonparametric methods, use of computer packages. Only one of MATH 4301G or 6301 may be counted toward a master¿s degree in mathematics.

**MATH 6303 - Multivariate Statistical Analysis - 3 cr.**

Prerequisite: MATH 4311 or 6311 or consent of department. Multivariate normal distribution, test of hypothesis on means, multivariate analysis of variance, canonical correlation.

**MATH 6304 - Regression Analysis - 3 cr.**

Prerequisite: MATH 4301 or 6301 or consent of department. Linear regression, regression diagnostics, multiple regression, nonlinear regression. Only one of MATH 4304G or 6304 may be counted toward a master's degree in Mathematics.

**MATH 6311 - Mathematical Statistics - 3 cr.**

Prerequisites: MATH 2109 or 2112 or consent of department. Theory of probability distributions, random variables and functions of random variables, multivariate and conditional distributions, order statistics, sampling distributions, theory of estimation and hypothesis testing. Only one of MATH 4311G or 6311 may be counted toward a master's degree in mathematics.

**MATH 6312 - Mathematical Statistics - 3 cr.**

Prerequisites: MATH 6311 or consent of department. Theory of probability distributions, random variables and functions of random variables, multivariate and conditional distributions, order statistics, sampling distributions, theory of estimation and hypothesis testing. Only one of MATH 4312G or 6312 may be counted toward a master's degree in mathematics.

**MATH 6321 - Sampling Theory - 3 cr.**

Prerequisite: MATH 4311 or 6311 or consent of department. Simple random sampling with and without replacement, sampling with varying probabilities, stratified sampling, cluster sampling, subsampling, systematic sampling, two-stage sampling, and sequential sampling.

**MATH 6331 - Categorical Data Analysis - 3 cr.**

Prerequisite: MATH 4301 or 4311 or 6301 or 6311 or consent of department. Analysis of contingency tables, exact small sample tests, large sample inference, logistic regression, logit, probit, extreme value, loglinear and other generalized linear models, model building and applications.

**MATH 6341 - Linear Statistical Models - 3 cr.**

Prerequisite: MATH 4311 or 6311 or consent of department. Multivariate normal distribution, matrix operations, distributions of quadratic forms, general linear hypotheses, standard models, computing techniques.

**MATH 6351 - Time Series Analysis - 3 cr.**

Prerequisite: MATH 4311 or 6311 or consent of department. Autocorrelation, spectral analysis and filtering, autoregressive (AR) models, moving average (MA) models, ARMA models, ARIMA models, model identification, forecasting, and estimation of parameters.

**MATH 6362 - Reliability Theory - 3 cr.**

Prerequisite: MATH 4311 or 6301 or 6311 or consent of department. Reliability of coherent systems, distributions in reliability, classes of life distributions, maintenance and replacement policies, availabilities, competing risks, reliability hypothesis testing, estimation of reliability functions, regression models for reliability data, and fault tree analysis.

**MATH 6370 - Statistical Consulting - 3 cr.**

Prerequisite: consent of the department. Theory and practice of effective statistical consulting. Communication with clients, problem solving, and report writing. May be repeated for credit. Students may not count more than six semester hours credit for MATH 6370 toward a degree in Mathematics.

**MATH 6373 - Advanced Data Analytics - 3 cr.**

Prerequisite: One of the following math courses: 4371/5371, 4301/5301, 4304/5304, 6301, 6304. Probabilistic approaches, model assessment and selection, regression models, kernel methods (support vector machines, principal component analysis), ensemble learning (bagging, boosting, Bayesian model averaging), naive Bayes classifiers, Bayesian networks, logic-based approaches, decision tree learning, rule induction, statistical model building, predictive modelling, Time series modeling. The focus of the class will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 6521 and CSCI 6522.

**MATH 6375 - Advanced Statistical Learning - 3 cr.**

Prerequisite: MATH 4301/5301, or 4304/5304, or 4311/5311, or 4312/5312. This course discusses some major statistical learning methods at an advanced level. The covered topics include penalized linear and non-linear regression, Kernel smoothing methods, model assessment and selection, model inference and averaging, additive and tree methods, neural networks, unsupervised machine learning, graphical models, high-dimensional problems, and related methods and new trends in statistical learning. The focus of the class will be on in-depth instruction of the statistical concepts and the related statistical analysis. The programming aspects of the statistical topics covered in this class are discussed in CSCI 6521 and CSCI 6522.

**MATH 6381 - Biostatistics - 3 cr.**

Prerequisite: MATH 6311 or consent of the department. Biostatistical design of medical studies, one- and two-sample inference, counting data, nonparametric, distribution-free and permutation models: robust procedures, simple and multiple regression, multiple comparisons, cross-over designs, discrimination and classification, and other topics.

**MATH 6382 - Statistical Analysis of Survival Data - 3 cr.**

Prerequisite: MATH 4301 or 4311 or 6301 or 6311 or consent of department. Failure times, censoring mechanisms, failure rates, survival functions, product limit estimators, covariates, Cox model, partial likelihood, exponential regression, rank tests, and other topics.

**MATH 6385 - Longitudinal Data Analysis - 3 cr.**

Prerequisite: MATH 4301 or 4311 or 6301 or 6311 or consent of department. Presentations of longitudinal data, general linear models for longitudinal data, parametric models for covariance structure, analysis of variance methods, marginal models, random effects models, methods for discrete longitudinal data.

**MATH 6450 - Measure and Integration - 3 cr.**

Prerequisite: MATH 4102 or consent of department. Measure theory, integration, types of convergence, absolute continuity, function spaces.

**MATH 6490 - Topics in Analysis - 3 cr.**

Prerequisite: consent of department.

**MATH 6998 - Advanced Readings in Mathematics - 1 min. cr. - 3 max. cr.**

Prerequisite: consent of department. This course may be repeated to a total of six credits. The course consists of directed readings designed to meet the needs and interests of the individual student; regular conferences between the student and the instructor are required. The section number will correspond with credit to be earned.

**MATH 7000 - Thesis Research - 1 min. cr. - 9 max. cr.**

To be repeated for credit until thesis is accepted. Section number will correspond with credit to be earned.

**MATH 7040 - Examination or Thesis Only - 0 cr.**

No credit. Open to students in a thesis program who have only (other than application for degree) the final typing and acceptance by the Graduate School of their thesis or dissertation or to students in a non-thesis program who have only (other than application for degree) to pass the final examination to complete graduation requirements.