Mathematics
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 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 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 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 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 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 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 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.