MTH 514 - Linear Algebra And Functions Of Several Variables
(4 credits) Vector spaces, linear transformations, eigenvalues, eigenvectors, canonical forms of matrices, matrix decompositions, applications of linear algebra, calculus of functions of several variables, Jacobians, Taylor’s formula, multiple integrals, surface integrals, and change of variables formula.
(4 credits) This course gives a rigorous introduction to the real numbers. Topics include sequences and series, basic topology of the real numbers, functional limits and continuity, the derivative, sequences and series of functions, the Riemann integral, and metric spaces. The major application is Fourier series. Credit cannot be earned for this course if a student has already taken MTH 415.
(4 credits) This course deals with the fundamentals of complex analysis, including basic properties of complex numbers, analytical functions, harmonic functions, integration, Taylor and Laurent series, residue calculus and conformal mapping, and their applications. Credit cannot be earned for this course if a student has already taken MTH 416.
(4 credits) A survey of combinatorial methods, including binomial coefficients and other special numbers, recurrence relations, calculus of finite differences, and generating functions, emphasizing exact evaluation of combinatorial sums in closed form. Credit cannot be earned for this course if a student has already taken MTH 420.
(4 credits) Prerequisite: MTH 567 or permission of instructor. The course will cover techniques of modeling data that are collected sequentially. Topics to be covered include a review of basic ideas of modeling a continuous variable, time series regression, autocorrelation, decomposition methods, ARMA (Autoregressve Moving Average) models, and ARIMA (Autoregressive Integrated Moving Average) models. The course will use a statistical programming language. The course will also require the completion of a time series analysis project. Data from a variety of fields will be studied. Credit cannot ve earned for this course if a student has already taken MTH 421.
(4 credits) Modeling techniques for probabilistic systems and analysis of Monte Carlo simulations. Discrete time Markov chains, Poisson process, Birth-and-Death process, Renewal process. Random walks and Brownian motion. Applications include queuing theory, financial models, populations, inventory theory, and optimization of stochastic systems.
MTH 525 - Mathematical Methods In Engineering And Science I
(4 credits) Part one of a two-part sequence devoted to methods of applied mathematics, including various topics in ordinary and partial differential equations, integral equations, and calculus of variations, as well as specific applications to engineering and the sciences.
MTH 526 - Numbers, Patterns and Operations for Middle School Teachers
(4 credits) Prerequisite: Teacher licensure or consent of Mathematics Department Chair. An in-depth study of mathematical topics in middle school curricula in the area of numbers, patterns, and operations. Topics include numeration concepts, concepts of measurement, study of rational and irrational numbers, proportionality, estimation, and operations. Credit does not count toward the M.A. or M.S. degree in Mathematics.
MTH 527 - Algebra and Functions for Middle School Teachers
(4 credits) Prerequisite: Teacher licensure or consent of Mathematics Department Chair. Emphasis on algebra as a powerful symbolic language for studying patterns, relations, and variation; for solving linear and quadratic equations and inequalities; and for modeling real-life situations. Emphasis is on variables and functions in symbolic and graphical forms, especially linear, quadratic, exponential, logarithmic, and inverse functions. Goals include developing a deep understanding of these topics as appropriate for middle school teachers. Credit does not count toward the M.A. or M.S. degree in Mathematics.
MTH 528 - Measurement and Geometry for Middle School Teachers
(4 credits) Prerequisite: Teacher licensure or consent of Mathematics Department Chair. This course is designed to increase the conceptual understanding of geometry for middle school teachers. Topics include dynamic geometry, integrating the use of computer software; basic geometry theorems and constructions; similarity, proportion, scaling, and geometric growth; tessellations; simple trigonometric relationships; van Hiele levels of geometric graphical representations; transformational geometry; and analytic geometry. Credit does not count toward the M.A. or M.S. degree in Mathematics.
MTH 529 - Data Analysis and Probability for Middle School Teachers
(4 credits) Prerequisite: Teacher licensure or consent of Mathematics Department Chair. Ratios, fractions, percentages, data collection, graphical experimentation, basic strategies of data analysis, some statistical methods to analyze data, and inference based on date and simulation. Credit does not count toward the M.A. or M.S. degree in Mathematics.
MTH 530 - Conversational Calculus for Middle School Teachers
(4 credits) Prerequisite: Teacher licensure or consent of Mathematics Department Chair. An introduction to the concepts of calculus. Pictures and hands-on experiments are used to develop an overview of the big ideas and an appreciation of how calculus helps us understand the real world. Includes differentiation, integration, and applications of calculus to the real world. Credit does not count toward the M.A. or M.S. degree in Mathematics.
(4 credits) Prerequisite: MTH 567 or permission of instructor. The course will cover techniques of modeling data for data that are categorical rather than continuous in nature. Topics to be covered include joint, marginal, and conditional probabilities, relative risk, odds ratios, generalized linear models, logistic regression, multi-category logit models, and loglinear models. The course will utilize data examples from the fields of biology, medicine, health, epidemiology, environmental science, and psychology. The course will use a statistical programming language. The course will also require the completion of a categorical data analysis project. Credit cannot be earned for this course if a student has already taken MTH 431.
(4 credits) Modeling of real-world problems using methods of probability theory such as Markov chains, queuing theory, decision analysis, and simulation.
(4 credits) Geometry of curves and parametric surfaces, Gaussian and mean curvatures, geodesics, and other topics as time permits, including minimal surfaces, non-Euclidean models, and aspects of relativity.
(4 credits) Linear programming, including the simplex method, sensitivity analysis, duality, and integer programming. Additional topics selected from LU decomposition, dual simplex algorithm, game theory, Karmarkar’s algorithm, as well as topics from nonlinear programming, such as steepest descent and Kuhn-Tucker conditions. Part one of a two-part sequence.
(4 credits) A historical approach to calculus emphasizing the difficulties in formulating and controversies surrounding the fundamental ideas of the subject.
(4 credits) Introduction to modern algebra with emphasis on topics relevant to the secondary mathematics curriculum, including congruence, fields, polynomials and roots, and applications.
(4 credits) An applied data analysis course. A quick review of techniques for analyzing a single variable will be followed by emphasizing methodologies including One Way Analysis of Variance, nonparametric statistics, and regression. The statistical methods taught will explore the concepts of estimation, hypothesis testing, normal distribution and p-value. The course emphasizes the link between statistical graphics and formal statistical tests and involve the use of a statistical programming language. Part one of a two-part sequence.
(4 credits) Prerequisite: MTH 514 or permission of the instructor. This is an introduction to quantitative methods assoicated with the analysis of human genetic data, with an emphasis on applied projects aimed at prediction of disease status of a new sample on the basis of observed samples and identification of biomarkers leading
to human disease. Topics will include overview of microarray, proteomics, and metablomics data, overview of supervised learning, linear methods for classification, kernel methods, boosting and additive trees, neural networks, support vector machines and flexible discriminants, and unsupervised learning. Students must be familiar with matrix notation and the statistical programming language R will be used in this course.
(4 credits) Introduction to the numerical methods of financial derivatives. Topics include an overview of the basic concepts of mathematical finance, computational tools such as binomial methods, finite-difference methods, and methods for evaluating American options and Monte Carlo simulation. Numerical experiments are conducted using software such as Matlab, Microsoft Excel, and Maple, but no previous familiarity with these packages is assumed. Part one of a two-part sequence.
(4 credits) Prerequisites: A grade of C or better in a course of level 300 or above in one of the following disciplines: MTH, CIS, EEC, ESC; or instructor permission. This course presents advanced topics in number theory. Topics may include primality testing, prime number generation, integer factorization, discrete logarithms, elliptic curves and advanced cryptographic protocols, and other topics chosen by the instructor. Credit cannot be earned for this course if a student has already taken MTH 482.
(4 credits) Systems of differential equations, local and global behavior of a vector field in the plane, discrete dynamical systems, structural stability, the Poincare-Bendixon theorem, bifurcations, chaos, and strange attractors.
(4 credits) Prerequisites: A grade of C or better in MTH 182, or a special permission from the instructor. Basic mathematical interest theory and time value of money, annuities, loan repayment, bonds, equations of value and yield rates, interest rate sensitivity, stocks and financial markets, arbitrage, term structure of interest rates and derivatives. It can be used to prepare for the SOA Exam FM/CAS Exam 2 (Financial Mathematics Exam).
(4 credits) Detailed study of a selected topic in advanced mathematics. Topic varies with instructor. May be taken for credit more than once, but no single topic may be repeated. Consult the Mathematics Department for current offerings.
MTH 626 - Mathematical Methods In Engineering And Science II
(4 credits) Prerequisite: MTH 525 or permission of instructor. Part two of a two-part sequence devoted to methods of applied mathematics, including various topics in ordinary and partial differential equations, integral equations, and calculus of variations, as well as specific applications to engineering and the sciences.
(4 credits) Prerequisite: MTH 537 or permission of instructor. Stochastic models, Markov chains, queuing theory, reliability theory, forecasting, and decision processes. Part two of a two-part sequence.
(4 credits) Prerequisite: MTH 567 or permission of instructor. The purpose of this course is to continue to explore the fundamental concepts involved in applied data analysis. We will study data analysis techniques that model differences in the response variable from independent factors. We will continue using the multiple regression model developed in MTH 567 to study model checking, two way analysis of variance, repeated measures, serial correlation, and multivariate response. We will also study categorical data techniques such as risk, odds, and logistic and Poisson regression. Part two of a two-part sequence.
(4 credits) Prerequisite: MTH 514 and MTH 567 or permission of instructor. Applications of
multivariate statistical methods to applications in medicine, biology, and the social sciences. The main topics of this course will adress the issue of multiple measures of a response variable of interest. Topics will include multivariate analysis of variance (MANOVA), principal components, factor analysis, canonical correlation analysis, and discriminant analysis, among others. Students must be familiar with matrix notation, and statistical software will be used in the course.
(4 credits) Prerequisite: MTH 577 or permission of instructor. Applications of numerical methods to real-life problems in science and engineering. Topics may include the following: initial value problems, the radar problem, the calibration problem, building exploratory environments, refined graphics, numerical approximation of orbits in the planar three-body problem, effect of spin on trajectories, least squares problems, and boundary value problems. Numerical experiments are conducted using software such as Matlab and Maple, but no previous familiarity with these packages is assumed. Part two of a two-part sequence.
(4 credits) Detailed study of a selected topic in advanced mathematics. Topic varies with instructor. May be taken for credit more than once, but no single topic may be repeated. Consult the Mathematics Department for current offerings.
(4 credits) Prerequisites: Good standing in the graduate program. Working with a faculty supervisor, a student will read papers in technical journals, choose a research topic, and write a technical report in mathematics, statistics, or applied mathematics.
(4 credits) An applied data analysis course that begins with a quick review of techniques for analyzing two independent samples with a quantitative response. Other covered methodologies include One and Two Way Analysis of Variance, nonparametric statistics, and regression. The statistical methods taught will explore the concepts of estimation, hypothesis testing, statistical significance and p-value. The course emphasizes the link between statistical graphics and formal statistical tests and involve the use of a statistical programming language. Part one of a two-part sequence.
(4 credits) We will continue using the analysis of variance model developed in MTH 767 to study model repeated measures. We will continue the multiple regression model to study serial correlation, multivariate response, as well as collinearity and leverage. We will also study categorical data techniques such as risk and odds as well as logistic and poisson regression. Part 2 or a two-part sequence.