Examines point and confidence interval estimation. Principles of maximum likelihood, sufficiency, and completeness: tests of simple and composite hypotheses, linear models, and multiple regression analysis if time permits. Analyzes various distribution-free methods. Same as APPM 5520 and MATH 4520. Requisites: Requires prerequisite course of APPM 3570 or MATH 4510 (minimum grade C-).
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Same as APPM 5540 and MATH 4540. Requisites: Requires prerequisite course of APPM 4520 or MATH 4520 (minimum grade C-).
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Same as APPM 5560. Requisites: Requires prerequisite course of APPM 3570 or MATH 4510 (minimum grade C-).
Covers discrete and continuous probability laws, random variables; expectations; laws of large numbers and central limit theorem; estimation, testing hypothesis, analysis of variance, regression analysis, and nonparametric methods. Emphasizes applications with an introduction to packaged computer programs. Same as APPM 5570. Requisites: Requires prerequisite course of APPM 1360 or MATH 2300 (minimum grade C-).
Covers an introduction to statistical learning. Develops linear regression, classification, model selection, regularization, tree-based methods and resampling methods. Models and methods are illustrated on actual datasets using statistical software. Same as APPM 5580. Requisites: Requires prerequisite courses of APPM 3570 or APPM 4570 and APPM 4520 (all minimum grade C-).
Introduces methods, theory and applications of statistical models, from linear models (simple and multiple linear regression), to hierarchical linear models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples and exercises will be demonstrated using statistical software. Same as APPM 5590. Requisites: Requires prerequisite course of APPM 4520 or APPM 4570 or MATH 4520 (minimum grade C-).
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced requisite, knowledge of a programming language. Same as MATH 4650. Requisites: Requires a prerequisite course of APPM 3310 or MATH 3130 or MATH 3135 (minimum grade C-).
Continuation of APPM 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving partial differential equations. Department enforced requisite, knowledge of a programming language. Same as MATH 4660. Requisites: Requires prerequisite course of APPM 4650 or MATH 4650 (minimum grade C-).
Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours. Department enforced prereqs., variable, depending on the topic. See instructor. Same as APPM 5720.
Introduces undergraduate students to the research foci of the Department of Applied Mathematics. May be repeated up to 9 total credit hours. Department enforced prereq., variable depending on the topic.
Introduces undergraduate students to the research foci of the program in applied mathematics. It is also designed to be a capstone experience for the program's majors. May be repeated up to 6 total credit hours. Department enforced prereq., variable depending on the topic. Similar to APPM 4955.
Department enforced prerequsite courses of APPM 2350 or MATH 2400 and APPM 2360 and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135. Same as APPM 4350. Requisites: Restricted to graduate students only.
Department enforced prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360 and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135. Same as APPM 4360. Requisites: Restricted to graduate students only.
Department enforced prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360. Recommended prereqs., APPM 3310, 4350 and 4650. Same as APPM 4380. Requisites: Restricted to graduate students only.
Department enforced prerequisite courses of APPM 2360 and APPM 3310 or MATH 3130 or MATH 3135 or instructor consent required. Same as APPM 4390. Requisites: Restricted to graduate students only.
Reviews basic ideas of complex analysis, including solutions of ODEs and PDEs of physical interest via complex analysis; conformal mapping, including Schwarz-Christoffel transformations and generalizations; computational methods; Riemann-Hilbert problems; and topics in asymptotic methods. Department enforced prereq., APPM 4360 or 5360. Requisites: Restricted to graduate students only.
Discusses the elements of basic real and complex analysis, Banach spaces, Lp spaces, and many relevant inequalities. Includes applications of existence and uniqueness of solutions to various types of ordinary differential equations, partial differential equations, and integral equations. Department enforced prereqs., APPM 4440 and 4450. Requisites: Restricted to graduate students only.
Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory, and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos, and Hamiltonian systems. Department enforced prereqs., APPM 2360 and 3310 and 4440. Requisites: Restricted to graduate students only.
Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral equations. Department enforced prereqs., APPM 4350 or MATH 4470 and APPM 4360 or MATH 4450. Requisites: Restricted to graduate students only.
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and applications to differential and integral equations. Department enforced prereq., APPM 5470. Requisites: Restricted to graduate students only.
Department enforced prereq., one semester calculus-based probability course, such as MATH 4510 or APPM 3570. Same as APPM 4520 and MATH 5520. Requisites: Restricted to graduate students only.
Studies basic properties, trend-based models, seasonal models modeling and forecasting with ARIMA models, spectral analysis and frequency filtration. Department enforced prereq., APPM 5520 or MATH 5520. Same as APPM 4540 and MATH 5540. Requisites: Restricted to graduate students only.
Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study. Same as APPM 4560. Requisites: Restricted to graduate students only.
