Applied Mathematics
APPM 1340-3. Calculus 1 with Algebra, Part A. Studies selected topics in analytical geometry and calculus: rates of change of functions, limits, derivatives and their applications. APPM 1340-1345 together are equivalent to APPM 1350. The sequence APPM 1340-1345 is specifically designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for APPM 1350. Prereqs., 2 years high school algebra, 1 year geometry, 1 semester trigonometry. Credit not granted for this course and MATH 1150.
APPM 1345-3. Calculus 1 with Algebra, Part B. Continuation of APPM 1340. Studies selected topics in calculus: derivatives and their applications, integration, differentiation and integration of transcendental functions. Algebraic and trigonometric topics are studied throughout, as needed. Prereq., APPM 1340. Credit not granted for this course and APPM 1350 or MATH 1300.
APPM 1350-4. Calculus 1 for Engineers. Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Prereqs., 2 years high school algebra, 1 year geometry, and 1/2 year trigonometry; or approval by faculty advisor. Credit not granted for this course and MATH 1080, 1081, 1090, 1100, 1300, 1310, APPM 1345, or ECON 1088. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.
APPM 1360-4. Calculus 2 for Engineers. Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor’s theorem, and infinite series. Prereqs., APPM 1350 or MATH 1300 (min. grade C-). Coreq., APPM 1720. Credit not granted for this course and MATH 2300.
APPM 1710-3. Introduction to Games Development 1. Designed for students with little or no programming background. Students learn to program with a tool such as ActionScript 3.0 using object-oriented techniques and classes offered by the programming language class hierarchy. Programs developed in the course address mathematical problems relating to such topics as carrying capacity, competition, and population cycle, among others. Coreq., APPM 1350. Same as ATLS 1710.
APPM 1720-3. Introduction to Games Development 2. Continuation of APPM 1710, this course addresses students with knowledge of a programming language such as ActionScript 3.0. Students learn to plan, develop and test Flash applications (games, simulations, and animations) that embody mathematical formulations of problems in areas such as transportation, nutrition, and alternative energy. Prereq., APPM 1710. Coreq., APPM 1360. Same as ATLS 1720.
APPM 2350-4. Calculus 3 for Engineers. Covers multivariable calculus, vector analysis, and theorems of Gauss, Green, and Stokes. Prereq., APPM 1360 or MATH 2300 (min. grade C-). Credit not granted for this course and MATH 2400.
APPM 2360-4. Introduction to Differential Equations with Linear Algebra. Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Prereq., APPM 1360 or MATH 2300 (min. grade C-). Credit not granted for this course and both MATH 3130 and 4430, both APPM 3310 and MATH 4430, or APPM 2380.
APPM 2450-1. Calculus 3 Computer Lab. Selected topics in analytic geometry and calculus with a focus on symbolic computation using Mathematica or Matlab. Coreq., APPM 2350.
APPM 2460-1. Differential Equations Computer Lab. Selected topics in differential equations and linear algebra with a focus on symbolic computation using Mathematica or Matlab. Coreq., APPM 2360.
APPM 2750-4. Java: Training and Mathematical Algorithms. Preparatory course for Java programming. Provides necessary background for Java language: basic object-oriented concepts, analysis, and design. Learn to create Java applets and applications, create graphic context, and identify the key features of Java foundation classes as well as other Java-related technology. Material is taught in the context of mathematical algorithms from calculus. Prereqs., APPM 1350 and programming experience. Recommended prereq., APPM 1360.
APPM 3010-3. An Introduction to Nonlinear Systems: Chaos. Both majors and minors in the physical sciences are introduced to classes of tools useful in the analysis of nonlinear systems. Prereqs., APPM 1360 and 2360.
APPM 3050-3. Scientific Computing in Matlab. Topics covered include: approximations in computing, computer arithmetic, interpolation, matrix computations, nonlinear equations, optimization, and initial-value problems with emphasis on the computational cost, efficiency, and accuracy of algorithms. The problem sets are application-oriented with examples taken from orbital mechanics, physics, genetics, and fluid dynamics. Prereqs., APPM 1360 and 2360.
APPM 3170-3. Discrete Applied Mathematics. Emphasizes selected applications of graph theory to computer science, engineering, operations research, social sciences, and biology. Topics include the basic properties of graphs and diagraphs, and their matrix representations. Relates graph properties to applications such as scheduling, architecture of parallel processors, gray codes, traveling salesman problems, and assignment problems. Prereq. or coreq., APPM 3310.
APPM 3310-3. Matrix Methods and Applications. Introduces linear algebra and matrices, with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses computational algorithms that implement these methods. Some applications in operations research may be included as time permits. Credit not granted for this course and MATH 3130. Prereq., APPM 2350.
APPM 3570-3. Applied Probability. Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, moment generating functions, law of large numbers, central limit theorem, Poisson process, and multivariate Gaussian distribution. Prereq., APPM 2350 or MATH 2400. Credit not granted for this course and ECEN 3810 or MATH 4510.
APPM 4120-3. Introduction to Operations Research. Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Prereqs., APPM 3310 or MATH 3130. Same as APPM 5120 and MATH 4120.
APPM 4350-3. Methods in Applied Mathematics: Fourier Series and Boundary Value Problems. Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions. Prereqs., APPM 2350 and 2360 (min. grade C-). Coreq., APPM 3310. Same as APPM 5350.
APPM 4360-3. Methods in Applied Mathematics: Complex Variables and Applications. Introduces methods of complex variables, contour integration, and theory of residues. Applies solving partial differential equations by transform methods, Fourier and Laplace transforms, and Reimann-Hilbert boundary-value problems. Also applies conformal mapping to ideal fluid flow and/or electrostatics. Prereqs., APPM 2350 and 2360, or 3310 (min. grade C-) or instructor consent. Same as APPM 5360.
APPM 4380-3. Modeling in Applied Mathematics. An exposition of a variety of mathematical models arising in the physical and biological sciences. Students’ modeling projects are presented in class. Topics can vary: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Prereqs., APPM 2350 and 2360. Recommended prereqs., APPM 3310, 4350, and 4650. Same as APPM 5380.
APPM 4390-3. Modeling in Mathematical Biology. Investigates how complex systems in biology can be studied using applied mathematics. Examines several case studies which include topics from microbiology, enzyme reaction kinetics, neuroscience, ecology, epidemiology, physiology, and bioengineering. Coreq., APPM 4350 or instructor consent. Same as APPM 5390.
APPM 4440-3. Undergraduate Applied Analysis 1. Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; Taylor and power series and sequences of functions. Prereq., APPM 2350 and 2360 or equivalent. Coreq., APPM 3310.
APPM 4450-3. Undergraduate Applied Analysis 2. Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and nonlinear approximation, inverse function and implicit function theorems, and a short introduction to metric spaces. Prereqs., APPM 2350, 2360, and 4440.
APPM 4520-3. Introduction to Mathematical Statistics. 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. Analyzes variance distribution-free methods. Prereq., MATH 4510 or APPM 3570. Same as APPM 5520 and MATH 4520.
APPM 4540-3. Introduction to Time Series. Single and multivariable regression, forecasting using regression models, time series models, and modeling with MA, AR, ARMA, and ARIMA models, forecasting with time series models, and spectral analysis. Prereqs., APPM 3570 or MATH 4510, and APPM 4520 or MATH 4520. Same as APPM 5540 and MATH 4540.
APPM 4560-3. Markov Processes, Queues, and Monte Carlo Simulations. Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time. 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. Prereq., APPM 3570 or equivalent. Same as APPM 5560.
APPM 4570-3. Statistical Methods. 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. Prereq., APPM 1360 or equivalent Calculus 2 course. Same as APPM 5570.
APPM 4580-3. Statistical Applications: Software and Methods. Combines statistical methods with practical applications and computer software. Develops commonly used statistical models such as analysis of variance as well as linear and logistic regression. The statistical models are implemented and interpreted in the context of actual data sets using available statistical software. Continuation of APPM 4570. Prereq., APPM 4570 or any course in statistics. Same as APPM 5580.
APPM 4650-3. Intermediate Numerical Analysis 1. 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. Prereqs., APPM 3310 or MATH 3130, and knowledge of a programming language. Same as MATH 4650.
APPM 4660-3. Intermediate Numerical Analysis 2. 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. Prereq., APPM 4650 and knowledge of a programming language. Same as MATH 4660.
APPM 4720 (1-3). Open Topics in Applied Mathematics. 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. Prereqs., variable, depending on the topic. See instructor. Same as APPM 5720.
APPM 4840 (1-3). Reading and Research in Applied Mathematics. Introduces undergraduate students to the research foci of the Department of Applied Mathematics. May be repeated up to 9 total credit hours. Prereq., APPM 3310 or MATH 3130. Recommended prereq., a course in ordinary or partial differential equations.
APPM 4950 (1-3). Seminar in Applied Mathematics. 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. Prereq., APPM 3310 or MATH 3130. Recommended prereq., course in ordinary or partial differential equations. Similar to APPM 4955.
APPM 5040 (1-2). Calculus Applications for High School Teachers. A fast-paced, intensive calculus course designed for high school mathematics teachers. Provides a deeper understanding of fundamental calculus concepts and an introduction to technological tools, including computer software used in the analysis of real-world problems. Offered through Continuing Education only. Prereqs., APPM 1350 and 1360. Recommended prereqs., APPM 2350 and 2360.
APPM 5050 (1-2). Discrete Math for K–12 Teachers. An intensive study of selected topics in discrete math, including Boolean algebra, inductive proofs, discrete probability, election theory and fair division, graph theory, and recursion. Focus on applications and technological tools to increase understanding. Offered through Continuing Education only. Prereq., one undergrad probability course. Recommended prereq., APPM 3310 or MATH 3130.
APPM 5070 (1-2). Applied Statistics for High School Teachers. A fast-paced, intensive course in statistics designed for high school mathematics teachers. Covers selected topics from probability and statistics, including random variables, central limit theorem, sampling design, regression, and interference. Uses technological tools, including Minitab and SPSS, to analyze real-world statistical problems. Offered through Continuing Education only. Prereq., undergraduate course in probability and statistics.
APPM 5120-3. Introduction to Operations Research. Same as APPM 4120 and MATH 5120.
APPM 5350-3. Methods in Applied Mathematics: Fourier Series and Boundary Value Problems. Restricted to graduate students. Same as APPM 4350.
APPM 5360-3. Methods in Applied Mathematics: Complex Variables and Applications. Prereq., graduate status in engineering or arts and sciences, or instructor consent. Same as APPM 4360.
APPM 5380-3. Modeling in Applied Mathematics. Same as APPM 4380.
APPM 5390-3. Modeling in Mathematical Biology. Same as APPM 4390.
APPM 5430-3. Methods in Applied Mathematics: Applications of Complex Variables. 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. Prereq., APPM 4360 or 5360, or instructor consent.
APPM 5440-3. Applied Analysis 1. 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. Prereqs., MATH 4310 and 4320, or equivalent; MATH 3130 or equivalent; or instructor consent.
APPM 5450-3. Applied Analysis 2. Continuation of APPM 5440. Prereq., APPM 5440 or instructor consent.
APPM 5460-3. Methods in Applied Mathematics: Dynamical Systems and Differential Equations and Chaos. 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. Prereqs., undergraduate courses equivalent to APPM 2360, 3310, and MATH 4310.
APPM 5470-3. Methods of Applied Mathematics: Partial Differential and Integral Equations. Studies properties and solutions of partial differential equations. Covers methods of characteristics for partial differential equations, well-posed problems, main results for the well-known equations, Green’s functions, and related integral equations. Prereqs., APPM 4350 and 4360, or MATH 4430, or equivalent.
APPM 5480-3. Methods of Applied Mathematics: Approximation Methods. 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. Prereq., APPM 5470 or instructor consent.
APPM 5520-3. Introduction to Mathematical Statistics. Same as APPM 4520 and MATH 5520.
APPM 5540-3. Introduction to Time Series. Same as APPM 4540 and MATH 5540.
APPM 5560-3. Markov Processes, Queues, and Monte Carlo Simulations. Prereq., APPM 3570 or equivalent. Same as APPM 4560.
APPM 5570-3. Statistical Methods. Same as APPM 4570.
APPM 5580-3. Statistical Applications: Software and Methods. Continuation of APPM 5570. Prereq., one semester of statistics. Same as APPM 4580.
APPM 5600-3. Numerical Analysis 1. Solution of nonlinear algebraic equations, interpolation, integration, approximation, and numerical linear algebra. Prereq., APPM 3310 or MATH 3130, and experience with a scientific programming language.
APPM 5610-3. Numerical Analysis 2. Numerical linear algebra, eigenvalue problems, optimization problems, and ordinary and partial differential equations. Prereq., APPM 5600 or MATH 5600.
APPM 5720 (1-3). Open Topics in Applied Mathematics. Same as APPM 4720.
APPM 6520-3. Mathematical Statistics. Emphasizes mathematical theory of statistics. Topics include distribution theory, estimation and testing of hypotheses, multivariate analysis, and nonparametric inference, all with emphasis on theory. Prereq., APPM 5520 or MATH 5520.
APPM 6550-3. Introduction to Stochastic Processes. Systematic study of Markov chains and some of the simpler Markov processes including renewal theory, limit theorems for Markov chains, branching processes, queuing theory, birth and death processes, and Brownian motion. Applications to physical and biological sciences. Prereqs., MATH 4310, MATH 4510 or APPM 3570, or APPM 4560, or instructor consent. Same as MATH 6550.
APPM 6610-3. Introduction to Numerical Partial Differential Equations. Covers finite difference, finite element, finite volume, pseudo-spectral, and spectral methods for elliptic, parabolic, and hyperbolic partial differential equations. Prereq., APPM 5600. Recommended prereq., APPM 5610 or graduate numerical linear algebra.
APPM 6640-3. Multigrid Methods. Develops a fundamental understanding of the principles and techniques of the multigrid methodology, which is a widely used numerical approach for solving many problems in such diverse areas as aerodynamics, astrophysics, chemistry, electromagnetics, hydrology, medical imaging, meteorology/oceanography, quantum mechanics, and statistical physics.
APPM 6900 (1-6). Independent Study. Introduces graduate students to research focuses of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 6940 (1-3). Master’s Degree Candidate.
APPM 6950 (1-6). Master’s Thesis. May be repeated up to 12 total credit hours.
APPM 7100-3. Mathematical Methods in Dynamical Systems. Covers dynamical systems defined by mappings and differential equations. Hamiltonian mechanics, action-angle variables, results from KAM and bifurcation theory, phase plane analysis, Melnikov theory, strange attractors, chaos, etc. Prereq., APPM 5460.
APPM 7300-3. Nonlinear Waves and Integrable Equations. Includes basic results associated with linear dispersive wave systems, first-order nonlinear wave equations, nonlinear dispersive wave equations, solitons, and the methods of the inverse scattering transform. Prereqs., APPM 5470–5480, PHYS 5210, or instructor consent.
APPM 7400 (1-3). Topics in Applied Mathematics. Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours. Prereq., instructor consent.
APPM 7900 (1-3). Independent Study. Introduces graduate students to research foci of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 8000-1. Colloquium in Applied Mathematics. Introduces graduate students to the major research foci of the Department of Applied Mathematics. Prereq., instructor consent.
APPM 8100-1. Seminar in Dynamical Systems. Introduces advanced topics and research in dynamical systems. Prereq., instructor consent.
APPM 8300-3. PDE and Analysis Seminar. Introduces the core methods in the analysis of nonlinear partial differential and integral equations or systems to graduate students. Provides a vehicle for the development, presentation, and corporative research of new topics in PDE analysis. Prereq., APPM 5440.
APPM 8600-1. Seminar in Computational Mathematics. Introduces advanced topics and research in computational mathematics. Prereq., instructor consent.
APPM 8990 (1-10). Doctoral Dissertation. All doctoral students must register for no fewer than 30 hours of dissertation credit as part of the requirements for the degree. No more than 10 credit hours may be taken in any one semester.
