Numerous graduate courses in other departments at the University, as well as the University of Colorado at Denver, in essence, are courses in applied mathematics and may be taken for credit toward graduate course work in Applied Mathematics. In fact, each graduate student must take a yearlong sequence outside the department. Consult a faculty advisor for more information and approval.
Acceptable 5000-level APPM sequences include the following (others require faculty advisor approval): 5430-5470, 5440-5450, 5460-5470, 5470-5480, 5520-5540, 5520-5560, 5570-5580, and 5600-5610.
The following courses, which are cross-listed as graduate/undergraduate courses, generally do not count toward the 30-credit-hour M.S. or Ph.D. requirement:
APPM 5350 (3) Methods in Applied Mathematics: Fourier Series and Boundary Value Problems
APPM 5360 (3) Methods in Applied Mathematics: Complex Variables and Applications
APPM 5720 (3) Open Topics in Applied Mathematics
All of the remaining courses listed below do count toward the 30-credit-hour M.S. or Ph.D. requirement:
APPM 5120 (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 4120 and MATH 4120/5120. (Normally offered spring semester)
APPM 5380 (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 may include GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Prereq.: graduate standing. Recommended: APPM 3310, 4350, and 4650. Same as APPM 4380. (Normally offered fall semester)
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. (Offered on a variable schedule)
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.: APPM 4440 and 4450, or equivalent; or instructor consent. (Normally offered fall semester)
APPM 5450 (3). Applied Analysis 2. Continuation of APPM 5440. Prereq.: APPM 5440 or instructor consent. (Normally offered spring semester)
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 3001 and MATH 4001. (Normally offered spring semesters of even-numbered years)
APPM 5470 (3). Methods of Applied Mathematics: Partial Differential and Integral Equations. 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. Prereqs.: APPM 4350 and 4360, or MATH 4430, or equivalent. (Normally offered fall semester)
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. (Normally offered spring semesters of odd-numbered years)
APPM 5520 (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.: one semester calculus-based probability such as MATH 4510 or APPM 3570. Same as APPM 4520 and MATH 4520/5520. (Normally offered spring and fall semesters)
APPM 5540 (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 5520/MATH 5520. Same as APPM 4540 and MATH 4540/5540. (Normally offered spring semester)
APPM 5560 (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 4560. (Normally offered fall semester)
APPM 5570 (3). Statistical Methods. Covers discrete and continuous probability laws, random variables; expectations; laws of large numbers and central limit theorem; estimation, testing hypotheses, 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 4570. (Normally offered fall and spring semesters)
APPM 5580 (3). Statistical Applications: Software and Methods. Continuation of APPM 5570. 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. Prereq.: one semester of statistics. Same as APPM 4580. (Normally offered spring semester)
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. Same as MATH 5600. (Normally offered fall semester)
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. Same as MATH 5610. (Normally offered spring semester)
APPM 6470 (3). Advanced Partial Differential Equations. Continuation of APPM 5470. Advanced study of the properties and solutions of elliptic, parabolic, and hyperbolic partial differential equations. Topics include the study of Sobolev spaces and variational methods as they relate to PDEs, and other topics as time permits. Prereq.: APPM 5470. (Normally offered spring semester)
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. Same as MATH 6520. (Offered on a variable schedule)
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 4001, MATH 4510 or APPM 3570, or APPM 4560, or instructor consent. Same as MATH 6550. (Normally offered by MATH in spring semesters of even-numbered years)
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. (Normally offered fall semesters of odd-numbered years)
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. (Normally offered spring semesters of odd-numbered years)
APPM 6900 (1-6). Independent Study. Introduces graduate students to research foci 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 6 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. (Offered on a variable schedule)
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 method of the inverse scattering transform. Prereqs.: APPM 5470-5480, PHYS 5210, or instructor consent. (Offered on a variable schedule)
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. (Normally offered fall and spring semesters)
APPM 8100 (1). Seminar in Dynamical Systems. Introduces advanced topics and research in dynamical systems. Prereq.: Instructor consent. (Normally offered fall and spring semesters)
APPM 8300 (1). 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. (Normally offered fall and spring semesters)
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.
Note: Transcripts might state "repeat - not for credit" when seminar courses are taken more than once. This statement is an artifact of the system and should be ignored. Repeated seminars will be credited toward the M.S. or Ph.D.