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Course Criteria
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3.00 Credits
This is an introductory course in stochastic processes. Its purpose is to introduce students into a range of stochastic processes, which are used as modeling tools in diverse field of applications, especially in the business applications. The course introduces the most fundamental ideas in the area of modeling and analysis of real World phenomena in terms of stochastic processes. The course covers different classes of Markov processes: discrete and continuous-time Markov chains, Brownian motion and diffusion processes. It also presents some aspects of stochastic calculus with emphasis on the application to financial modeling and financial engineering. Credit may not be granted for Math 481 and Math 542. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This course will introduce the student to modern finite dimensional stochastic analysis and its applications. The topics will include: a) an overview of modern theory of stochastic processes, with focus on semimartingales and their characteristics, b) stochastic calculus for semimartingales, including Ito formula and stochastic integration with respect to semimartingales, c) stochastic differential equations (SDE's) driven by semimartingales, with focus on stochastic SDE's driven by Levy processes, d) absolutely continuous changes of measures for semimartingales, e) some selected applications. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This course is about modeling, analysis, simulation and prediction of dynamical behavior of complex systems under random influences. The mathematical models for such systems are in the form of stochastic differential equations. It is especially appropriate for graduate students who would like to use stochastic methods in their research, or to learn these methods for long term career development. Topics include white noise and colored noise, stochastic differential equations, random dynamical systems, numerical simulation, and applications to scientific, engineering and other areas. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This course introduces various methods for understanding solutions and dynamical behaviors of stochastic partial differential equations arising from mathematical modeling in science and engineering and other areas. It is designed for graduate students who would like stochastic methods in their research or to learn such methods for long term career development. Topics include: Random variables, Brownian motion and stochastic calculus in Hilbert spaces; Stochastic heat equation; Stochastic wave equation; Analytical and approximation techniques; Stochastic numerical simulations via Matlab; Dynamical impact of noises; Stochastic flows and cocycles; Invariant measures, Lyapunov exponents and ergodicity; and applications to engineering and science and other areas. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Properties of stationary, random processes; standard discrete parameter models, autoregressive, moving average, harmonic; standard continuous parameter models. Spectral analysis of stationary processes, relationship between the spectral density function and the autocorrelation function; spectral representation of some stationary processes; linear transformations and filters. Introduction to estimation in the time and frequency domains. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
This is an introductory course in mathematical finance. Technical difficulty of the subject is kept at a minimum by considering a discrete time framework. Nevertheless, the major ideas and concepts underlying modern mathematical finance and financial engineering are explained and illustrated. Credit may not be granted for Math 485 and Math 548. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Topological spaces, continuous mappings and homeomorphisms, metric spaces and metrizability, connectedness and compactness, homotopy theory. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Graph theory is the study of systems of points with some of the pairs of points joined by lines. Sample topics include: paths, cycles, and trees; adjacency and connectivity; directed graphs; Hamiltonian and Eulerian graphs and digraphs; intersection graphs. Applications to the sciences (computer, life, physical, social) and engineering will be introduced throughout the course. This course runs concurrently with Math 454 but projects and homework are at the graduate level. Credit will not be granted for both Math 454 and Math 553. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Graduate level treatment of applied combinatorics; posets: product and dimension, lattices, extremal set theory and symmetric chain decomposition; combinatorial designs: block designs, Latin Squares, finite fields, block designs and Steiner systems, finite projective planes; coding theory: error-correcting codes, Hamming and sphere bounds, linear codes, codes from liar games and adaptive coding. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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3.00 Credits
Development of the calculus of tensors with applications to differential geometry and the formulation of the fundamental equations in various fields. 3. 000 Credit Hours 3. 000 Lecture hours Levels: Graduate Doctoral, Graduate Business, Graduate, Undergraduate Schedule Types: Lecture College of Science & Letters College Applied Mathematics Department
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