Analytics and Modeling

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Course Descriptions (for new courses: most 500 level courses already have UG counterparts)

 

CS 525. Simulation and Modeling.

Cr. 3. An introduction to computer simulation of mathematical models of discrete and continuous phenomena. Some standard simulations are examined; others implemented using a simulation language. Prerequisites: a course in calculus, a course in probability and statistics, and a course in programming.

 

CS 565. Interactive Computer Graphics.

Cr. 3. Study of the fundamentals of interactive computer graphics systems and software.  Emphasis is placed on graphics primitives, geometric transformation and projection, methods of creating visual realism, and selected graphics algorithms.  Prerequisites: CS 158 and MATH 131.

 

CS 572.  Computability and Computational Complexity.

Cr. 4. Emphasis on the limits to the power of computation and a systematic analysis of the algorithms that harness it.  Computability topics include the Chomsky hierarchy, several automata and language models, and demonstrations of uncomputable problems.  Complexity topics include various design strategies such as greedy, divide and conquer and backtracking, and fundamental computing algorithms, such as searching, sorting, graphs, trees, pattern matching and computational geometry, with a short foray into distributed algorithms.  Prerequisites: CS 257 and MATH 269.

 

MATH 520. Dynamical Systems.

Cr. 3. Theory and applications of mathematical models of dynamical systems (discrete and continuous).  Topics include linear and non-linear equations, linear and non-linear systems of equations, bifurcation, chaos and fractals.  Prerequisites: MATH 132 or permission of the instructor.

 

MATH 521. Mathematical Models of Infectious Disease.
Cr. 3. An application of mathematical methods and concepts to the study of infectious diseases. Analysis of outbreaks and control methods (such as vaccinations), using differential equations and elementary matrix algebra. Prerequisite: MATH 131 and one of MATH 140, MATH 240, and PSY 201. This course is usually offered online during the summer semester.

MATH 523. Game Theory (formerly MATH 520).

Cr. 3. The fundamentals of game theory are covered including dominance, Nash equilibria, and

evolutionarily stable solutions. Various models of strategic games are explored and applications to

economics, biology, and other disciplines are discussed. Prerequisites: MATH 131 and MATH 240. Usually offered during summer sessions.

 

MATH 530. Partial Differential Equations.

Cr. 3. Theory of and solution techniques for Partial Differential Equations of first and second order, including the heat equation and wave equation in rectangular, cylindrical, and spherical coordinates.  Tools include Fourier series, Bessel Functions, Legendre Polynomials and transform techniques.  Prerequisites: MATH 253 and (234 or 265).

 

MATH 543. Time Series Analysis.

Cr. 3. This course studies statistical modeling and forecasting of time series, which are observations made sequentially through time. Applications of time series discussed are selected from finance, economics, health sciences, meteorology, and many other fields. Periodic computer lab sessions with the software R. Prerequisite: MATH 340 or ECON 325.

 

MATH 570. Numerical Analysis.

Cr. 3. Analysis and implementation of numerical techniques such as polynomial interpolations, root finding, matrix solutions to systems of equations, numerical solutions to differential equations (the finite difference method), and numerical integration, with an emphasis on theory and error analysis.  Prerequisites: MATH 234 or 264.

 

MATH 571. Experimental Mathematics.

Cr. 3. A study of the role of computation and experimentation in mathematical proof. Students learn to write code in a mathematical programming language (e.g. Maple), and then apply programming skills to a variety of mathematical problems.  Topics include enumeration, continued fractions, high precision computing, and numerical integration, among others.  Students will also study famous proofs that integrate computation in nontrivial ways and the current state of automated theorem proving/automated proof checking software. Prerequisites: MATH 264.

 

CTS 530. Meteorological Computer Applications

Cr. 3. Same description as MET 330.

 

CTS 545. Evolutionary Algorithms.

Cr. 3. An introduction to evolutionary algorithms, genetic programming, and other complex adaptive systems. Students will apply these techniques to the solution of multi-objective optimization problems in science, mathematics, and engineering. Prerequisites: a course in probability and statistics and a course in programming.