Undergraduate Course Descriptions Winter/Spring 2010-2011 by DePaul University

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Page 345 of Undergraduate Course Descriptions Winter/Spring 2010-2011

mat 370 advanced linear algebra vector spaces basis and dimension matrix representation of linear transformations and change of basis diagonalization of linear operators inner product spaces diagonalization of symmetric linear operators principal-axis theorem and applications cross-listed mat 470 prerequisites mat 262 and either 141 or 215 mat 372 logic and set theory topics in axiomatic set theory formal logic and computability theory prerequisites mat 215 or 141 mat 381 fourier analysis and special functions the course covers the basic principles of discrete and continuous fourier analysis and some of its applications currently used in scientific modeling students will use the computer to implement the computational algorithms developed in the course some of the topics covered will include fourier transforms and their application to signal and image processing discrete fourier series the fast fourier transform algorithm and applications to digital filtering and the radon transforms and its applications to tomography prerequisites mat 262 or equivalent mat 384 mathematical modeling modeling of real world problems using mathematical methods includes a theory of modeling and a study of specific models selected from deterministic stochastic continuous and discrete models cross-listed with mat 484 prerequisites mat 220 or 262 and 348 or 351 or instructor consent mat 385 numerical analysis i use of a digital computer for numerical computation error analysis gaussian elimination and gauss-seidel method solution of non-linear equations function evaluation cubic splines approximation of integrals and derivatives monte carlo methods cross-listed with mat 485 prerequisites mat 262 or mat 220 and either 149 152 162 or 172 and a programming course mat 386 numerical analysis ii cross-listed with mat 486 csc 386/486 theory and algorithms for efficient computation including the fast fourier transform numerical solution of non-linear systems of equations minimization of functions of several variables sparse systems of equations and corresponding eigenvalue problems prerequisites mat 385 mat 387 operations research i:linear programming cross-listed as mat 487 the linear programming problem and its dual the simplex method transportation and warehouse problems computer algorithms and applications to various fields prerequisites mat 262 or 220 and any introductory programming course mat 388 operations research ii optimization theory cross-listed as mat 488 integer programming non-linear programming dynamic programming queuing theory game theory prerequisites mat 387 or instructor s consent mat 389 operations research iii advanced topics prerequisites mat 388 or instructor s consent mat 390 mathematics reading and research the course will provide students with a hands-on experience about research in mathematical sciences students will attend seminars and research colloquia and will actively participate at discussions about the topics presented students will reflect on the connections between various areas of modern mathematics the challenges of structuring and solving problems and the personal experience of doing mathematics as a final project each student will prepare and present a mathematical expository paper describing a current area of research emphasizing its relevance to mathematics in general and its connections to real world problems this course may be used to satisfy the junior-year experiential learning jyel requirement prerequisites instructor s consent mat 391 studies in demography the course introduces students to the study by statistical methods of human populations in terms of type of data sources population composition growth fertility mortality morbidity health migration and urbanization in addition the course has a major component which emphasizes the study of current characteristics of the populations of developing countries in comparison with some developed countries including the united states of america students are required to present and submit a research project with comparative analysis of demographic statistics obtained on several developing and developed countries mat 395 topics in mathematics consult course schedule for current offerings course may be repeated for credit when title and content change variable credit allowed prerequisites instructor s consent mat 396 senior thesis research a thesis option is available to mathematics majors who wish to pursue an extended independent project