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Course Criteria
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0.00 - 3.00 Credits
(3-0) Cr. 3. S. Prereq: 414 or 465 or 501. Theory of analytic functions, integration, topology of the extended complex plane, singularities and residue theory, maximum principle.
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0.00 - 3.00 Credits
Cr. 3. F. Prereq : 414 or 501. Measure and integration with special emphasis on Lebesgue measure, modes of convergence of sequences of functions, decomposition of measures, differentiation, metric spaces, Lp spaces.
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0.00 - 3.00 Credits
Cr. 3. S. Prereq: 515. Continuation of Math 515. Hilbert and Banach spaces, product integration, Fubini's theorem, other topics at the discretion of the instructor.
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0.00 - 3.00 Credits
Cr. 3. F. Prereq : 481 or 503. Finite difference methods for partial differential equations, with emphasis on parabolic and hyperbolic equations, hyperbolic conservation laws, and other partial differential equations from application areas. Topics include convergence, stability and implementation issues.
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0.00 - 3.00 Credits
(3-0) Cr. 3. F. Prereq : 414 or 465 or 501. Techniques of classical and functional analysis with applications to partial differential equations, integral equations, and boundary value problems for ordinary differential equations. Vector spaces, metric spaces, Hilbert and Banach spaces, important function spaces, contraction mapping theorem, distributions, Fourier series and Fourier transform, linear operators, spectral theory of differential and integral operators, Green s functions and boundary value problems, weak solutions of partial differential equations and variational methods, calculus in Banach spaces and applications.
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0.00 - 3.00 Credits
Cr. 3. S. Prereq: 519. Continuation of Math 519.
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0.00 - 3.00 Credits
(3-0) Cr. 3. S. Prereq: Cpr E 308, or one of Math 471, 481; experience in scientifi c programming; knowledge of FORTRAN or C. Development, analysis, and testing of effi cient numerical methods for use on current state-of-the-art high performance computers. Applications of the methods to the students' areas of research.
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0.00 - 3.00 Credits
(3-0) Cr. 3. S. Prereq: Math 301 or Cpr E 310 or Com S 330. Basic concepts of secure communication, DES and AES, public-key cryptosystems, elliptic curves, hash algorithms, digital signatures, applications. Relevant material on number theory and fi nite fi elds.
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0.00 - 3.00 Credits
(Cross-listed with Cpr E, InfAs). (3-0) Cr. 3. S. Prereq: Cpr E 531 or E E 524 or Math 533/Cpr E 533/InfAs 533. Basic principles of steganography and watermarking. Algorithms based on spatial domain approaches, transformations of data, statistical approaches. Techniques for images, video, and audio data. Communications models for data hiding. Analysis, detection and recovery of hidden data. Military, commercial and e-commerce applications. Known theoretical results. Software packages for data hiding. Social and legal issues, case studies, and digital rights management issues that affect technological development of steganography and watermarking. Current developments in the area.
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0.00 - 3.00 Credits
(3-0) Cr. 3. Prereq : Enrollment in the master of school mathematics program or professional studies in education. Offered on a 3-year cycle, offered SS. 2008. Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12.
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