This course focuses on encoding and decoding, vector spaces over finite fields, linear codes, parity-check matrices, syndrome decoding, Hamming Codes, and Cyclic Codes. This course will be taught from an applied mathematics perspective and is intended towards senior undergraduates and graduate students of Mathematics, sciences, engineering, and business students interested in operational research. The second part of the course will be devoted to constrained optimization problems, linear programming, interior-point methods, quadrative programming, and sequential quadratic programs. Familiarity with basic calculus and linear algebra is necessary. Mathematical Modeling and Optimization Differential equation models of wide variety of physical, social, and biological phenomena presented.
Qualitative analysis is introduced and used to investigate models.
Optimal criteria are incorporated to convert models to optimal control problems. Pontriagin's maximal principle is used to find analytic solutions. Numerical solutions to optimal control problems are also treated. Stability, error estimates, applications to engineering problems. Numerical Linear Algebra Floating point arithmetic, numerical solution of systems of linear equations using Gaussian elimination and its variants, numerical techniques for eigenvalues, error analysis, and implementation of algorithms on computer.