New Mathematics Courses
Descriptions of those courses that are too new to appear in the catalog.
Math 620 - A Survey of Error-correcting Coding
A mathematically rigorous survey of Error-Correcting Codes with emphasis on their parameters and their algorithmic efficiency for coding and decoding. Reed Solomon Codes, Goppa Codes, Reed Muller Codes, Algebraic Geometry Codes. Coding and Decoding based on Fast Fourier Transform algorithms.
Math 621 - Mathematical Theory of Error-Correcting Codes
Theoretical aspects of coding theory normally not covered in Math 512. The main subject is the study of the combinatorial constraints inherent to codes and their corresponding criteria for optimality.
Math 622 - Mathematical Theory of Information
Rigorous introduction to Mathematical Information Theory. Entropy, Channels, Conditional Entropy, Mutual Information, Huffman Encoding, Shannon theory.
Math 623 - Mathematical Theory of Convolutional Codes
This course surveys various approaches to the structure theory of convolutional codes. They are considered as vector spaces over fields of Laurent expansions, as modules over rings of polynomials and as graph codes. All necessary algebraic background beyond linear algebra is presented in the class, including concepts related to modules over principal ideal domains and ideas regarding trellises and other relevant types of graphs.
MATH 629 - Numerical Analysis: Linear Algebra
Prerequisites: 511; 544 or 546; no credit if 640A
In-depth analysis of numerical aspects of problems and algorithms in linear algebra.
MATH 639 - Numerical Analysis: Approximation Methods
Prerequisites: 544; no credit if 640B
In-depth treatment of numerical approximation techniques, including differentiation and integration.
MATH 649 - Numerical Analysis: Differential Equations
Prerequisites: 544; 541 or 549 or 645A; no credit if 640C
In-depth treatment of numerical methods for ordinary differential equations; introduction to methods for partial differential equations.
