Regular courses (from the Algebra and Discrete Math Group)

  MthSc 851:  Abstract Algebra I
 MthSc 852:  Abstract Algebra II
 MthSc 853:  Matrix Analysis
 MthSc 854:  Theory of Graphs
 MthSc 855:  Combinatorial Analysis

Topic courses
Introduction to Cryptography
Advanced topics in Cryptography
Coding Theory
Advanced Topics in Coding Theory
Finite Fields
Algebraic Curves
Introduction to Computational Algebra I
Introduction to Computational Algebra II
Quantum Computing

Offered in Spring 1996, 1998, 2000 as MthSc 985 or 856
To be offered in Spring 2002
Dr. Shuhong Gao, Instructor
 

The purpose of this course is to acquaint the students with classical and modern methods of cryptography and their uses in modern communication systems.  Main topics:  Shannon's theory, conventional cryptosystems, DES, AES,  finite fields and elementary number theory,  RSA, Diffie-Hellman key exchange scheme, ElGamal cryptosystem, digital signature schemes, elliptic curves and elliptic curve cryptosystems, hash functions, pseudorandom numbers, identification schemes, and zero knowledge proofs.

Offered as MthSc 985 or 856
Dr. Joel Brawley, Instructor

This course covers  basic finite field theory and applications.

Offered in Fall 1998 as MthSc 985
Dr. Shuhong Gao, Instructor

This course covers some basic results about algebraic curves that are useful in constructing error-correcting codes and in implementing public-key cryptosystems.  Basic concepts in algebraic geometry and  commutative algebra to be covered include varieties, polynomial and rational maps, divisors,  (prime) ideals, function fields, valuations,  local rings,  Riemann-Roch Theoremetc.

Offered  as MthSc 985 or 856
Dr. Jenniffer Key, Instructor

Offered in Spring 2001 as telecommuting course ECET857
Dr. John Komo, Instructor

This was a telecampus course which provides the student with a solid background in the area of coding theory.  After discussing the algebraic background for many codes, the course develops cyclic codes, BCH codes, Reed-Solomon codes as well as convolutional codes at the end of the course.  This web page has the course handouts and assignments.  Videotapes of the course can be obtained from Dr. Komo.

Offered as MthSc 985 or 856
Dr. Jennifer Key, Instructor

This course covers topics of curent interest.

Offered in Spring 2001 as MthSc985
Dr. Shuhong Gao, Instructor

This was a specialized topics course in the area of computer algebra.  The course focused heavily on the theory and applications of Grobner bases.  Coding theory was emphasized as an area of application and the course developed some new decoding techniques for Reed-Solomon codes and Hermitian codes.

Offered in Fall 2001 as MthSc985
Dr. Shuhong Gao, Instructor
 

Outline: Fast Fourier transforms, fast multiplication of polynomials (integers), fast decoding of RS codes, sparse linear systems (from coding theory, cryptography and computer algebra), Krylov subspace methods (Lanczos and bi-orthogonal methods), Wiedemann's method a la Berlekamp-Massey,  block algorithms (Coppersmith's and Montgomory's) and their analysis.

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