**Master of Science in Applied Mathematics**

** concentration in
Mathematical Theory of Communication Systems**

**Description**

The goal of this program is to prepare students for employment in the communications industry. Students will work with a broad spectrum of mathematics pertinent to communications including coding theory, cryptography, information theory, Fourier signal analysis, linear systems, and modulation methods. Courses are designed to give students rigorous mathematical training while maintaining a focus on practical engineering problems. The program is also good preparation for doctoral work in electrical engineering or applied mathematics.

Students in the program are mentored by faculty members who are active researchers in the theory and practice of communication. The current areas of research of the faculty include coding theory, especially low-density parity-check codes, algebraic geometry codes and codes over rings, data compression, modulation, and signal detection and analysis.

Graduates of the program should find interesting employment opportunities. The communications industry is expanding rapidly with the dramatic growth in the use of cellular telephones, personal communication devices, and the internet for electronic commerce. San Diego is one of the nations leaders in communications technology. Qualcomm, the biggest private employer in San Diego County, pioneered the use of CDMA technology which is now used in wireless networks and handsets all over the world. Science Applications International Corporation (SAIC), founded in La Jolla, is an international force in telecommunications. The San Diego offices of Hewlett Packard, Texas Instruments, the U. S. Navy and many other firms do significant work in communications.

**Faculty **

James Bond: (Senior staff scientist at SAIC and Adjunct Professor of Mathematics at SDSU) Signal Processing, Low-Density Parity-Check Codes, Data Compression, and Modulation Theory

Stefen Hui: Signal Processing, Low-Density Parity-Check Codes, Control Theory

Carmelo Interlando: Coding Theory, Cryptography, and Number Theory

Michael O’Sullivan: Coding Theory, Algebaric Geometry

William Root: Algorithmics and High Performance Computing

Advisor: Stefen Hui, hui@math.sdsu.edu, 619-594-6197, GMCS 523

**Admission Requirements **

To be admitted to the program, the student should have training equivalent to that required for an undergraduate degree in mathematics or electrical engineering with a strong background in mathematics. Students with degrees in other areas but have strong mathematical backgrounds may also be considered for admission. In addition, all students must satisfy the general requirements for admission to the university with classified graduate standing.

The Department maintains a web page with further information on admission and financial support.

**Course Work**

The following courses are required:

Math 522 Number Theory

Math 525 Algebraic Coding Theory

Math 623 Linear Algebra and Matrix Theory

Math 626 Cryptography

Math 667 Mathematical Aspects of Systems Theory

Math 668 Applied Fourier Analysis

The requirements may be modified under certain circumstances subject to the approval of the program adviser.

Courses under development are: (Two of these have been taught as special topics courses, Math 696.)

Undergraduate Level Cryptography

Undergraduate Level Information Theory

Graduate Level Coding Theory

Graduate Level Information Theory

Recommended elective courses are:

Math 534B Advanced Calculus

Math 543 Numerical Analysis

Math 627 A & B Modern Algebra

Math 630 A & B Functions of a Real Variable

Math 631 A & B Functions of a Complex Variable

Math 693 A & B Advanced Numerical Analysis

Graduation Requirements

The graduate division requirements for a Master’s degree are that a student complete 30 units of course work at the 500, 600 or 700 level. As noted above under Course Work, this program has a number of required courses. In addition, a master’s thesis must be completed, which counts for 3 units of the 30.

The thesis is written under the direction of a faculty member who works closely with the student in both the research and the writing of the thesis. The student can choose any faculty member in the program to be the thesis adviser. The student and the adviser will determine the topic of the thesis, generally on a topic of interest to both. The average student takes 6 months or less to complete a thesis.

The Department of Mathematics and Statistics offers many other courses of interest to students in the program, including complex analysis, real analysis, number theory, abstract algebra and matrix analysis. Some of the these activities are listed in the home pages of faculty members.