Advisor: Dr. Carmelo Interlando,  619-594-7237, GMCS-581

Admissions and Financial Support:
Please see the Overview and Admissions page for information about applying to the program and for information about teaching assistantships.

General Requirement: 
General requirements for unclassified standing, classified standing, and advancement to candidacy are described in the Graduate Bulletin.  Students should file an Official Program soon after the beginning of the final year of study.  An Official Program must be filed prior to taking the last nine units of graduate course work.
 
1.  Introduction.  The goal of the Mathematics of Communication program is to prepare the students for the communications industry and to support the local communications industry by o ffering workshops, short courses, and consulting services. We plan to become an active research and education center for the mathematics of communication and attract students, visitors, and funding.
 
The communications industry in San Diego is led by Qualcomm, which is the biggest private employer in San Diego County, Science Applications International Corporation (SAIC), which is an international company with a signi cant local presence, and the U.S. Navy. The ever expanding use of cellular telephones, personal communication devices, and the Internet for electronic commerce will fuel the continued growth in the communications industry. Official Programs are filed with the approval of the Graduate Advisor and the Thesis Advisor.
 
2.  Faculty. The faculty in the program consists of Drs. Jérôme Gilles, J. Carmelo Interlando, and Michael O’Sullivan.  Jérôme Gilles is a former member of the Centre de Mathématiques et de Leurs Applications (CMLA) at the Ecole Normale Supérieure of Cachan (France). His work entails applied harmonic analysis, wavelets and their geometrical extensions,  functional analysis, application of signal processing in neuroscience (analysis of electroencephalogram signals involved in epilepsy and Parkinson’s disease), image modeling/analysis and restoration, and target detection and identification, area monitoring (intrusion detection).  J. Carmelo Interlando holds a doctorate in mathematics with concentration in cryptology and a doctorate in electrical engineering with concentration in communications. His research interests include algebraic number theory, sphere packings, algebraic coding theory, cryptography, and Boolean function complexity. Michael O’Sullivan’s research interests include algebraic statistics, algebraic geometry codes, decoding algorithms, low- density parity-check codes, ring-linear codes, computational algebraic geometry, algebraic curves and surfaces.
 
3. Preparation for Admission. Before entering the program, a student must have completed the following upper division courses: one upper division course in abstract algebra (Mathematics 320),  two courses in analysis (to include Mathematics 330), two courses in differential equations (Mathematics 337 and either 531 or 537), one course in programming or numerical analysis (Mathematics 340), one course in linear algebra (Mathematics 524), and one course in statistics (Statistics 350A or 551A). A student with inadequate undergraduate preparation may be accepted conditionally but will be required to complete courses for the removal of the deficiency in the first year of study.

4. Required Coursework.

MATH 525. Algebraic Coding Theory
MATH 620. Groups, Rings, and Fields
MATH 626. Cryptography 
MATH 630. Applied Real Analysis
MATH 668. Applied Fourier Analysis 

One course selected from:  
MATH 621. Advanced Topics in Algebra 
MATH 633. Advanced Topics in Analysis

One course selected from:  
MATH 625. Algebraic Coding Theory 
MATH 667. Mathematical Aspects of Systems Theory

Two additional courses in Mathematics or in a related area, e.g., Electrical Engineering, Statistics, with approval of the program adviser: One must be a 500- or 600-level course, while the other can be an independent research course, e.g., Mathematics 797 or 798.

MATH 799A. Thesis: Students must be registered for this course during the semester in which they will defend their thesis. Before registering for Mathematics 799A, students must submit their specific Program of Study (POS) to Graduate Affairs for their approval. The POS is filed by the Graduate Advisor with the approval of the Thesis Advisor.

5.  Graduation Requirements. A student must complete the required course work satisfactorily and meet University requirements for graduation; consult the Graduale Bulletin for further information. In addition, a thesis is required for this degree program.

6.  Contact Information. For further information, please contact Advisor Dr. Carmelo Interlando 619-594-7237

rev: 01/05/18