FACULTY OF NATURAL SCIENCES

Department of Mathematics

Address : Box 23355, San Juan, Puerto Rico 00931-3355

Telephone : (787) 764-0000, exts. 2204, 7318

Fax : (787) 281-0651

Home Page : http://www.math.uprrp.edu

DEGREE OFFERED

PhD in Mathematics

FACULTY

Isadore Brodsky , PhD, University of Maryland, 1972, Professor.
Computer science ; database theory; functional analysis; logic; set theory .

Iván Cardona , PhD, Florida State University, 1987, Professor.
Geometric topology; three-dimensional manifolds and knot theory .

Francis Castro , PhD, City University of New York, 1998, Associate Professor.
Algebraic geometry; number theory .

Italo J. Dejter , PhD, Rutgers University, 1975, Professor.
Graph theory; combinatorial design; error-correcting codes; algebraic combinatorics .

M. Reza Emamy-K , PhD, University of California at Berkeley, 1981, Professor.
Convex and discrete geometry; polytopes; threshold logic; hypercube optimization .

Raúl Figueroa , PhD, University of Iowa, 1988, Professor.
Finite geometries; finite fields; combinatorics; algebraic geometry .

Guihua Gong , PhD, State University of New York at Stony Brook, 1990, Professor.
Functional analysis; operator algebras; index theory; global analysis; non-commutative differential geometry .

Puhua Guan , PhD, Ohio State University, 1985, Professor.
Symbolic computation; hypercube structure; cellular automata .

Heeralal Janwa , PhD, Syracuse University, 1986, Professor.
Coding theory; combinatorics; discrete mathematics; cryptography; algebraic geometry over finite fields and applications; computational algebraic number theory; high performance computing; applications of parallel computation to CISE; bioinformatics.

Alexander Kelmans , PhD, Soviet Academy of Sciences, 1968, Professor.
Graph theory; combinatorial optimization; discrete optimization and algorithms; network reliability; random graphs; matroids and polymatroids; algorithms complexity .

Valentín Keyantuo , PhD, University of Franche-Comté, France, 1992, Professor.
Functional analysis; semigroups of operators; evolution equations; partial differential equations .

Liangqing Li , PhD, University of Toronto, 1995, Professor.
Functional analysis; operator algebras .

Jorge M. López , PhD, University of Oregon, 1975, Professor.
Harmonic analysis; mathematics education .

Javier Luque , PhD, Massachusetts Institute of Technology, 1984, Associate Professor.
Continuous non-linear optimization .

Cornel Pasnicu , PhD, University of Bucharest, 1987, Professor.
Functional analysis; operator algebras .

Philip Pennance , PhD, University of Puerto Rico, 1989, Professor.
Discrete mathematics .

Luis Raúl Pericchi , PhD, University of London, Imperial College,1981, Professor and Director.
Mathematical statistics; Bayesian statistics applications; computational statistics .

María Eglée Pérez , PhD, Central University of Venezuela, 1994, Assistant Professor.
Bayesian statistics; biostatistics .

Jorge Punchín , PhD, University of Delaware, 1978, Professor and Graduate Program Coordinator.
Functional analysis; partial differential and integral operators in non-homogeneous boundary value problems .

Ana H. Quintero , PhD, Massachusetts Institute of Technology, 1980, Professor.
Mathematics education .

Dieter Reetz , PhD, Freie Universität, Berlin, 1979, Professor.
Applied stochastic processes .

Pedro J. Rodríguez-Esquerdo , PhD, University of California at Santa Barbara, 1983, Professor.
Probability and statistics; quality control .

Pablo Salzberg , PhD, Catholic University of Chile, 1975, Professor.
Discrete mathematics; computational geometry; statistics .

Silviu Teleman , PhD, University of Bucharest, 1968, Professor.
Partial differential equations; abstract harmonic analysis; functional analysis; theory of operators; Von Neumann algebras; Choquet theory .

Mahamadi Warma , PhD, University of Ulm, 2002, Assistant Professor.
Linear and nonlinear differential and partial differential equations; regularity of solutions of partial differential equations; potential theory; semigroup of linear and nonlinear operators; evolution equations.

ASSOCIATED FACULTY

Carlos Corrada , PhD, University of Southern California, 2001. Associate Professor, Department of Computer Science.
Computer science; communication theory.

Mariano Marcano , PhD, State University of New York at Stony Brook, 1998, Associate Professor.
Bio-Mathematics: inverse problem in renal physiology.

Oscar Moreno , PhD, University of California at Berkeley, 1973, Professor, Department of Computer Science.
Information theory; algebraic coding theory; finite fields; search algorithms using symbolic and parallel computation.

Edusmildo Orozco Salcedo, PhD, University of Puerto Rico Río Piedras Campus. 2005, Assistant Professor.
Physiological evaluation of the individual’s physical aptitude among several populations.

Ivelisse Rubio, PhD, Cornell University, 1998, Professor.
High performance computation; parallel programming; mathematical and computational model calculation for genetic networks.

DOCTORAL PROGRAM

The Doctor of Philosophy Program in Mathematics was approved by the Puerto Rico Council on Higher Education on September 19, 2000. It is the first doctoral program in Mathematics to be offered in Puerto Rico. Its mission is to prepare students to become top-level research professionals in academics, industry, and government. Students can specialize in the following three areas of research:

Pure Mathematics

Discrete Mathematics

Computational Mathematics

Requirements for Admission

Applicants must meet the general requirements for admission to graduate studies at the Río Piedras Campus. In addition, the Department of Mathematics Graduate Program requires the following:

1. Application for Admission-Graduate Program in Mathematics.
2. Application for Admission to Graduate Studies in paper or electronic format.
3. Three official copies of academic transcripts that include all courses taken at the university level.
4. Three Recommendations for Graduate Studies, at least two from professors who can attest to the applicant’s skills in mathematics, in paper or electronic format.
5. Official evidence of the bachelor’s degree in Mathematics, or its equivalent. Applicants must have taken or will be required to take the equivalent of at least one semester of Linear Algebra, two semesters of Modern Algebra, and two semesters of Advanced Calculus. Proficiency is shown by passing a placement examination or passing with a grade of B or A the corresponding courses in Algebra (MATE 5101-5102) and Analysis (MATE 5301-5302).
6. Minimum grade point average of 3.00 on a 4.00 scale.
7. Official scores on the GRE (Graduate Record Examination) Subject Test in Mathematics.

An applicant who does not meet all the requirements may be admitted as a provisional student if the Graduate Committee decides that the applicant has the potential to succeed in the doctoral program once all conditions for admission have been fulfilled.

Requirements for Graduation

Candidates must fulfill the general requirements for graduation from the Río Piedras Campus. In addition, they must satisfy the following requirements of the Department of Mathematics Graduate Program:

1. Complete all required courses, a minimum of 69 credits (54 credits in required and suggested courses, 6 credits in electives related to the doctoral dissertation, 3 credits in a master’s seminar, 3 credits in a doctoral seminar, and 3 credits in the doctoral dissertation), with a grade point average of 3.00.
2. Pass a written comprehensive examination in three areas: Analysis, Algebra, and in the student’s area of specialization.
3. Pass an oral examination for PhD candidacy.
4. Advance to PhD candidacy. Before applying for candidacy, students must demonstrate aptitude and knowledge in Spanish and English, maintain a grade point average of 3.00 on a 4.00 scale, pass a written comprehensive examination at the doctoral level, and pass the oral examination for PhD candidacy.
5. Write and publicly defend a dissertation of original research.
6. Submit the approved official dissertation to the Department of Mathematics.

Program of Study

On a date to be announced by the Graduate Committee, a placement exam will be administered in Algebra, including Linear Algebra, and Analysis (Advanced Calculus, including Functions of Several Variables). Students who do not pass the exam or who are absent on the day of the exam will be requested to enroll in the corresponding course in Algebra (MATE 5101-5102) and/or Analysis (MATE 5301-5302). To qualify for the PhD degree, students are required to pass the exam (and will have three opportunities to do so in a period of time not to exceed two years after entering the doctoral program) or pass the corresponding courses with a grade of B or A.

Only 6000 or higher level courses will count toward a degree in the graduate program.

Description of Courses (PDF)