Pure Mathematics

The Department of Mathematical Sciences has a lively research group in the areas of complex and harmonic analysis, topology, category theory, abstract algebra, differential geometry and logic, leading to a Master degree in Science, M.S. Coursework and requirements are primarily aimed at preparing students for careers in research and teaching at the college level.

Applicants should have an undergraduate degree in Mathematics or its equivalent. Candidates are expected to have approved undergraduate courses in Linear Algebra, Algebraic Structures, basic Topology and Advanced Calculus.

In addition to the requirements of the Office of Graduate Studies, the Master of Science degree in Pure Mathematics, with thesis (Option I), requires:

1. 9 credits in core courses

  • MATE 6201, Abstract Algebra
  • MATE 6261, Real Analysis I
  • MATE 6540, Topology

2. 9 credits from the following (area of specialization)
  • MATE 5049, Calculus of Variations
  • MATE 5055, Vector Analysis
  • MATE 5056, Tensor Analysis
  • MATE 5150, Linear Algebra
  • MATE 6202, Abstract Algebra II
  • MATE 6262, Real Analysis II
  • MATE 6301, Complex Variable
  • MATE 6530, Differential Geometry I
  • MATE 6531, Differential Geometry II
  • MATE 6551, Algebraic Topology
  • MATE 6670, Differential Manifolds
  • MATE 6627, Topics in Analysis I
  • MATE 6628, Topics in Analysis II
  • MATE 6631, Topics in Mathematical Logic
  • MATE 6693, Topics in Algebra I
  • MATE 6694, Topics in Algebra II
  • MATE 6993, Topics in Differential Geometry I
  • MATE 6994, Topics in Differential Geometry II

3. 6 credits outside the area of specialization or major. The requirement of a minimum of two out-of-discipline courses is to ensure cross-disciplinary breadth. The courses must be related to mathematics and should be chosen in a coherent way. These should be of level 5000 or higher. It is recommended that student choose these courses with the help of their advisor.

  • 6000 or 5000 level courses not listed in the area of specialization
  • 6000 or 5000 level courses outside the math department

4. 2 credits in Seminar

  • MATE 6991, Seminar (1 credit)
  • MATE 6992, Seminar (1 credit)

5. 6 credits in Thesis

  • MATE 6999 ( 6 credits )

Option II: project option: the course and examination requirements are similar to Option I, however the 6 Thesis credits must be replaced by 6 Project credits. An oral examination on the project is also required.

Option III, no project, no thesis: the student should approve a minimum of 36 course credits:

  • A minimum of 27 credits at graduate level
  • A minimum of 21 credits in the area of specialization
  • A minimum of 6 credits in courses related to, but outside the area of specialization.


List of faculty associated with this track and their research areas:

Luis F. Cáceres, (Logic, Algebra, Math Olympiads and Problem Solving)

Gabriele Castellini, (Categorical Topology)

Omar Colón (Non-Linear Dynamics of Discrete Dynamical Systems. Math Olympiads)

Stan Dziobiak (Graph Theory)

Wieslaw Dziobiak, (Algebraic Logic)

Victor Ocasio (Logic, Computability, Computable Estructures)

Reyes M. Ortiz, (Commutative Rings with Identity; Factorizations; Application of the General Theory of Factorization in Graphs, Number Theory and others)

Wilfredo Quiñones, (Applied Mathematics and Analysis)

Hector Salas Olaguer, (Operador theory)

Freddie Santiago Hernandez, (Differential Geometry)

Alejandro Vélez, (Analysis, PDEs, Potential Theory, Fractal Geometry)

Julio Vidaurrázaga, (Riemannian Geometry, Positive Curvature, Geometry)

Uroyoan Walker, (Linear Algebraic Group, Galois Cohomology)

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