### Program Courses Offered by CCOM Professors

**MATE6680** - **Computational Analysis I (Master's Degree in Applied Mathematics)** (3 )

*Numerical analysis aims to provide computational methods to study and solve mathematical problems involving real variables. Because the methods provide approximations to the true solution of the problem, the study of errors is very important to numerical analysis. In this course we will: provide the mathematical foundations of numerical methods; analyze the method basic theoretical properties—stability, accuracy, and computational complexity; and illustrate the method performances by means of computational examples and counterexamples by using the MATLAB® programming language. The numerical methods learned in this course are important to approximate the solutions of mathematical models of scientific problems.
Course audience: graduate students of computational sciences and applied mathematics.*

**MATE6681** - **Data Structures I (Master's Degree in Applied Mathematics)** (3 )

**MATE6682** - **Algorithms** (3 )

*This is a hybrid (on–line and face–to–face) course that teaches solid foundations to solve computational problems with an algorithmic approach. In this course we present advanced design techniques such as greedy methods, divide–and–conquer, dynamic programming, and randomized algorithms. Asymptotic notation as well as amortized analysis is introduced as means to measure complexity of algorithms. Most of the examples are related to bioinformatics and graph applications. An introduction to parallel algorithms is given through the model of dynamic multithreading programming. Finally, an introduction to NP–completeness is presented. *

**MATE6682** - **Data Structures II** (3 )

**MATE6690** - **Computational Analysis II (Master's Degree in Applied Mathematics)** (3 )

*This is a course on numerical methods for differential equations. We will study methods of function approximations, numerical methods for ordinary differential equations: initial value problems and boundary value problems, and numerical methods for one-dimension partial differential equations.*

**MATE6882** - **Optimization** (3 )

*This is a course on nonlinear optimization, both unconstrained and constrained. We will study optimality conditions and the basic numerical optimization methods with their convergence analysis. The numerical methods include: basic descent methods, conjugate direction methods, quasi Newton algorithms, reduced gradient method, gradient projection method, penalty and barrier methods, duality, and Lagrange methods. The material learned in this course is relevant to operation research, actuarial science, and mathematical modeling among others. An optimization problem is needed whenever one wants to optimize the performance of a system with the help of a mathematical model.*

**MATE8990** - **Algorithms for Molecular Biology** (3 )

*Topics covered will include biological sequences, assembly, sequence alignments, sequence phylogeny, sequence database searches, gene prediction, and whole genome analysis, including transcriptome and microarray analysis, gene clustering and application of statistics to gene profiling data.
We will emphasize the fundamental theory behind the analysis, and also present practical problems and their solutions. The course will use open–source bioinformatics tools, and show how to construct such tools using biopython, a set of libraries for bioinformatics in the python programming language.
The course is designed for graduate and advanced undergraduate students in computer science. A basic knowlege of biology is assumed. Students from other disciplines are invited to participate, but will have to make up the background. *

### More Information

For more information about permits for enrollment in graduate courses go to:

http://graduados.uprrp.edu/admisiones/solicitud_admision.htm

For information on Financial Aid for the Masters of Applied Mathematics go to:

http://graduados.uprrp.edu/noticias/agosto_2011/convocatoria-apoyo-investigacion11-12.pdf

http://www.prlsamp.org/

Contacts

Ivelisse Rubio

Carlos Corrada

Mariano Marcano