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Introductory graduate courses are offered in algebra , real analysis , complex analysis , numerical analysis , linear and nonlinear functional analysis , algebraic topology , combinatorics , differential geometry , ordinary differential equations , partial differential equations , control theory , applied mathematics , probability , statistics , mathematical finance and computational molecular biology . Programs of Study The department offers degree programs leading to the Master of Arts in Mathematics and Applied Mathematics , the Master of Science in Applied Mathematics , Statistics , Mathematical Finance and Computational Molecular Biology and the Doctor of Philosophy in Mathematics and Applied Mathematics . The fellow will conduct research in the areas of algebraic geometry and computational algebraic geometry on problems motivated by questions in image recognition , image database indexing and computer vision as part of an ongoing joint academic / industry research effort . Biology emphasizes machine learning approaches to gene discovery , characterization of protein sequence-structure-function relationships , protein-protein interactions , discovery of genetic networks from expression data , and information theoretic , and grammatical analysis of DNA and protein sequences , and computational geometric analysis of protein structures . The Statistical Science minor is designed to provide students in other disciplines with opportunities to extend their modeling and data analysis skills beyond introductory courses , to complement existing courses offered in other departments within their major , and to enhance such offerings to the benefit of students in terms of breadth of exposure to modern statistical thinking and computational statistical methods . The conference was noteworthy for the mixture of core linear algebraists , numerical linear algebraists , and applied and computational linear algebraists present . During 2005-2010 there are several graduate fellowships available to applicants interested in research-based graduate training in Bioinformatics and Computational Molecular Biology . I am affiliated with the Laboratory for High-Performance Algorithm Engineering and Computational Molecular Biology specializing in high-performance computing and phylogenetic reconstruction .