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The Master of Science (MS) program in Computer Science at Stony Brook University is designed for students aiming for professional careers in business, industry, or government. It focuses on applied computer science, emphasizing programming, software development, computer systems, and relevant theoretical foundations. Students gain practical experience through project work, involving analysis, design, evaluation, and implementation. A new concentration in Data Science and Engineering is available, which can be noted on your transcript upon completion. Students can choose from three project options: a Basic Project (course-based), an Advanced Project (two-semester, faculty-guided), or a Thesis Option (research-focused with dissertation defense).
This dissertation explores the field of complex dynamics, focusing on anti-holomorphic actions and the iteration of rational maps. It delves into Schwarz reflection maps, a class of anti-holomorphic dynamics, building upon previous work in the field. The research adapts the classical Douady-Hubbard straightening theorem to develop a semi-local theory for the dynamics of these Schwarz reflections, particularly those with parabolic behavior at the cusp point. The study also investigates one-parameter families of these maps, which arise from Shabat polynomials and are indexed by rooted planar trees. The findings demonstrate that the parameter spaces and escape loci for these families are connected and simply connected, implying that the connectedness loci are themselves connected. The research identifies similarities to the Mandelbrot set, showing the presence of many renormalizable parameters that lead to smaller copies of Multibrot and Multicorn sets within the connectedness loci. Furthermore, it is shown that non-renormalizable parameters are combinatorially rigid.