Mathematics - Master's degree
http://hdl.handle.net/1721.1/7845
2018-05-25T18:44:26ZArithmetic properties and decomposability of Jacobians
http://hdl.handle.net/1721.1/115665
Arithmetic properties and decomposability of Jacobians
Park, Soohyun, S.M. Massachusetts Institute of Technology
We first give an overview of methods used to study the decomposability of Jacobians of curves over the complex numbers. This involves studying the action of a finite group on an abelian variety in general. Next, we use methods for point counting properties of curves over finite fields to study the decomposability of Jacobians over number fields and finite fields. For example, we show that the genus of curves over number fields whose Jacobians are isomorphic to a product of elliptic curves satisfying certain reduction conditions is bounded and give restrictions on curves over number fields whose Jacobians are isomorphic to a product of elliptic curves.
Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 27-29).
2018-01-01T00:00:00ZList coloring in general graphs
http://hdl.handle.net/1721.1/112878
List coloring in general graphs
Sengupta, Rik
In this thesis we explore some of the relatively new approaches to the problem of list-coloring graphs. This is a problem that has its roots in classical graph theory, but has developed an entire theory of its own, that uses tools from structural graph theory, probabilistic approaches, as well as heuristic and algorithmic approaches. This thesis details two approaches one can take to understand list-coloring and prove results for several classes of graphs; one of them is to use the idea of graph kernels, and the other is to look at list-edge-coloring. In this thesis we present the state-of-the-art research on these two problems. We begin by setting up definitions and preliminaries, and then go into each of these two topics in turn. Along the way we briefly mention some of the very new research on the topics, including some new approaches developed for the purpose of writing this thesis. We finish with a survey of some of the major open problems that still remain in the area.
Thesis: S.M., Massachusetts Institute of Technology, Department of Mathematics, 2015.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 30-31).
2015-01-01T00:00:00ZStatistical models and mental health: an analysis of records from a mental health center
http://hdl.handle.net/1721.1/101302
Statistical models and mental health: an analysis of records from a mental health center
Kaplan, Edward Harris
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE; Bibliography: leaf 67.
1982-01-01T00:00:00ZRewriting rules applied to the formation of strategy in games,
http://hdl.handle.net/1721.1/95542
Rewriting rules applied to the formation of strategy in games,
Lewis, Clayton
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1968.; Bibliography: leaf 27.
1968-01-01T00:00:00Z