At any given time, the Number Theory Group has two or more postdocs, and up to 10 graduate students. Comments are closed. Research Paper Topics … The research of the number theory group encompasses classical and algebraic number theory, computational number theory, and especially the modern subject of arithmetic geometry. Duke is a leading analytic number theorist, known for many basic contributions, including the settling, using modular forms, of a well-known equidistribution problem dating back to Gauss. We have large groups of researchers active in number theory and algebraic geometry, as well as many individuals who work in other areas of algebra: groups, noncommutative rings, Lie algebras and Lie super-algebras, representation theory, combinatorics, game theory, and coding. A prerequisite for all of this research is Math 371, and several topics would … Whether it is on biology, physics, science, literature, history, or psychology, this approach works at all levels of education. On the other hand, recent applications of arithmetic geometry to communications protocols (such as strong cryptography and error correcting information transmission schemes) have brought the tools of the field to bear on crucial problems of Internet technology. Are there positive integers (a,b,c) satisfying a^n+b^n=c^n when n>2?) This assignment was supported with suggested/scheduled individual weekly meetings with me of 30 minutes to one hour per student to discuss progress and answer questions.These projects were developed as final projects for the Graduate Number Theory course on Modular Forms at the University of Georgia, which I taught in Spring 2009. topics in number theory MATH690-05.01 A selection of topics from algebraic number theory, arithmetic geometry, automorphic forms, analytic number theory, etc. The group has 5 permanent faculty: Don Blasius, William Duke, Haruzo Hida, Chandrashekhar Khare, and Romyar Sharifi. Undergraduate research with Dr. Doud can include topics such as modular forms with connections to Galois representations, diophantine equations, elliptic curves, and LLL-reduced lattices. That said, all the projects I am likely to suggest are in number theory. This is a challenging pre-algebra course. [A2A] As a high schooler, you likely don't have the prerequisites to do actual mathematical research. Blasius has made basic contributions to the special values of L-functions, and pioneered, with J. Rogawski, the use of endoscopy in the study of Galois representations. Another way of choosing the best research paper topic is based on the subject, whether you are a college or high school student.
These projects were developed as final projects for the Undergraduate Number Theory course at Duke University, which I taught for four consecutive Spring semesters (2004-2007). Number Theory – Grades 6 & 7* *Refers to the level of mathematics and not to the actual age. No new results are expected of them. For more information about the Number Theory group, please consult their The number of Fields Medals (the mathematical equivalent of the Nobel prize) awarded for work in the area is a testament to its centrality in modern fundamental mathematics. explaining and proving their main theorem) and also to give a one hour final presentation to their peers (fellow undergraduates in the class). If the student ... "Generalizing the Relation between the 2-Domination and Annihilation Number of a Graph", Honors Thesis. How can one explicitly find all the solutions of an explicit polynomial equation in two variables? There is a weekly number theory seminar and typically several ongoing instructional seminars devoted to the study of current research papers or topics, and the presentation of research … This assignment was supported with suggested/scheduled individual weekly meetings with me of 30 minutes to one hour per student to discuss progress and answer questions.These projects were developed as final projects for the Graduate Number Theory course on Modular Forms at the University of Georgia, which I taught in Spring 2009. There is a weekly number theory seminar and typically several ongoing instructional seminars devoted to the study of current research papers or topics, and the presentation of research of group members at all levels. The research of the number theory group encompasses classical and algebraic number theory, computational number theory, and especially the modern subject of arithmetic geometry.Arithmetic geometry is the study of number-theoretic problems informed by the insights of geometry—among them algebraic geometry, topology, differential geometry, and discrete geometries related to graph theory and group theory.
Students were asked to choose a “serious topic in Number Theory” (of which the projects were my suggestions with useful references) to write a final paper of at least 10 pages explaining their topic (i.e. Students were asked to choose a “serious topic in Number Theory” (of which the projects were my suggestions with useful references) to write a final paper of at least 10 pages explaining their topic (i.e. explaining and proving their main theorem) and also to give a one hour final presentation to their peers (fellow graduate students in the class). Where the work features as part of a broader write-up, the link is under ``description".