Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
1605 Jefferson Park AveCharlottesville, Virginia 22904
Zero-cycles over arithmetic fields and reciprocity laws
Source: U.S. National Science Foundation (NSF)
June 01, 2020 – May 31, 2023
A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320.
Review of topics from Math 3351 including vector spaces, bases, dimension, matrices and linear transformations, diagonalization; however, the material is covered in greater depth with emphasis on theoretical aspects. The course continues with more advanced topics including Jordan and rational canonical forms of matrices and introduction to bilinear forms. Additional topics such as modules and tensor products may be included. Prerequisite: MATH 3351
This course provides a framework for the completion of a Distinguished Major Thesis, a treatise containing an exposition of a chosen mathematical topic. A faculty advisor guides a student through the beginning phases of the process of research and writing. Prerequisite: Acceptance into the Distinguished Major Program.
Reading and study programs in areas of interest to individual students. For third- and fourth-years interested in topics not covered in regular courses. Students must obtain a faculty advisor to approve and direct the program.
Studies groups, rings, fields, modules, tensor products, and multilinear functions. Prerequisite: MATH 5651, 5652, or equivalent.
Studies the foundations of algebraic geometry.
Theory of number fields and local fields, ramification theory, further topics as chosen by instructor.