The well-known trace map on matrices can be generalized to a map on other algebraic objects. Undergraduates, graduates students and experts in Representation Theory, Commutative Algebra and Algebraic Geometry have been driving recent developments in the theory of trace modules and finding exciting new applications in all of these these fields. This course will serve as an introduction to mathematical research with the aim of producing original research in modern trace theory. Students in this tutorial will read and synthesize research papers, discuss the formation of research questions in pure mathematics, and engage in original mathematical research.
The Class: Format: tutorial
Requirements/Evaluation: oral presentations; writing assignments (summarizing papers, reflections on mathematical research, original research); participation in the course project
Prerequisites: Math 355
Enrollment Preferences: Juniors and Seniors
Distributions: Division III Quantitative/Formal Reasoning
QFR Notes: This is post-core math class; students will be required to produce mathematical proofs.