In Spring 2024 I am teaching: MA 753 Algebraic topology

In Spring 2023 I was teaching:

MA 407-001
Modern Algebra

  • LECTURES: Tuesday and Thursday 1:30pm-2:45pm in 2102 SAS
  • BRIEF DESCRIPTION: Modern algebra is the study of the structure of sets with operations on them.Common operations such as addition and multiplication are generalized to apply to sets such as matrices or polynomials. Topics include: groups, isomorphism theorems, generators and relations, group actions,fundamental theorem of finite abelian groups, and introductory ring and field theory

MA 591-001
Special Topics in Topology and Geometry and their Applications

  • LECTURES: Tuesday and Thursday 11:45am-1:00pm in 1220 SAS
  • BRIEF DESCRIPTION: What is the shape of the universe: is it curved or flat? How can we extract information from high-dimensional data? Which combinations of copy number aberrations of genes cause cancers? Answers to all of these questions hinge on the notion of shape, which is the central notion of the mathematical fields of Geometry and Topology. In order to get the answers we will build a set of mathematical tools and understand ideas from these areas such as curvature, homology, and category theory.
    Topology aims at studying intrinsic structures of a given object or space. It captures properties of an input object that cannot be removed without tearing the object apart. It is a powerful tool for describing essential features of shapes. On the other hand, geometry is the quantitative study of shape using lengths and angles. Recently, there has been a new trend in developing computational topological and geometric methods for data analysis. Such methods have been incorporated with statistics and machine learning tools and successfully applied in a broad range of fields including computer graphics (e.g, feature identification), visualization (e.g, contour trees), sensor networks (e.g, hole detection), machine learning (e.g, clustering), and computational biology (e.g. breast cancer genomics, lung topology).

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