Undergraduate Summer School Mini-Courses (May 21-25, 2013) Important: Arrival day is May 20th with an orientation session at 4 pm
Undergraduate Session Notes
*We would like to thank Daniel Hast for these class notes.
• p-adic numbers and p-adic integration, Margaret M. Robinson (Mt. Holyoke College). This course is an introduction to Igusa local zeta functions. SYLLABUS
Example, Resolution, Slides
• Tropical geometry, Dustin Cartwright (Yale University). Tropical geometry is a way of studying algebraic varieties through their tropicalizations, which are combinatorial and polyhedral objects. I will give an introduction to tropical geometry and its applications to singularities and enumerative problems. SYLLABUS
Problems - Day 1, Problems - Day 2, Problems - Day 3, Problems - Day 4
• Singular Learning Theory, Shaowei Lin (Institute for Infocomm Research, A*STAR Singapore, previously from UC Berkeley)". Many difficult problems in machine learning are victims of the curse of singularities. As the big data becomes more important, the key mathematical issues need to be analyzed at a deeper level. In this course, we give a brief introduction to singular learning theory, a powerful geometric approach recently developed by Sumio Watanabe. No prior knowledge of statistics is required. SYLLABUS
Problems - Day 1, Problems - Day 2, Problems - Day 3, Problems - Day 4, PowerPoint 1, PowerPoint 2, PowerPoint 3
Requirements: It is expected that participants have had previous exposure to abstract algebra.
Please feel free to contact us at cmnd@nd.edu with any questions.