Undergraduate Summer School 2013

The Undergraduate Summer School provides opportunities for talented undergraduate students to enhance their interest in mathematics. This program is open to undergraduates at all levels, from first-year students to those who have just completed their undergraduate education. There will be many organized activities, with some specifically targeted at students at the introductory level and others at more advanced students. There will also be time for study groups and individual projects guided by advisors, as well as other activities.

The 23nd Annual PCMI Summer Session will be held June 30 – July 20, 2013.

Click HERE to apply to the Undergraduate Summer School program.

 

2013 Course Descriptions:

Basic Course: Curvature of space and time

Iva Stavrov, Lewis & Clark College.

Prerequisites:

Students should have completed a minimum of one course in each of:

  • linear algebra,
  • multivariable calculus,
  • ordinary differential equations,
  • one upper-division proof-based course.

Familiarity with ∊‌–∂ proofs is required; a course in real analysis or topology is strongly recommended.

Abstract:

The goal of this course is to develop an understanding of curved geometries and the role differential equations play in the study thereof. Special attention is given to examples arising from general relativity.

 

Advanced Course: Introduction to geometric differential equations

Paul T. Allen, Lewis & Clark College.

Prerequisites:

Students should have completed a minimum of one course in each of:

  • linear algebra,
  • multivariable calculus,
  • ordinary differential equations,
  • real analysis or advanced calculus.

Abstract:

Many geometric problems can be addressed by studying associated differential equations which, due to their geometric origins, often have interesting analytic features. In this course we explore, by means of several examples, the rich interplay between geometry and differential equations. We emphasize the extent to which analytic results, and difficulties, concerning differential equations can be interpreted in a geometric light. The course concludes by examining some current topics of research in geometric analysis.