 
Summary: A Survey of Modern Geometry  Spring 2011 Math Colloquium
Instructor: Alex Troesch
atroesch@umail.ucsb.edu
Faculty: Guofang Wei
wei@math.ucsb.edu
Time: Monday 4:00pm5:20pm
Old Little Theater 164B
The subject of geometry is considered to be one of the most intuitive areas of mathematics and questions
related to shape and distance have engaged thinkers since the earliest civilizations. Euclid's "Elements" gave
a definitive treatment of classical geometry over 2000 years ago, but for many that is where the story ends.
Geometric thought has a rich history which is often at the forefront of modern science, engineering, and current
mathematical research. This course is a seminar intended to engage students with a limited background in formal
mathematics as well as aspiring mathematicians by asking fundamental questions about geometric spaces and
the important properties which define and characterize them. We will address various answers to these questions
which have been studied throughout history. Additionally, we will explore the intuitive and counterintuitive
consequences of geometric ideas and their applications.
Grading: A maximum of two units may be earned in this course. One unit will be awarded for consistent
attendance, and one additional unit will be awarded for work on the homework assignments.
Homework: Each week a short problem set will be assigned, consisting from one to three problems of various
types. Each set is expected to be completed and turned in at the beginning of the next
