Tufts Spring Break, Mar 23-25, 3-5pm
Prerequisites
Undergraduate real analysis or graduate standing in engineering/computer sciences/mathematics or consent of instructor
Course description
Measure theory plays a critical role in fields such as computer science, engineering, and statistics, because it provides a theoretical framework for modeling uncertainty in complex situations. In this workshop, we address questions such as:
- What is measure?
- How do you integrate against measure?
- How does Lebesgue integration (aka abstract integration) compare to Reimann integration?
- How can we “change measure”, and what does it mean to take the derivative of measure w.r.t another measure? (This is the Radon-Nikodym Theorem.)
- What are the different “modes of convergence” ?
Course goal
To provide a helpful theoretical grounding in introductory measure theory. The course will be mathematical in nature, but targets engineers, computer scientists, and statisticians.
Format
We will use theorems, proofs, examples, pictures, language, and discussion to help make the main ideas tangible. Each session will be divided up into approximately 20 minute blocks, so that we can toggle between presentation and interactive learning.
Primary Reference
The primary reference is: Probability and Measure Theory (2nd Edition), Robert Ash and Catherine Doleans-Dade. This is a rigorous mathematics textbook, but it is written for a target audience that includes engineers, statisticians, and computer scientists.
Online
Mike Wojnowicz