Teaching Statement

by Jim Pitman Departments of Statistics and Mathematics The University of California, Berkeley The most current version of this statement is available online with hyperlinks at http://stat-www.berkeley.edu/users/pitman/teaching.html

Introduction Following are some remarks on courses I have taught in the last few years, my general teaching philosphy, and my interest in providing open access to expository material.

Statistics 134, Concepts of Probability This is a a one semester course aimed primarily at students who have done a year of calculus. Only a minority of these students, however, have any real facility with calculus. To ensure that all students leave the course with at least some basic understanding of probability concepts unobscured by technical difficulties, in the first half of the semester I emphasize fundamental ideas of probability in a discrete setting, without reliance on calculus. Then I develop these ideas further using calculus tools in the second half of the semester. My experience is that students learn more from intuitive explanations, diagrams and examples than they do from theorems and proofs. In lectures I deal quickly with the main points of theory, then spend most class time on problem solving and applications of the main ideas. Perhaps most valuable thing for students to learn (and the hardest thing to teach) in a course like this, is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more students see this happen in class, and the more they do it themselves in exercises, the better they grasp the basic ideas. I developed a textbook for this course based on the above philosophy, (Probability, Springer 1993) after almost ten years of class testing preliminary versions at Berkeley and other institutions. A very important part of this text is the large collection of problems it contains. These problems and their solutions have been incorporated into a database for the course which is accessible on the Statistics Department's computer system to teaching assistants and instructors. I am currently working on developing various online supplement to this textbook, such as a glossary. A preliminary form of software I have developed for this purpose, with content from Philip Stark's Glossary of Statistical Terms, can be seen at http://bibserver.berkeley.edu/cgi-bin/gloss.

Statistics 205, Probability Theory This is a graduate level introduction to probability theory. There are now a variety of textbooks available for this course. I follow my own development of the core material with reference to Durett's textbook for details and problems. The heart of this course is the weekly problem sets. Students typically find these challenging, as they often demand synthesis of ideas from various sources. Again, the emphasis on problem solving helps to actively engage the students in the material. Over the years, students have written up lecture notes from this course, most of which can now be seen on the course homepage: http://bibserver.berkeley.edu/205/ I am working on developing these notes into an interactive web-based resource, with hyperlinked cross references, which should be of great value as a teaching aid. As another resource for this course, I have developed a searchable database of problems from past PhD qualifying examinations in probability.

Open access to expository material I am interested in development of web-based resources as a means of showing students at various levels what career paths are available to them, and giving them overviews of various branches of knowledge, such as probability and stochastic processes, which are difficult to obtain from conventional textbooks. I see this as part of a broad program, which I am promoting across all of mathematics, and encouraging others to promote in further branches of science and human knowledge, to provide free online access to high quality expository and review material. That is intended both to assist in professional development, and to combat recent trends towards partitioning and privatization of knowledge. Last year, David Aldous and I collaborated with the IMS and the Bernoulli Society to launch the open access survey journal Probability Surveys which publishes survey articles in theoretical and applied probability. The style of articles may range from reviews of recent research to graduate textbook exposition. Articles may be broad or narrow in scope. The essential requirements are a well specified topic and target audience, together with clear exposition. We are in the process of launching a companion journal Statistics Surveys to provide a similar outlet in Statistics. I am working more broadly to promote the creation of similar survey journals in other branches of mathematics, and on software for indexing and navigating professional quality expository online material in mathematics. A first attempt at indexing software is provided by MatNav: A Mathematics subject Navigator. This mathematics subject navigator incorporates data from the 2000 Mathematics Subject Classification (MSC2000) provided by Zentralblatt MATH[ZM]. The navigator also recognizes the cruder classifications provided by arXiv categories, the Open Directory Project, and the Core Subject Taxonomy for Mathematical Sciences Education which has been approved by a diverse group of people interested in developing digital libraries housing electronic resources in the mathematical sciences. The navigator provides links to searches over specific databases including MR, ZM, Google, Google Scholar, the Euler portal, and the Front to the Mathematics ArXiv. Links are also provided to a number of other online resources indexed by the MSC 2000, including Dave Rusin's Mathematical Atlas, Wikipedia, and Mathematics Online. The navigator is designed so it is simple to add links to any online resource which allows searches by subject keywords, or by keys of a subject taxonomy known to the navigator.

In the same vein, David Aldous, Dave Rusin and myself have agreed to develop Dave Rusin's Mathematical Atlas into an electronic journal of the same name, as indicated at http://bibserver.berkeley.edu/proposals/atlas.html. Together with suitable linking and navigation software such as provided by MatNav, we intend this to provide the encyclopedic index of mathematical subjects envisioned by the The Mathematics Survey Project http://mathsurvey.org/.

File translated from T_EX by T_TH, version 3.60.
On 1 Dec 2005, 08:50.