Blumberg's Mathematics

Welcome to the pages for the July, 2000 edition of "Foundations of Mathematics," a four-week course offered in the College Preparation Program at Columbia University, as part of the Summer Program for High School Students. The primary goal of this course is to introduce students to varieties of, and approaches to, higher mathematics that they may not have experienced in high school. As you can see from the syllabus, the course is fairly intensive, meeting twice each week for two-hour sessions, so admittedly the development of college-level stamina is a goal of the course as well.

The purpose of this web site, which will be maintained throughout the course, and then be available to students during the year, is to help students with their work, to encourage them to learn more about the material we're studying, to foster additional community between the students in different sections of the course, and to provide a resource that will (I hope) continue to be useful after the four weeks we were all at Columbia together. Although the Columbia program does not provide students with personal computer accounts, students are able to use public ColumbiaNet terminals in the libraries, dormitories and other buildings at the University, as well as some networked computers in the Lewisohn Hall labs of the Division of Special Programs. Each week I will post my notes at this site, in advance of the class sessions, as well as copies of the homework assignments. Answers to the homework sets were posted too, once the due date had passed. Similarly, the final exams will posted after the last final exam had been given. The site also includes a Reference Page that is meant to facilitate further explorations of the material covered in this short course.

If you have any questions, comments or suggestions, I would be happy to hear from you. Send mail to

What's Currently Available?:

July 2001 Note: During the four weeks of July, the answer keys to the homework sets for all previous years (1996-2000) will not be accessible.

Also available is the questionnaire about technology and education, with questions for students and parents, that is distributed to all students in the course during the first week of classes (the link is to a PDF file).

© 2000 Roger B. Blumberg