Class Meetings: M and W, 11:00-12:15, WDS 0104. See here for the schedule of classes and assignments.
Instructor: Prof. Jonathan Rosenberg
Office: Room 2114, Mathematics Building
campus phone: 55166
email: jmr@math.umd.edu
Mathematics is one of the greatest accomplishments of human civilization. This course will examine mathematics in a somewhat unusual way, not as a finished product to be studied out of a textbook, but as a process of discovery that has progressed for centuries and is still under development.
We will examine selected writings by great mathematicians from the past, such as Euclid, Newton, Gauss, and Hilbert. The course is not in any way intended as a substitute for more traditional math courses such as the calculus sequence. Instead, it will deal with questions which are rarely, if ever, treated in such courses, such as:
Students will be assigned works by famous mathematicians (short papers, letters, excepts from books, etc.) to read and present to the rest of the class for discussion. There will be no exams, but regular class participation is expected and one major paper will be required. This is a discussion seminar, not a lecture course.
The following texts are collections of papers (all in English or translated into English). They will be supplemented by additional papers and letters extracted from various mathematicians' collected works.
The following third text gives a good overview of mathematics history:
CORE: Mathematics & Formal Reasoning [MS]
The only prerequisite is four years of high-school level mathematics and an interest in finding out what mathematics is about. An interest in history or literature will also be useful. Ability to read a foreign language is not required, as all sources will be studied in English translation if not originally written in English. However, if you can read Latin, French, or German, that is an added bonus, since most of the course materials were originally written in one of those languages, and there is always an advantage to reading the original over a translation.
Students will be assigned works by famous mathematicians (short papers, letters, excerpts from books, etc.) to read and present to the rest of the class for discussion. There will be no exams, but regular class participation is expected, and a few short papers and one longer paper will be required. This is a discussion seminar, not a formal lecture course. Thus failure to attend class regularly will be penalized in assigning grades.
The course will be divided into six units, covering:
Probably we will spend the most time on units 3 and 4, but the exact allocation of time to the various units will be up to the class. As it is finalized, the schedule of classes and assignments will be posted here. See here for the schedule from the last time the course was taught. Within each unit, each class period will be devoted to a separate paper or text. Everyone in the class will be expected to read the text ahead of time, but one or two students will "prepare" it in detail and lead the class discussion. The role of the instructor will be to help students outside of class, to explain difficult points, and to help focus the discussion. After each class, the student(s) leading the discussion will be expected to prepare a written discussion of the text (1 or 2 pages should suffice) based on some of the points discussed in class. These written exercises should be turned in no later than one week after the class discussion of the text, and will be graded. Each student will probably serve as discussion leader 2 times during the semester.
Course grades will be based on class discussion, the short written exercises, and one major paper (on a topic chosen by the student in consultation with the instructor) to be turned in at the end of the semester.
Please go to Course Eval UM to fill in your course evaluation before Friday, May 11.