MATH 195 - Class Webpage

Advanced Topics in Mathematics: Transcendental Number Theory - Spring 2015

General information

Time and place:    T Th 2:45 - 4:00 pm, RN 105
Instructor:             Lenny Fukshansky
Office:                   Adams 218
Phone:                   (909) 607 - 0014
Email:                    lenny@cmc.edu
Office hours:         (tentatively) T Th 4:00 - 5:30 pm, or by appointment

Course announcement: PDF

Lecture notes: PDF

Midterm: PDF LaTeX

Prerequisite: MATH 60 is required, but either MATH 171 or MATH 131 is recommended, mainly for the purposes of mathematical maturity. The necessary ideas from algebra and analysis will be covered in class, as needed.

Material to be covered:

A selection of classical topics from the theory of transcendental numbers and the closely related area of Diophantine approximations. These are beautiful and exciting branches of mathematics, which have truly flourished in the 19th and 20th centuries and have been distinguished by several Fields Medal awards. We will discuss such celebrated results as Dirichlet’s theorem, Liouville’s construction of the first transcendental number, transcendence of e and π and generalizations, Thue-Siegel-Roth theorem, and many others.

Grading policy

Class attendance and reading the material in the lecture notes as we progress are required parts of the course. There will be a number of suggested homework exercises throughout the semester, which will not however be collected. The grade will be based on one take-home midterm exam (50%) and on the final project (50%).

The grading scale used for this class will be:

95-100% = A, 90-94% = A-
85-89% = B+, 80-84% = B, 75-79% = B-
70-74% = C+, 65-69 % = C, 60-64% = C-
57-59% = D+, 52-56% = D, 50-51% = D-
0-49% = F

I reserve the right to introduce a curve (up or down) at the end of the semester depending on the class's overall performance.

Special policies

Please notice that confidentiality reasons prevent me from providing you with any information regarding your performance in this class except for in person. Please DO NOT email or call with any kind of grade inquiries.

The following are basic rules that all students should follow in order not to disturb the class.

Please make sure to turn off all you cellular phones, pagers, and any other devices that make noise before entering class.
Please do not come late or leave early; if on some occasion it is necessary and cannot be avoided, please do it in a way that does not disturb the class.

Important dates

February 2, Monday: Last day for adding courses for the Spring semester.

March 12, Thursday: Last day to drop courses; last day to opt for CR/NC grading in elective courses.
March 16-20, Monday-Friday: Spring break.
May 6, Wednesday: Last class meeting.

Announcements

Please notice that confidentiality reasons prevent me from providing you with any information regarding your performance in this class except for in person. Please DO NOT email or call me with any kind of grade inquiries.

The instructor reserves the right to make changes to the class policies.

All printed handouts and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.