MATH 195 - Class Webpage
Advanced Topics in Mathematics:
Transcendental Number Theory - Spring 2026
General information
Time and place:
T
Th 9:35 - 10:50 am, RN 105
Instructor:
Lenny Fukshansky
Office:
Adams 218
Phone:
(909) 607 -
0014
Email:
lenny@cmc.edu
Office hours:
TW 4:00 - 5:00 pm, Th 1:00 - 2:00 pm, or by appointment
Course
announcement: PDF
Textbook / lecture notes: to be provided
Prerequisite: Familiarity with Abstract
Algebra (MATH 171/172) and some basic Analysis (MATH 131/135) is
desirable. 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 irrational and
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 see some classical irrationality proofs and
discuss such celebrated results as Dirichlet’s theorem,
Liouville’s construction of the first transcendental number,
transcendence of e and π and the more general
Lindemann-Weierstrass theorem, Thue-Siegel-Roth theorem, Siegel's
lemma, Schanuel's conjecture and its ramifications, and other
related topics.
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
The following are basic rules that all students should follow in
order not to disturb the class.
- Please make sure to turn off or silence your cell phones and
any other devices that make noise before entering class. Please
do not text or multitask in any way during the lecture: you are
expected to focus and pay full attention during our meetings.
- 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 without record.
- March 14-22, Saturday
- Sunday: Spring break.
- April 17, Friday: Last day to opt for CR/NC grading
in elective courses; last day to withdraw voluntarily from a
full semester course with a grade of "W".
- May 5, Tuesday:
Last class meeting.
Announcements
There
will be no class on February 24 and 26. Make up
classes will be arranged as needed.
The instructor reserves
the right to make changes to the class policies.