MATH 195 - Class Webpage

Advanced Topics in Mathematics: Geometric Number Theory - Spring 2019

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 exam: PDF LaTeX

Final exam: PDF LaTeX

Prerequisite: MATH 171 is required.

Material to be covered:

The goal of this course is to introduce geometric ideas underlining some classical arithmetic results. It turns out that many completely algebraic or arithmetic questions can be reformulated into this geometric framework. In this course, we will introduce Minkowski's fundamental convex body theorem and discuss some of its far-reaching applications and connections. Possible topics to be covered include lattices and quadratic forms, introduction to Minkowski's geometry of numbers, applications of geometry of numbers to Diophantine approximation and transcendence, Lagrange's four squares theorem, Minkowski-Hlawka theorem, finiteness of class number, and other related topics as time allows.

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 take-home final exam (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 4, Monday: Last day for adding courses for the Spring semester.
March 14, Thursday: Last day to drop courses; last day to opt for CR/NC grading in elective courses.
March 18 - 22 Monday-Friday: Spring break.
May 7, Tuesday: 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.