MATH 195 - First
Day Handout
Advanced Topics in Mathematics:
Algebraic Number Theory - Spring
2010
General information
The
class webpage is a good source for all class related information; in
particular, homework assignments will be posted on the class webpage
weekly.
Please check it regularly.
Textbook:
(Required) Algebraic Number
Theory and Fermat’s Last Theorem (3rd sub edition), by Ian
Stewart and David Tall (published by AK Peters, Ltd.)
Course description:
Algebraic Number Theory originated in 1637 with the legendary note by
Pierre de Fermat on the margins in his copy of ``Arithmetica” by
Diophantus:
It is impossible to separate a cube
into two cubes, or a fourth power into two fourth powers, or in
general, any power higher than the second into two like powers. I have
discovered a truly marvelous proof of this, which this margin is too
narrow to contain.
Since the publication of Fermat’s note, hundreds of professional
mathematicians and amateurs were trying to reproduce Fermat’s
miraculous proof. Although an actual proof of this statement was only
produced in 1994 by Andrew Wiles, numerous attempts to prove Fermat’s
claim played a crucial role in developing our modern understanding of
the algebraic theory of numbers. The goal of the present course is to
give an introduction to the subject and some of its methods.
Prerequisite:
MATH 172, or MATH 171 along with
instructor's consent
Material to be covered:
The topics will include algebraic number fields and rings of integers
along with a detailed study of their properties; discriminant, norm,
class number, and some partial cases of Fermat’s Last Theorem.
Additional topics may be covered if time permits.
Grading policy
Class attendance and reading the
material in the textbook as we progress are required parts of
the
course. There will be three problem sets assigned throughout the
semester, on which the grade for the course will be based (one third of
the grade per each problem set). These assignments and their due dates
will be posted on the class webpage as we progress. Late problem sets
will not be accepted.
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 and university policies
-
February 1, Monday: Last
day for adding courses for the Spring semester.
-
March
11, Thursday: Last day for all students (except for HMC) to
drop courses
in
the Spring semester (HMC drop deadline: April 16, Friday)
- March 15 - 19 (Monday - Friday):
Spring break
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.