# Math 77. Advanced Topics in Algebra: Algebraic Number Theory

Spring 2012

• Instructor:         Enrique Treviño

• Lectures:           TR 1:15pm-2:30pm in Science Center 145

• Office Hours:    Tuesday and Thursday from 3pm to 5pm and by appointment.

• Office:               Science Center 139

• Email:

• Phone Ext.:        #5764

Announcements

Homework 8 is due Thursday April 19, 2012 by 5pm if class is attended, otherwise by 1:15pm. The homework consists of the following exercises:
Chapter 9: 1, 3
Chapter 10: 1, 3
and the following problem.

Homework 7 is due Thursday April 12, 2012 by 5pm if class is attended, otherwise by 1:15pm. The homework consists of the following exercises:
Chapter 6: 1
Chapter 7: 6
Chapter 8: 1, 2, 3

Homework 6 is due Thursday March 29, 2012 by 5pm if class is attended, otherwise by 1:15pm. The homework consists of the following exercises:
Chapter 4: 8, 12, 16
Chapter 5: 1, 2, 9, 11
Problems recommended but not needed to turn in:
Chapter 4: 11, 12, 18
Chapter 5: 3,4,5, 7, 15

Textbook

Algebraic Number Theory and Fermat's Last Theorem (3rd edition) by Ian Stewart and David Tall.

Topics we will cover

Our goal in this class will be to learn enough number theory to be able to show Kummer's theorem in the first case of Fermat's Last Theorem. To get there, we will learn about algebraic numbers, number fields, unique factorization domains, factorization into ideals, etc. We will also cover other number theoretic topics such as Minkowski's theorem (the geometry of numbers) and its use on the four squares theorem. We might also do an introduction to elliptic curves.

The course grade will be based on:
Homework 30%,
Midterm (take-home) 20%,
Presentation 20%,
Final Exam (take-home) 30%.

Homework

There will be written homework due roughly every week. Collaboration in the homework is permitted, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.

Presentation

Each student will give a presentation on a topic of their choosing (it has to be approved by me). I will post several options on the website later in the semester and the student is free to suggest more. The length of the presentation will be depend on the topic but it should be at least 20 minutes long and at most the length of one class (75 minutes).

Accommodations Statement

If you believe that you need accommodations for a disability, please contact Leslie Hempling in the Office of Student Disability Services, located in Parrish 130, or e-mail lhempli1 to set up an appointment to discuss your needs and the process for requesting accommodations. Leslie Hempling is responsible for reviewing and approving disability-related accommodation requests and, as appropriate, she will issue students with documented disabilities an Accommodation Authorization Letter. Since accommodations may require early planning and are not retroactive, please contact her as soon as possible. For details about the Student Disabilities Service and the accomodations process, visit http://www.swarthmore.edu/x7687.xml.

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Leslie Hempling in the Office Of Student Disability Services.