Elementary algebraic number theory, Kevät 2017
Teacher: Hui, Gao
Scope: 5 cr
Topics: In this course, we study some basic notions and classical theorems in algebraic number theory. As the title "algebraic" suggests, we will need to build some tools from abstract algebra to study numbers. In fact, to prove our main theorems, we will also use techniques from "geometry of numbers". In this course, we will try to explain some of the most fundamental ideas and techniques in number theory, yet in a basic and accessible way. Some of these techniques find applications in other branches of mathematics as well.
Prerequisites: Algebra II.
- NOTE: This course will last just 1 period (7 weeks). There will not be any continuation in the 4th period.
- My personal homepage: https://sites.google.com/site/huigaomath/home
- My email address: email@example.com My Office: Exactum A423
week1: Noetherian rings and modules. (3.1 of Book). Chapter 1 of Book (modules over PID).
week2: Book, Section2.1 until almost end of 2.6. Exercise session on Friday.
week3: Section 2.7, 2.9. Then defined Dedekind domain. Had exercise session on Wednesday.
week4: finished Chapter 3. (Noetherian rings are already covered in week 1). Had exercise session on Monday.
week5: finishe proof of finiteness of class number; stated unit theorem. had exercise session on Mon and Fri.
week6, finished proof of unit theorem on Wed. Then start Zariski toplogy.
week7. finished Zariski topology, tensor product. Introduced roughly category, functor, sheaf, affine scheme. Talked about Fermat Last Theorem in the final lecture (almost 40 people attended the talk!)
Monday 14:15-16:00, BK106 Wednesday 14:15-16:00, BK106
We will use Pierre Samuel's book "Algebraic Theory of Numbers" (Chapter 1 to 4) as a guiding book. (We will use materials from other sources as well)
Did you forget to register? What to do?
- Homework 1 PDF file Due time: Before 13:00, Jan 26 (Thursday)
- HW 2.pdf Due: Before 13:00, Jan 30 (Monday)
- HW 3 corrected.pdf Due: Before 23:00, Feb 4 (Saturday)
- HW4.pdf Due: Before 16:00, Feb 10(Friday)
- HW 5.pdf Due: Before 16:00, Feb 15 (Wednesday)
- HW 6 corrected.pdf Due: Before 16:00, Feb 22 (Wednesday)
- HW7.pdf Due: Before 16:00, Feb 27(Monday) HW7 survey result.pdf
|3rd period||Fri||14:15-16:00||BK106||Hui Gao|
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