This course is suitable for advanced undergraduate students and master students.

The only Prerequisite: Algebra II.

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.

Course material

We will use Pierre Samuel's book (the old version in 1970) "Algebraic Theory of Numbers" (Chapters 1 to 4 only) as a guiding book. (We will use materials from other sources as well)

The course book that we use is not available in university library. It is a rather old book (published in 1970), and is difficult to find. Here I put a link to find a pdf scan (I found it a year ago from a professor's course webpage, but the link disappeared). Please use it for this course only, and do not distribute the link.

Exams
There will not be exams.
There will be exercises. To pass the course, you need to score 50% on the total exercises.
There are no different grades, just passed or non-passed.

My email address: hui.gao@helsinki.fi
My Office: Exactum A423
My personal homepage: https://sites.google.com/site/huigaomath/home