Algebraic Number Theory I   Syllabus  (Graduate course,   Spring 2025)

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Professor: Yoonjin Lee

Office: Science Complex B313

Text Books:
Number Fields by D. Marcus, Springer
A Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics) by K. Ireland and M. Rosen (2nd ed.), Springer

Course requirements:
Elementary Number Theory,   Abstract Algebra I, II

Course Description:
Number Theory has been studied for its long and rich history, its wealth of easily accessible and fascinating questions and its intellectual appeal, but even for practical applications to Cryptology and Coding Theory in recent years. Algebraic Number Theory has many attractive and instructive topics. Throughout this course we study comprehensive and advanced concepts of Algebraic Number Theory, assuming students have some background of Elementary Number Theory and Abstract Algebra (Groups, Rings and Fields). The following topics plan to be covered throughout this semester even though some other topics may be added and some topics may be omitted.

Course Outline :
The Gaussian Integers, Integrality
Integrality, Review of some Field Theory
Traces and Norms, Discriminants, Integral Bases
Integral Bases
Ideals, Dedekind Domains
Lattices, Minkowski Theory

Grading Scheme:
HW Assignments, Quizzes, Presentation 50%
Final Exam 50%

Schedule of Exams:
Final Exam:   June 18, 2025 (Wed.)

Grades and policy:
*  You will be evaluated throughout the whole semester by means of a comprehensive Final Exam, Homeworks, Quizzes and Presentations.
*  No make-up exams will be given. No late homeworks will be accepted.

Class expectations:
Students are expected to attend all the lectures. You have to spend enough time for reviewing the material on a regular basis. The best way to learn the material is to spend enough time thinking about the homework problems virtually every day as our class progresses. In addition, you are encouraged to discuss the homework assignments with others, but you must write up your own solutions and turn them in individually.