## 以下講義適合數學系高年級或碩士生

• In this very short note, our objective is to classify quadratic forms over the field of rational numbers, i.e., the Hasse-Minkowski theorem.
Prerequisite for reading this note is elementary knowledge of the p-adic numbers.
• A Short Course on Linear Representations of Finite Groups
• The primary goal of this note is to introduce a beginner to the finite dimensional representations of finite groups.
Prerequisite for reading this note is basic group theory and linear algebra.
• A note on Complex Representations of GL(2,Fq)
• This note is a sequel to ``A Short Course on Linear Representations of Finite Groups''. We concentrate on the representations for the groups of invertible 2 by 2 matrices over finite fields.
Prerequisite for reading this note is ``A Short Course on Linear Representations of Finite Groups''.
• A Brief Introduction on Local Class Field Theory
• We introduce the Local Class Field Theory and use Lubin-Tate extension to prove the ``Existence Theory''.
Prerequisite for reading this note, apart from Galois theory, is merely a standard introduction to the theory of local fields.
• Factorization in Commutative Rings
• We show that an Euclidean domain is always a principle ideal domain and a principle ideal domain is always a unique factorization domain. We also provide examples to show that the converse of these statements are not true.
This note is suitable for college students who knows basic ring theory.
• 一個 Zariski 的定理
• 介紹證明 Hilbert's Nullstellensatz 所需的 Zariski 的定理. 並介紹 algebraic element 和 integral element 之間的關係以及 vector space 和 module 之間的關係.
基本知識需要知道大學代數中 ring 和 field 的性質.
以下是摘錄自一些書的檔案並不是完整的講義
• Problems in Algebraic Number Theory
• 利用作習題的方式介紹一些代數數論的基本知識。 預備知識需對代數有基本的認識。
• Introduction to Coding Theory
• 編碼學的簡介﹝大部分的定理並無證明﹞。 預備知識僅線性代數及一些有限體的基本知識，適合大三以上同學。