Quadratic Forms over Q

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,F_q)

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.

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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。