Course Calender

Course Calender

SAYT1014 Towards Modern Algebra (EPYMT) 數學英才精進計劃 ── 近世代數初探

Key facts for Summer 2018:

Lecturer: Dr. LI Chun Che Charles
Date : 16, 17, 19, 20, 23, 24, 26, 27, 30 July 2018
Examination Date : 2 August 2018
Time :To be announced
Tuition fee :To be announced

Go to official website

The central themes of classical algebra includes the study of polynomials, finding roots of polynomials, solving system of equations, Compass-and-straightedge construction. In response to these problems, modern abstract algebra was introduced during 19th century.

In this course, we start with classical algebra topics which include using radicals to solve cubic and biquadratic equations, bisection method, compass-and straightedge constructions, construction of regular-17-gon, relationship between roots and coefficients, symmetric polynomials, closed formula of sum of powers, among other things.

We will then introduce abstract algebraic structures including groups, fields, vector spaces with emphasis on concrete examples. We will introduce concrete math objects, including complex numbers, quadratic fields, quaternions, polynomials, additive and multiplicative group mod n, permutation groups, elliptic curves, finite fields, among other things, to illustrate the concepts of the algebraic structures.

經典代數以多項式的研究、尋找多項式的根、求解方程組,圓規直尺作圖等問題為中心課題。針對這些問題,數學家在19 世紀被引入現代抽象代數。

在這個課程中,我們從經典代數開始,討論如何使用根式解三次方程及四次方程、使用二分法求解方程、圓規直尺作圖問題、利用圓規直尺構造正則十七邊形、根與係數之間的關係、對稱多項式、求 k 次和公式等。

接著我們將引入抽象代數結構,包括群,域,向量空間。我們將介紹具體的數學對象,包括複數、二次域、四元數、多項式、模為 n 的加法和乘法群、置換群、橢圓曲線、有限域等,來說明這些代數結構。


Organising units:   Department of Mathematics, CUHK
Category:   Category I – University Credit-Bearing
Learning outcomes:   Upon completion of this course, students should be able to:
  1. Know how to manipulate polynomials, solve polynomials, relations of roots and coefficients;
  2. Understand algebraic structures: groups, fields, vector spaces;
  3. Understand concrete examples of groups, fields, vector spaces;
  4. Learn how to manipulate algebraic structures.
Learning Activities:
  1. Lecture
  2. Exercise and assignment
Medium of Instruction:   Cantonese supplemented with English
Assessment:   Essay test or exam
Recognition:   No. of University unit(s) awarded: 1
* A certificate will be awarded to student who fulfilled the course requirements.
Expected applicants:   Students who have high competence in abstract mathematical reasoning, and are promoting to Secondary 4 or Secondary 5
Organising period:   Summer 2018
Application method:   SAYT Online application
Official website: