課程資訊
課程名稱
幾何概論
INTRODUCTION TO GEOMETRICAL METHODS AND THOUGHT 
開課學期
97-2 
授課對象
理學院  數學系  
授課教師
蔡宜洵 
課號
MATH5422 
課程識別碼
221 U5380 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期三7,8,9(14:20~17:20) 
上課地點
新401 
備註
總人數上限:50人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/972geom 
課程簡介影片
 
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課程大綱
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課程概述

This is a one term course.
Chapter 1 begins with a reflection on Euclidean Geometry as a revolutionary step in human civilization, then on criticisms of logical structure of Euclid's Elements, and finally on reformulation of the axiom system given by D. Hilbert in 1899.
Chapter 2 starts with the so called Absolute Geometry-geometry without Euclid's parallel axiom, and a few equivalent forms of parallel axioms. It discuss Non-Euclidean Geometry before the fomulation of Lobachevsky and Bolyai.
Chapter 3 focus on the most remarkable invention of Lobachevsky and Bolyai, namely the idea of horocycles and horospheres, its use in Non-Euclidean geometry, including explicit formula for angle of parallelism etc.
Chapter 4 discuss Spherical Geometry in both Euclidean and Non-Euclidean case, problems on consistency and Beltrami-Klein model and Poincare model.
Chapter 5 shall study in some detail B. Riemann's famous lecture on "On the hypotheses which lie at the foundations of geometry" in 1854, generally own as Riemann' s Habilitation lecture. 

課程目標
Course Goal:
It was said that the creation of Non-Euclidean geometry was the most consequential and revolutionary step in mathematics since Greek times. In the book "Geometry: Euclid and beyond" R. Hartshorne in preface wrote" I hope this material will become familiar to every student of mathematics, and in particular to those who will be future teachers". The planning of the current course was partially inspired by these remarks. Hopefully it may fill in some gaps in current mathematics curriculum. 
課程要求
Knowledge from Advanced Calculus (real number system) and Linear algebras would be helpful, but not absolutely necessary. 
預期每週課後學習時數
 
Office Hours
另約時間 
參考書目
Kulczycki, S., "Non-Euclidean Geometry";
Greenberg, M.J., "Euclidean and non-Euclidean geometry, Development and History"
 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
期中考 
40% 
 
2. 
期末考 
40% 
 
3. 
隨堂測驗 
0% 
 
4. 
作業 
20% 
 
5. 
報告 
0% 
 
 
課程進度
週次
日期
單元主題
第9週
4/15  期中考 
第17週
6/10  最後一堂課 
第18週
6/17  提交essay
期末考