실체에 이르는 길(로저 펜로즈)

http://scienceon.hani.co.kr/archives/13582

 

preface

• 분수와 equivalence class 의 예

 

 

1 The roots of science

• the main thrust of this book has to do with the first of these mysteries: the remarkable relationship between mathematics and the actual behaviour of the physical world.

 

 

2 An ancient theorem and a modern question

• 피타고라스 정리
• 곡면의 미분기하학과 리만기하학
• * homogeneity (every point the same) and isotropy (every direction the same),

 

 

3 Kinds of number in the physical world

• 실수
  
  • p-adic number 를 안다면, 실수에 대해 더 많은 것을 생각할 수 있다
• 정수와 반입자
  
  • In fact, according to 20th-century physics, there is now a certain sense in which it is meaningful to refer to a negative number of physical entities. 
• 유리수와 물리의 관계는 아직 unclear

 

 

4 Magical complex numbers

• 복소수 소개

 

 

5 Geometry of logarithms, powers, and roots

 

 

7 Complex-number calculus