Difference between revisions of "Topology and Geometry"

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==content==
==content==
{{:Lecture content:Topology and Geometry 1}}
{{:Lecture content:Topology and Geometry 2}}
{{:Lecture content:Topology and Geometry 3}}
{{:Lecture content:Topology and Geometry 4}}
{{:Lecture content:Topology and Geometry 5}}
{{:Lecture content:Topology and Geometry 6}}
{{:Lecture content:Topology and Geometry 7}}
{{:Lecture content:Topology and Geometry 8}}
{{:Lecture content:Topology and Geometry 9}}
{{:Lecture content:Topology and Geometry 10}}
{{:Lecture content:Topology and Geometry 11}}
{{:Lecture content:Topology and Geometry 12}}
{{:Lecture content:Topology and Geometry 13}}
{{:Lecture content:Topology and Geometry 14}}
{{:Lecture content:Topology and Geometry 15}}


#[[Lecture:Topology and Geometry |Lecture 1]]
#[[Lecture:Topology and Geometry 2|Lecture 2]]
## Solving problem by deformation
## Understanding by turning it to a higher dimension
## Introduction to Basic Building Blocks of Topology and Geometry
### n-ball <math>B^n</math>
### (n-1)-sphere <math>S^n , n-1</math> (Don't know why I can't write the )
### what is the different between circle and disk
#[[Lecture:Topology and Geometry 3|Lecture 3]]
## The Operation of I:product
### m-cube <math>I^m</math>
## m-torus <math>T^m</math>
## The multiplication of shape in Topology and Geometry
## Quotient in topology
### all kinds of quotient example
### using cut to understanding quotient
#[[Lecture:Topology and Geometry 4|Lecture 4]]
## Quotient in topology
### using cut to understanding quotient
## Introduction to <math> \Sigma g </math> and <math> Ng </math>
## [[Homeomorphism]]
#[[Lecture:Topology and Geometry 5|Lecture 5]]
##The transformation between  <math> \Sigma g </math> and <math> Ng </math>
##Overflow
##The L dimension object vs K dimension object in M dimension
#[[Lecture:Topology and Geometry 6|Lecture 6]]
#[[Lecture:Topology and Geometry 6|Lecture 6]]
##[[Isotopic]]
##[[Isotopic]]
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Some interesting websites<ref>Gaurish, Gaurish4Math on Topology ,https://gaurish4math.wordpress.com/tag/tadashi-tokieda/, last accessed: July 22, 2021</ref> that referred to this lecture series.
Some interesting websites<ref>Gaurish, Gaurish4Math on Topology ,https://gaurish4math.wordpress.com/tag/tadashi-tokieda/, last accessed: July 22, 2021</ref> that referred to this lecture series.
<ref>{{:Lecture:Topology and Geometry 1}}</ref>


=References=
=References=

Latest revision as of 13:49, 26 July 2021

Introduction to Topology and Geometry

This is a course that Henry and Ben are studying during 2021.

content

Lecture 1: Mobius Strip

  1. Mobius strip
  2. In Topology and Geometry There are three points to remember.
    1. There is so much more to mathematics than numbers and formulas. (For example, there is pictorial thinking)
    2. Always draw pictures whenever you work on mathematics.
    3. There is so much more to pictures than photos of objects.


Lecture 2

  1. Solving problem by deformation
  2. Understanding by turning it to a higher dimension
  3. Introduction to Basic Building Blocks of Topology and Geometry
    1. n-ball
    2. (n-1)-sphere (Don't know why I can't write the )
    3. what is the different between circle and disk


Lecture 3

  1. The Operation of I:product
    1. m-cube
  2. m-torus
  3. The multiplication of shape in Topology and Geometry
  4. Quotient in topology
    1. all kinds of quotient example
    2. using cut to understanding quotient


Lecture 4

  1. Quotient in topology
    1. using cut to understanding quotient
  2. Introduction to and
  3. Homeomorphism


Lecture 5

  1. The transformation between and
  2. Overflow
  3. The L dimension object vs K dimension object in M dimension

Lecture content:Topology and Geometry 6 Lecture content:Topology and Geometry 7 Lecture content:Topology and Geometry 8 Lecture content:Topology and Geometry 9 Lecture content:Topology and Geometry 10 Lecture content:Topology and Geometry 11 Lecture content:Topology and Geometry 12 Lecture content:Topology and Geometry 13 Lecture content:Topology and Geometry 14 Lecture content:Topology and Geometry 15




  1. Lecture 6
    1. Isotopic
    2. The relationship between isotopic and homeomorphic
    3. outside the shape inside the shape
    4. The positive and negative intersection
      1. There is no tangent vector intersection in Topology
  2. Lecture 7
    1. The positive and negative intersection
      1. There is no tangent [vector] intersection in Topology
    2. Intersect transversely
  3. Lecture 8
    1. Jordan curve theorem
      1. If you have a closed curve which does not intersect itself it will divide the plan into two parts.
    2. Fixed Point Theorem
  4. Lecture 9
  5. Lecture 10
  6. Lecture 11
  7. Lecture 12
  8. Lecture 13
  9. Lecture 14
  10. Lecture 15



Also, we should make proper reference[1], and it will show at the Reference section.

Some interesting websites[2] that referred to this lecture series.

[3]

References

  1. ↑ Tokieda, Tadashi (12 May 2014). Topology and Geometry. 3/15. African Institute of Mathematical Sciences. 
  2. ↑ Gaurish, Gaurish4Math on Topology ,https://gaurish4math.wordpress.com/tag/tadashi-tokieda/, last accessed: July 22, 2021
  3. ↑ Tokieda, Tadashi (12 May 2014). Topology and Geometry. 1/15. local page: African Institute of Mathematical Sciences. 
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