【区别：代数拓扑 (Algebraic Topology) 微分拓扑 (Differential Topology ) 微分几何 ( Differential Geometry ) 代数几何 (Algebraic Grometry ) 交换代数 (Commutative Algebra ) 微分流形 (Differential Manifold ) ？】月如歌：并不能理解什么叫做楼主所说的配对。我简要谈下我对于上述所列名词的理解。…
Sheaves do not belong to algebraic geometry:
Excellent video for the curious minds! Who cares about Topology such as Torus (aka donut) or Mobius Strip ? They can be used to prove difficult math such as the unsolved problem “Inscribed square/rectangle inside any closed loop”.
To understand the Topology on Loops, please view the lecture here : Homotopy (同伦) and the Fundamental Group (群) of surface.
拓扑: 两绳困绑, 只要一人翻手就能解脱。
1st speaker :
◇ History: Riemann discovered Topology on his papers left behind after death. He told friend Betti.
◇ Betti Number: number of
– ‘scissors’ cut to make a tree (in 2 dim),
– ‘drill’ cut to make a disc (in 3 dim).
◇ Evolution (bacteria, viruses) using Topology ‘Barcoding’ technique.
病菌(viruses / bacteria)是白骨精多变 (mutate), Topology (拓扑)是孙悟空的火眼金睛, 妖怪不能遁形, 骗得了常人, 骗不过老孙, “三打白骨精”。
◇ Liquid Crystal: Homology
Mathematics is divided into 2 major branches:
1. Analysis (Continuity, Calculus)
2. Algebra (Set, Discrete numbers, Structure)
In between the two branches, Poincaré invented in 1900s the Topology (拓扑学) – which studies the ‘holes’ (disconnected) in-between, or ‘neighborhood’.
Topology specialised in
– ‘local knowledge’ = Point-Set Topology.
– ”global knowledge’ = Algebraic Topology.
The local data of consumer behavior uses ‘Point-Set Topology’; the global one is ‘BIG Data’ using Algebraic Topology.