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landsgevaer commented 7 months ago

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AlgTop18: Classification of combinatorial surfaces II

In this lecture we present the traditional proof of the most important theorem in Algebraic Topology: the classification of (two-dimensional) surfa...

1,830 views

landsgevaer said:

@alfredorestrepo Otherwise they would have been put side by side in the previous step and both be in either the top part or the bottom part. Given that they were not, they must both point to the right (or both to the left)

• 36:26 Add to

  AlgTop14: The Ham Sandwich theorem and the continuum

  In this video we give the Borsuk Ulam theorem: a continuous map from the sphere to the plane takes equal values for some pair of antipodal points....

  2,180 views

  landsgevaer said:

  @2:30 "no continuous function ... for any P in S2" should be understood as "no continuous function ... for all P in S2" to avoid some ambiguity; clearly, there are functions for which f(p*)=f(p*) for at least some p

  .

• 49:27 Add to

  Lec 30 | MIT 18.06 Linear Algebra, Spring 2005

  Lecture 30: Linear Transformations and Their Matrices.

  View the complete course at: http://ocw.mit.edu/18-06S05

  License: Creative Commons BY-NC-...

  40,199 views

  landsgevaer said:

  This lecture could just as well have appeared in the beginning, as the very first one, to introduce the meaning of a matrix (except for the part about using eigenvectors as a basis, of course).

• 49:12 Add to

  Lec 18 | MIT 18.06 Linear Algebra, Spring 2005

  Lecture 18: Properties of Determinants.

  View the complete course at: http://ocw.mit.edu/18-06S05

  License: Creative Commons BY-NC-SA

  More inform...

  35,869 views

  landsgevaer said:

  Property 2 wasn't needed as a fundamental property, since it follows from property 3.

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