Sequences and Limits

• Cauchy-Schwarz inequality
• Triangle inequality (small mistake at 3:34 where should be )
• Limits and inequalities
• Convergence lemma
• Limit results
• Supremum (and infimum)
• Limit of monotone sequence
• Bolzano-Weierstrass in one dimension
• Bolzano-Weierstrass in k dimensions
• Cauchy sequences
  I’ve made a small mistake in minute 14: the expression should be the following:
  
• Lemma 1
• Open and closed sets
• Inf and sup of compact set

Functions

• A lemma on continuity of functions
  In minute 14 the reference to should obviously be to .

Extreme and Intermediate Value Theorems

• Theorem of the maximum

Berge’s maximization theorem

• part 1
• part 2

Contraction mapping theorem

Sperner’s lemma

Brouwer’s fixed point theorem

Kakutani’s fixed point theorem