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Let U⊆C be open. Let f:U→C be a holomorphic function and γ be a closed curve in U. Which statement is correct? You learn this here:  https://tbsom.de/s/ca 

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Consider the complex function f:C→C given by f(z)=z² + iz.The function holomorphic because it is... 
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A quiz for the new video! Let V be a complex vector space with inner product ⟨⋅,⋅⟩ and U⊆V be a finite subset given by U={b1,b2,…,bk}. What is not correct in general? You learn this here:  https://tbsom.de/s/ala 

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Quick question! In which area do you feel (more or less) at home besides mathematics?

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Recall your Functional Analysis knowledge about subspaces. Let X = C([0, 1], R) be the Banach space carrying the supremum norm. Let Y be the space of the real polynomial functions defined on [0,1]. What is correct? You learn related stuff here:  https://tbsom.de/s/fa 

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Recall your Real Analysis knowledge about uniform convergence. Let (f1,f2,f3,…) be a sequence of functions fn:[0,1]→R given by fn(x)=x/n² − 2 − 1/n. Is the sequence uniformly convergent? You learn this here:  https://tbsom.de/s/ra 

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Recall your Real Analysis knowledge about the supremum norm. Let f, g be two functions f,g:[0,1]→R given by f(x)=x−1 and g(x)=x². What is the distance between both functions ∥f−g∥∞ given by the supremum norm? You learn this here:  https://tbsom.de/s/ra 

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Recall your Real Analysis knowledge about limits. Let f:[a,b]→R be a differentiable function with f′(x)>0 for all x. What does the mean value theorem imply? You learn this here:  https://tbsom.de/s/ra 

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Recall your Real Analysis knowledge about limits. Find the correct answer for the question given in the picture. You learn this here:  https://tbsom.de/s/ra 
Just post a comment :)

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Recall your Linear Algebra knowledge about linear independence. Is the family (v) consisting of a single vector linearly independent? You learn this here:  https://tbsom.de/s/la 

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