Read the summary and the most important questions on Deep Learning in Python

• 1 Week 1

• 1.2 book chapter 2 and 3.4

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• What is the extensional and intensional notation of a set?

  • The extensional notation of a set names the members of a set.'
    
  • e.g. {1,0,5}

  • the intensional notation of a set is naming the condition the members must satisy 
  • e.g. {|x| < 2}

• What is the axiom of extensionality?

  • This axiom states that sets are equal if they consists of the same members
    
  • the order or length of the set does not have to be the same
  • e.g. {1,0,0,1} and {1,1,1,0,1,0} are equal.

• What is the difference between a set and a bag?

  • A set does not remember the order of elements or repetitions of one element.
    
  • bags remember the repetitions but not the order
  • {1, 0, 1}={1, 1, 0} but neither is equal to {1, 0}
    
  • bags can also be referred to as multisets

• How are bags often denoted?

  • You write the element and how much it occurs:
    
  • instead of {1, 1, 1, 1, 0, 1, 0, 0} we would write {"1" : 5, "0" : 3}
    

• What is the difference between lists and tuples?

  • In programming, lists and tuples are both vectors of values.
    
  • lists are mutable however, my_list[1] <- 99 would change the second component in the list to 99
  • tuples are not mutable, the order or content of the tuple cannot be altered.

• What is an indicator function or characteristic function?

  
  We can have a set A and we may wish to create a function of x which gives a
  value 1 to all values which are members of A and 0 to all other values for x.this is used for one-hot encoding

• What is the image of a set?

  The set of outputs B given a set of inputs A is called an image and denoted by f [A] = B.
  If we look for a set of inputs A given the set of outputs B, we are looking at its inverse image denoted by f^−1[B] = A (we can use the same notation for individual elements f^−1(b) = a)

• What is a monotone function?

  A function for which for the entire domain, the following holds:
  if a < b, then f (a) ≤ f (b) or if a > b then f (a) ≥ f (b).
  so if the input is larger/smaller, the output is also larger/smaller
  Depending on the direction, this is called an increasing or decreasing function, and if we have < instead of ≤, it is called strictly increasing (or strictly decreasing).

• What is a step function?

  A function which is continuous in some parts but not everywhere

• What are convergent and divergent functions?

  If the outputs of the function f approach a value c (and settle in it), we say that the function converges in c. If there is no such value, the function is called divergent.