Recurrence relations for counting actions in recursive algorithms, more examples can be found here: https://www.geeksforgeeks.org/dsa/recurrence-relations-a-complete-guide/ 

More PageRank examples includes detailed mathematics : https://pi.math.cornell.edu/~mec/Winter2009/RalucaRemus/Lecture3/lecture3.html 

PageRank recurrence Interactive https://www.mathsuniverse.com/pagerank  allows you to create a directed graph and works out the PageRank by multiplying the probability by the number of nodes in the network graph |V| to give an expected value. To get the PageRank as a probability divide the results given after several iterations by |V| the number of nodes in the graph.  Note: This particular interactive doesn't handle sink nodes (dangling nodes).

Python library NetworkX has a built-in PageRank function https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.link_analysis.pagerank_alg.pagerank.html 

These introductory youtube videos are helpful in understanding how/what we are measuring to work out the efficiency of algorithms.

• Big O Notation (The internet vs pigeons) https://www.youtube.com/watch?v=v4cd1O4zkGw

• Big O Notation (Story behind it)  https://www.youtube.com/watch?v=Q_1M2JaijjQ

• Big O Notation (What is it?) https://www.youtube.com/watch?v=__vX2sjlpXU

Combinatorial Explosions

• Exponential Growth: How Folding Paper Can Get You to the Moon (Youtube) https://youtu.be/AmFMJC45f1Q

• Combinatorial Explosions: How many ways can you arrange a deck of cards? (Youtube) https://youtu.be/uNS1QvDzCVw

• Check out the Travelling Salesman problem - the number of tours for a n=3038 city TSP is astoundingly immense http://www.math.uwaterloo.ca/tsp/problem/pcb3cnt.html   Which is a Combinatorial Explosion!!!! 

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