Algorithms

Course see:

Algorithms Part 1 - https://www.coursera.org/course/algo
Algorithms Part 2 - https://www.coursera.org/course/algs4partII

List of Algorithms - http://en.wikipedia.org/wiki/List_of_algorithms con Theoretical Computer Science - http://en.wikipedia.org/wiki/Theoretical_computer_science

Decision Theory

Minimax - http://www.flyingmachinestudios.com/programming/minimax/

Cluster Analysis

K-Means Clustering - http://datasciencelab.wordpress.com/2013/12/12/clustering-with-k-means-in-python/

Combinatorial Optimisation

Graph Theory - Routing

Krukals Minimum Spanning Tree Algorithm - http://www.markhneedham.com/blog/2012/12/23/kruskals-algorithm-using-union-find-in-ruby/
Djikstras Shortest Path - http://www.maxburstein.com/blog/introduction-to-graph-theory-finding-shortest-path/
Travelling Salesman - http://blog.showmedo.com/python-showmedos/solving-the-travelling-salesman-problem-tsp-with-python/

Graph Theory - Search

A* - http://rubyquiz.com/quiz98.html

Bloom Filter (Testing for member of a set) - https://www.igvita.com/2008/12/27/scalable-datasets-bloom-filters-in-ruby/

Linear Algebra Algorithms

Finding the Eigenvalues of a matrix - http://en.wikipedia.org/wiki/Eigenvalue_algorithm

Information Theory

Strings

Levenshtein Distance - http://rosettacode.org/wiki/Levenshtein_distance#Ruby

Automaton Theory

Automaton Theory, see - http://en.wikipedia.org/wiki/Automata_theory

Finite State Machines - http://en.wikipedia.org/wiki/Finite-state_machine and https://gocardless.com/blog/statesman/
Behaviour Trees - https://www.altamiracorp.com/blog/employee-posts/behavior-trees-in-ruby
Conways Game of Life (Cellular Automata) - http://gamedevelopment.tutsplus.com/tutorials/creating-life-conways-game-of-life--gamedev-558

Celullar Automata was used in the early days to depict artificial life. Neural networks are also used:

http://en.wikipedia.org/wiki/Artificial_life

Computability Theory

Building a Turing Machine Simulator - http://reinh.com/blog/2011/09/03/building-a-turing-machine-simulator-with-ruby-part-1.html

Type Theory

Hindley–Milner type inference algorithm - http://smallshire.org.uk/sufficientlysmall/2010/04/11/a-hindley-milner-type-inference-implementation-in-python/comment-page-1/

Swarm Intelligence

Ant Colony Optimisation - https://practicingruby.com/articles/ant-colony-simulation
Langtons Ant (A two dimensional Turing machine) - http://en.wikipedia.org/wiki/Langton%27s_ant
Partical Swarm
Bee Colony
Grey Wolf
Bat
Birds

Queuing Theory

See -

Markov Chains - http://brandonbyars.com/2007/05/06/tdding-a-markov-chain/

Genetic Algorithms

Basic Introduction - http://www.sitepoint.com/genetic-algorithms-in-ruby-part-i/