Web Links for Chapter 6
Page 220, Basic Principles
Basic principles are addressed at http://www.cs.odu.edu/~toida/nerzic/content/counting/basic_principles.html.
Page 229, Permutations and Combinations
For a basic introduction see http://mathforum.org/dr.math/faq/faq.comb.perm.html.
Page 236, Catalan Numbers
In April 2002, Preda Milhailescu announced that he had proved Catalan's conjecture.
For a list of some of the items counted by the Catalan numbers and pictures of them, see http://www-history.mcs.st-and.ac.uk/~history/Miscellaneous/CatalanNumbers/catalan.html.
Page 241, Algorithms for Generating Permutations and Combinations
For information about generating permutations with links to implementations, see http://www.cs.sunysb.edu/~algorith/files/generating-permutations.shtml. My own source code for generating permutations is perm.c.
Page 247, Probability
See the Virtual Laboratories in Probability and Statistics at http://www.math.uah.edu/stat/. The Probability Web at http://www.mathcs.carleton.edu/probweb/probweb.html is a collection of probability resources.
Page 252, Birthday Problem
A simulation is at http://www.mste.uiuc.edu/reese/birthday/intro.html.
Page 261, Generalized Permutations and Combinations
Check http://www.ping.be/~ping1339/tel.htm.
Page 266, Binomial Coefficients and Combinatorial Identities
For a discussion of the binomial theorem, see http://mathworld.wolfram.com/BinomialTheorem.html.
Page 268, Pascal’s Triangle
A biography of Pascal is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pascal.html.
Page 271, Pigeonhole Principle
A discussion of the Pigeonhole Principle and lots of examples are at http://www.cut-the-knot.com/do_you_know/pigeon.html. A biography of Dirichlet is at http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html.