Sect 5. Counting

CONCEPTS

  Rules of sum, product, inclusion-exclusion
  Countability: countable, countably infinite, uncountable, diagonalization
  Permutations and combinations with and without repetitions
  Binomials
  Pigen hole principle

NOTATION

SKILLS
  
  1. Know rules of sum, product, inclusion-exclusion
     E.g., Find size of simple sets defined by union, product, etc.
  2. Understand countability	
     E.g., prove NxN is countable
     E.g., prove set of infinite strings over 0/1 is uncountable
  3. Know definition permutation and combination
     E.g., Compute size of sets defined by permutations
     E.g., Compute size of sets defined by combinations
     E.g., solve simple problems involving combinatorics
  4. Know pigen hole principle
     E.g., apply the principle to simple problems
  
SOURCES

  Wikibooks: Counting principles
  https://en.wikibooks.org/wiki/IB/Group_5/Mathematics/Higher/Algebra,_functions,_and_equations/Counting_principles
  https://en.wikibooks.org/wiki/Probability/Combinatorics (so-so)
  https://en.wikibooks.org/wiki/Applicable_Mathematics/Counting_Techniques (simple)

  *** Recommended ***
  Wikipedia: Cantor's enumeration
  https://en.wikipedia.org/wiki/Countable_set
  
  *** Recommended ***
  Wikipedia: Cantor's diagonalization
  https://en.wikipedia.org/wiki/Cantor's_diagonal_argument

  *** Recommended ***
  Youtube: Countable and Uncountable Sets (Part 1 of 2) by Rob Shone
  https://www.youtube.com/watch?v=sT9hAmaot8U
  Youtube: Countable and Uncountable Sets (Part 2 of 2) by Rob Shone
  https://www.youtube.com/watch?v=fRhdpyaOhEo

  Youtube: Infinity is bigger than you think by Numberphile
  https://www.youtube.com/watch?v=elvOZm0d4H0

  *** Recommended ***
  Youtube: Discrete Math 1 by TheTrevTutor, videos 26-36, combinatorics
  https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz


  *** Recommended ***   
  Lerma, sect 5 (Combinatorics)

  Smid, chap 3 (Combinatorics)

  LLM sect 7.1.2-7.1.3 (Countability)

  ADS sect 2 (Combinatorics)

  BDS sect 1.2-1.3 (Combinatorics)

  Hammack sect 3 (Combinatorics)
          sect 13 (Countability) (!!! lots of examples and exercises !!!)

  Levin chap 1 (Combinatorics)