MS-A0402 - Foundations of Discrete Mathematics, Lecture, 27.2.2023-21.4.2023

Topic outline

• Materials
  • 

    Lecture notes File

    PDF document

    Update 14.4:

    example 4.32 - numerical error fixed
    

     
    

    Update 27.3:
    

    • Added Section 2.3.1 Distributing Objects into Boxes (as disuccsed in lecture). Note that this adds a bit of new material and replaces the previous material on Stirling numbers which used non-standard notation and terminology.
      
    • Other minor typos and added explanations here and there. In particular the explanation for the inclusion-exclusion formula for three sets. The argument here is a special case of the general proof and so it may help you understand the reasoning.
      

    
    

    Update 24.2: Here are last years lecture notes. Some updates to the intro pages will be made before the start of the course.
    

    We will mostly follow the material in these lectures notes that have been developed for this course series by Ragnar Freij-Hollanti and complied in the current format by Tuomas Sahlsten last year. Please report any errors that you find.
    

    
    

  • Additional resources

    There are various choices for books that support this course.
    

    
    

    The following are freely available:

    
    

    Here are 3 books recommended by the American Insitute of Mathematics https://aimath.org/textbooks/approved-textbooks/

    • https://aimath.org/textbooks/approved-textbooks/bender-williamson-dm/
      
    • https://aimath.org/textbooks/approved-textbooks/doerr-levasseur/
    • https://aimath.org/textbooks/approved-textbooks/levin/

    Two other books:
    

    • Kenneth Bogart: Combinatorics Through Guided Discovery.
      
    • Richard Hammack: Book of Proof.
      

    
    

    There is also this physical book, which is not necessary to get:

    • Kenneth H. Rosen: Discrete mathematics and its applications.