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Describe some of the earliest uses of the pigeonhole principle by Dirichlet and other mathematicians

Describe    some    of    the    earliest    uses    of    the    pigeonhole    principle    by    Dirichlet    and    other    mathematiciansEach    writing    assignment    is    worth20    pointsshould    include    the    following    sections:Background    (3    points):This    is    a    discussion    of    how    thenon-­‐mathematical    and    mathematical    portions    of    your    topic    fittogether.Youmight    include    a    historical    background    of    the    topic,    definitions    of    terms,    thediscrete    mathematicsideasthat    are    addressed(e.g.induction,    logical    fallacy,    etc.),    and    some    explanation    about    why    these    ideas    were    useful.Examples    (10    points):In    most    of    your    writing    assignments    you    are    asked    to    discuss    and    describe    an    aspect    of    discretemathematics.    Give    two    of    three    examples    or    techniques    of    the    topic    under    discussion.    Give    generalinformation    and    alsospecific    examples    of    the    topic.Bibliography(2    points):List    the    references    you    used    to    complete    this    report.    Just    list    title    and    author    for    any    booksandarticlesyou    used.    You    should    also    include    a    list    of    people    that    you    consultedor    any    other    form    of    help    that    you    received.For    example,    you    might    obtain    some    of    your    information    from    the    internet;    in    this    case,    you    could    include    thewebsite.You’ll    need    at    least    one    bookor    articleas    a    reference,    preferably    two,    and    a    total    of    atleast    two    reference

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