Date: Thu, 11 October 2007 15:50:20 -0500 (Central Daylight Time)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-02-fall@uni.edu
Subject: HW due on Tuesday, two problems...

Hi 080 students,

     The HW that will be due on Tuesday is:

        Problem #1:

        Prove that for all n >= 1 that

             2 + 4 + ... + 2n = n(n + 1)

          and

        Problem #2:

        Prove that for all n >= 1 that
                                         n(5n + 1
             3 + 8 + ... + (5n - 2) =  -------------
                                            2
    Be sure that your inductive proofs are:

       1. following the pattern you see for all examples in class
          and on the web page.

              http://cns2.uni.edu/~jacobson/inductive.html

       2.  neatly written, very readable, recopied if it got messy.

           Every time you rewrite a proof to make it look better,
           you get better at doing inductive proofs and have a deeper
           understanding of them.

       3.  On separate pieces (sheets) of paper.  Only one will be
           collected depending on how the Neko cat race comes out,
           of if the computers are all down, how the COIN FLIP comes
           out as to Heads or Tails.

       4.  Good preparation for the inductive proof quiz on October 23rd.

    Study the SETs and SET THEORY material at this web page link:

         http://cns2.uni.edu/~jacobson/setsSupplement.html

    Study suggestions for sets and the link to it are at our class web page:

         http://cns2.uni.edu/~jacobson/c080.html

    Look over today's handout and the proof that the set of PRIME numbers
    is an INFINITE set, i.e. that there is no largest PRIME number.

    Here are the first 200 PRIME numbers:

    2    3    5    7   11   13   17   19   23   29   31   37   41   43   47
   53   59   61   67   71   73   79   83   89   97  101  103  107  109  113
  127  131  137  139  149  151  157  163  167  173  179  181  191  193  197
  199  211  223  227  229  233  239  241  251  257  263  269  271  277  281
  283  293  307  311  313  317  331  337  347  349  353  359  367  373  379
  383  389  397  401  409  419  421  431  433  439  443  449  457  461  463
  467  479  487  491  499  503  509  521  523  541  547  557  563  569  571
  577  587  593  599  601  607  613  617  619  631  641  643  647  653  659
  661  673  677  683  691  701  709  719  727  733  739  743  751  757  761
  769  773  787  797  809  811  821  823  827  829  839  853  857  859  863
  877  881  883  887  907  911  919  929  937  941  947  953  967  971  977
  983  991  997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069
1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187
1193 1201 1213 1217 1223

     Tuesday (last Tuesday was 10/09) was a Prime number date.

     Notice that Halloween is a prime number and that Christmas eve eve
     is also a Prime number.   1031 is prime and 1223 is prime.

     1031 is Halloween.
     1224 is Christmas eve, so 1223 is Christmas eve eve.
                               ----

     1223 just happens to be the 200th prime number.

     Internet security and crytography is very reliant upon PRIME numbers!

    Mark