2019 Term 1

Term 1 --- Week 1

8   : Ralph     : Why mathematicians do proofs.
                  Counting lines & regions created by lines between all pairs of vertices on a circle?
                  Why are triangular numbers triangular.
                  Gauss's proof of the formula for the sum of the first n natural numbers.
                  (Two minute description of modular forms.)
9   : Zoltan    : 2014-JO-40-spr, Q1 with fully presented proof.
10  : William   : 2014-JO-40-spr, Q1 with fully presented proof.
                                  Q2 worked out ideas only --- unfinished.
11  : David     : 2014-SO-40-spr, Q1.
12  : Peter     : 2014-SO-40-spr, Q1, Q3 complete.
                                  Q4 part done.

Term 1 --- Week 2

8   : Ralph     : Sets, N,Z,Q,R,C. Comparisons of sets.
                  Demonstration that |N| = |2N| = |Z| = |Q|.
                  Cantor's proof that |N| < |R|
                  What are complex numbers.
9   : Zoltan    : 2014-JO-40-spr, Q2 with fully presented proof.
10  : William   : 2014-JO-40-spr, Q2, Q3 with fully presented proof.
11  : Tamiru    : 2014-SO-40-spr, Q2.
12  : Peter     : 2014-SO-40-spr, Q4 completed correctly. Q2 started.
                  Complex numbers, e^(i*theta), e^(i*pi)+1=0,
                  Fundamental theorem of Algebra, Q,R, C=R(i).
                  Algebraic numbers, Q(sqrt(2)), Q(cuberoot(2)), transcendental numbers.
                  N as unary, N in place notation, N in prime power notation.

Term 1 --- Week 3

8   : Zoltan    : Brussell sprouts (game),
                  2014-JO-40-spr, Q1 complete, Q2 partially done,
                  The horrible game.
9   : William   : 2014-JO-40-spr, Q3 done, Q4 partial.
10  : David     : 2014-JO-40-spr, Q4, Q5 done.
11  : Peter     : 2014-SO-40-spr, Q3, Q4 completed. Q5 started.
12  : Tamiru    : 2014-SO-40-spr, Q2 completed. Q5 started.


Term 1 --- Week 4

8   : Zoltan    : Horrible game f(n) = sum_{p-prime, p|n} p (very very difficult).
                  2014-JO-40-spr, Q1 Two distinct solutions.
9   : Ralph     : 2014-JA-40-spr, Played with all the questions ... none completed.
10  : David     : 2014-JA-40-spr, Q1, Q2 done. Q3 started.
11  : Ralph +   : 2014-SA-40-spr, Q1.
      Tamiru    : 2014-SO-40-spr, Q5.
12  : Tamiru    : 2014-SO-40-spr, Q5.


Term 1 --- Week 5

8   : Kifan     : 2014-JO-40-spr, Q2 completed. Q3 started.
9   : Zoltan    : 2014-JA-40-spr, Played with all the questions. Q6 almost complete.
10  : David     : 2014-JA-40-spr, Q3, Q4 almost complete.
11  : Ralph     : 2014-SA-40-spr, Q2 started. Completed arbitrary triangles.
12  : ---       : 2014-SA-40-spr


Term 1 --- Week 6

8   : Peter     : 2014-JO-40-spr, Q4 and Q5 partially done.
                  Introduction to induction.
9   : Liam +    : 2014-JA-40-spr, 2014-JA-40-spr, Q9 complete.
      Chris
10  : David     : 2014-JA-40-spr, Q3, Q4 completed.
11  : Ralph     : 2014-SA-40-spr, Q2 completed proof. Required following:
                  Discussed continuous and discontinuous functions.
                  Discussed the intermediate value theorem.
12  : Zoltan    : 2014-SA-40-spr, Q5 partial progress, found 4 < best <= 8. 
                  Found a winning strategy with 8 moves for Peter.
                  Proved that there is none with 4 moves for Peter.

Term 1 --- Week 7

8   : Zoltan    : 2014-JO-40-spr, Q4 wrote up proof.
                  Horrible game -- Triangular numbers.
                  2014-JO-40-spr, Q5 Ali Baba repeated n=2,3,4,5, failed n=6.
                  Challenge 1^3+2^3+3^3+...+n^3.
9   : Liam      : 2014-JA-40-spr, completed Q3.
10  : Ralph     : EFM
11  : David     : 2014-SA-40-spr, Q3.
12  : Kifan +   : 2014-SA-40-spr, Q5. 
      Tryon