All classes attended a Math and Art exhibition put on by ANU.
8 : Zoltan : Proof of ToT 2006 Spring JO Q2.
9 : Tryon : Mathemagic - Part 1
10: Liam : Make biggest sequence of cardinals from 4 single
digit numbers and + - x / ^ operators.
11&12 : Peter : Group axioms and examples.
8 : Zoltan : Half solved ToT 2006 Spring JO Q3.
9 : Elizabeth : Towers of Hanoi ... Induction.
10: Liam : Ants walking in a square problem.
11&12 : Peter : Rings, modular arithmetic, unit groups (Z/NZ)*.
8 : Zoltan : ToTT 2006 Spring JO Q3 explicit working.
Talked through Q5.
9+10:Ralph : A study of the addition and multiplication
tables for Z/NZ when N=2,3,4,5,6,7,8.
Compared N=prime to N=composite and noticed
the former were all fields ... but not the latter.
11+12:Peter: Rings, mostly Z/NZ. Claim axb=0 --> no inverse to a or b.
Claim in Z/NZ there is a^{-1} iff (a,N)=1.
Australian (Mathematics) Training Tournament : 1pm-4pm
8 : Zoltan : ?????????
9 : Tryon : Mathemagic
10: Srinivasa : Basic Boolean algebra in computer programming.
De Morgan's Laws.
(A and B) or C versus A and (B or C)
Basics of induction (sum of 1..n).
11+12:Peter: Ring theory, unit groups, GEA, CRT, Z/(pq)
phi(N=pq), RSA.
8 : Chris : Introduction to surds and continued fractions.
(Secretly Pell's equation.) Squares with square digits
like 361 = 36 & 1.
9 : Kai & Z : Combinatorial problems. Placing dominoes on an 8x8 grid
with and without the 2 opposite corners removed.
Game of placing coins (with no overlap) on a rectangular table.
10: Srinivasa : Exchanging two integer variables without intermediate variables.
Cryptography. Box analogy for asymmetric key crypto.
Factorisation problem (RSA)
Beginning number theory on GCD and LCM.
11+12:Tryon: Mathemagic. Via card games.
8 : Ralph : The pizza slicing theorem. (Also known as the Moser problem.)
What is the maximum number of regions that you can create
in a circle with n nodes on the circumference and every
pair connected by an edge. Experiment, prediction, pattern
recognition, theory, and proof.
9 : Elizabeth B. : Ramsey numbers game - n dots, 2 colours, try to form a
monochromatic triangle.
10: Srinivasa : Analyse Towers of Hanoi by looking at the details.
Linear and binary search algorithm.
11+12:Zoltan: Horrible game.