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.
8 : Ralph : The ribbon around the equator problem. Insert 30cm, take up the slack
and what can fit under it, (a) light, (b) ant, (c) mouse.
Then calculate the answer.
Coring the earth from the north pole to the south pole to leave
a remaining ring of material of height 6 cm. What is its volume?
9 : Chris : Introduction to surds and continued fractions.
(Secretly Pell's equation.) Squares with square digits
like 361 = 36 & 1.
10: Srinivasa : Induction exercises. The usual suspects.
11+12:Peter: The RSA cryptosystem and factoring integers of the form N=pq.
8 : Ralph : We began by trying to understand why a unit square has area 1.
After realising that this is a definition, we derived areas
of rectangles, triangles and circles.
Defined the voume of a unt square and used it to derive volume
formulas for rectangular prisms, pyramids, cylinders, cones,
From these we derived that
hemisphere = cylinder - cone,
and then used that to compute the volume of a sphere and dome.
9 : Chris : ????
10: Tryon : Mathmagic (with cards).
11+12:Peter: Shor's quantum factorisation algorithm.