2019 Term 3

Term 3 --- Week 1

8     : Ralph   : Magic squares, (3x3 and 4x4). Compute row sum without solving.
                  Symmetries of magic squares ... rearrange to make diagonals magic.
                  Matrix operations (2x2) addition, multiplication, 
                  additive and multiplicative identities. 
                  Non-square matrix multiplication (2x3) by (3x2) gives (2x2).                     
9     : Ellen   : Invariants.
10+11 : Peter   : Vectors, matrices, linear algebra.
12    : (Ralph) : Brief description of Cyberchef.
                  The Theorem that won WWII "Permutations are in the same conjugacy class 
                  if they have the same cycle type". 
                  Example : show (123)(45) and (134)(25) are in the same conjugacy class.

Term 3 --- Week 2

8     : Ralph   : A circle touches a square at two adjacent corners and
                  at tangentially on the side opposite those two corners.
                  Which has the longer perimeter, the circle or the square?
                  Played the game in which the winner is the first to 
                  collect a set of integers from (1..9) such that some 
                  subset of 3 integers add up to 15. No repeats, no reuse.                
9     : Zoltan  : 1992 Telecom Junior Contest ... question 1.
                  Horrible game.
10    : Tryon   : Games and Invariants (Fiona's)
        Chris
11    : David   : Games and Invariants (Fiona's). Questions 2a and b.
        William
12    : Peter   : Vector spaces, modules, higher dimensional calculus,
                  partial derivatives, differential equations, heat equation.

Term 3 --- Week 3

8     : Ralph   : Edge minimisation series for square, equilateral triangle
                  and regular hexagon.                
9     : Zoltan  : 1992 Telecom Junior Contest ... question 2.
                  Horrible game.
10    : Chris   : Games and Invariants (Fiona's) ... Q3, Q13.
11    : David + : Games and Invariants (Fiona's). Question 3.
        William
12    : Ellen   : Invariants ... worked through most questions on the sheet.


Term 3 --- Week 4

8     : Zoltan  : Paths through digraph, e.g. Pascal's triangle.
                  Horrible game.
                  AIC (=CAT) 2013 Junior paper.
9     : Chris   : Edge minimisation series for square, equilateral triangle
                  and regular hexagon.                
10    : Ellen   : Pidgeon hole principle.
11+12 : Anand   : Symmetry groups of bounded planar regions.


Term 3 --- Week 5

8     : Zoltan  : AIC (=CAT) 2013 Junior paper.
                  Dynamic programming and recursion (for Q10 "hopping").
                  Horrible game.
9     : Chris   : Discussed self-similar objects and described lines, triangles,
                  squares with self-reference.
                  We also played the chaos game.
10    : Liam    : Edge minimisation series for square.
                  Lots of logic riddles.
11    : Ellen + : Pidgeon hole principle.
        William
12    : Ralph   : Discussions about Liouville's transcendental,
                  most reals are transcendental, continued fraction representation
                  and quadratic irrationals, edge minimisation problem,
                  obtaining the n-th hexadecimal digit of pi without computing previous digits.

Term 3 --- Week 6

8     : Chris   : Worked through self similar worksheet.
9     : Liam    : Logic riddles and information theory.
10+11+12 : Diji : 45 minute talk on Perfect Numbers plus questions.
10    : Tryon   : Computational thinking in mathematics --- Project Euler.
11    : William : Geometry algorithm fundamentals, representations, and basic calculations.
12    : Zoltan  : Discussions of topological matters like addinng a point to a line
                  or a plane to get a circle or sphere respectively.


Term 3 --- Week 7

8     : Zoltan  : Combinatorial games - Chocolate + analysis, Brussels sprouts,
                  choc black + analysis, and the horrible game.
9     : Chris   : Continued fractions and how to aproximate square roots.
10    : Tryon   : Computational thinking in mathematics
11    : William : Algorithms for points inside and outside of polygonal domains, 
                  classification, Voronoi diagrams, Fortune's Algorithm
12    : David + : 1992 Telecom Senior Contest problems
        Tamiru