8 : Anand : Some elementary computations to begin with.
This was followed by Cantor's diagonalisation to show
there is no bijection between N and R (in simpler words).
9 : Chris : The ‘clock game’ – using digits (419) to make targets from 0 to 51.
Exploring factorials, fractional roots and other strange notations.
10: Tamiru : a) Diagonal of a unit regular pentagon is golden ratio.
b) Use induction to prove 2^n > n^2 for n >=5.
11+12:Ralph: N < Z < Q < R < C < H.
Compared the effect of i on the complex plane to
the effect of the 2x2 matrix J = [[0, -1], [1, 0]]
on the Cartesian plane.
Both are rotation by 90 degrees anticlockwise.
Gave the isomorphism from a+ib --> [[a, -b], [b, a]].
Finished with the quaternions H={a+ib+cj+dk}.
8 : Tryon : Mathemagic.
9&10: Chris : Angle sum of points in an n-pointed star
including "turning number" t.
11+12:Ralph: Solving equations without solving equations.
Positivity : 2x+4 = 0 in N.
Divisibility : 3x+5 = 0 in Z.
Squares : 9x^2-4 = 0 in Q.
Contradiction : x^2-2 = 0 in Q.
Positivity : x^2+172y^6+42z^42 + 5 = 0 in R.
Legendre symbol for solving x^2 = a (mod p).
8 : Tryon : Flatland and sphereland.
9 : Tamiru : Modular arithmetic.
Proof that the diagonal of a regular pentagon with
a unit edge is the golden ratio.
10: Asilata: An exploration of the "numbers game" on graphs.
If there is time we may be able to pin down all the graphs
that can have a finite numbers game.
11+12:Chris: Searching for interesting squares (19^2 = 36|1).
Using continued fractions to solve Pell's equation.
8 : Tamiru : Modular arithmetic.
9+10: Chris : Arithmetic squares and modular inverses.
11+12:Zoltan: Horrible game.
Bulgarian maths competition 1995.
8 : Zoltan : Horrible game. Counting rectangles in a grid.
9+10: Chris : Euclidean algorithm (from a geometric standpoint).
11+12:Tryon : Bulgarian maths competition 1996.
(& Leonardo & Elizabeth)
8 : Tamiru : Modular arithmetic and number systems.
9 : Zoltan : Horrible game. 2016 Intermediate MC.
10 : Tryon : 1995/1996 Bulgarian maths competition.
Some hypercube / tesseract questions.
11+12:Asilata : Finite state machines.
8 : Chris : Exploring ratios in A4 paper with Pythagoras.
Index laws with negative and fractional indices.
9 : ElizaB : Basics of induction proofs.
10 : Tryon : Flatland and sphereland.
11+12:Zoltan: 1996 Bulgarian mathematics competition.
8 : Chris : Sequences introduction (Newton's method),
repeated average method to approximate square roots.
(Inspired by A4 paper dimensions.)
9 : Tamiru : Solving congruences.
10 : Eliz_B : Proofs by induction.
11+12:Zoltan: 1996 Bulgarian mathematics competition.