2020 Term 3
Term 3 --- Week 1
8+9 : Peter : Began Pascal's triangle, powers of 11, place notation.
Different bases, long addition, long multiplication, long division, fractions.
New symbol x with +,x,/,fractions in Z[x] leading to Q[x].
10 : Zoltan : Fibonacci sequence and vector spaces.
11+12: Ralph : Divisibility in Z, followed by the number of divisors and
sum of divisors functions (tau(n) and sigma(n)).
Perfect numbers: compared Euclid's theorem and Euler's theorem.
Played with rings Z[sqrt{2}] and Gaussian integers Z[i].
CCSE : Paul : Introduction to embedded systems and single-board computers (http://tinkercad.com).
Example is a community air quality project (https://sensor.community/) which
highlights issues of security of IoT devices using best practice guidelines.
See the single board computer github for details.
Term 3 --- Week 2
8 : Chris : Elementary set theory, sizes of sets followed by
Cantor's diagonal argument.
9 : Tamiru : Numbers in different bases.
10 : Zoltan : Fibonacci sequence and vector spaces.
11+12: Ralph : Rational points on lines, circles, cubics, elliptic curves.
The chord method for generating new rational points from old ones.
Newton polygon of a polynomial to estimate its genus.
CCSE : Josh + : AI for games and start to program an AI for Halite.
Paul See https://www.kaggle.com/c/halite.
(Unfortunately, technical difficulties hampered this session.)
Discussion of Virtual reality used to alleviate anxiety and
provide de-sensitisation.
Term 3 --- Week 3
8 : Tamiru : Base-n number conversions.
9+10 : Peter : Pascal's triangle, Pascal's tetrahedron.
11+12: Chris : Set theory. Integration theory.
CCSE : Josh : More AI for games with kaggle.
Term 3 --- Week 4
8 : Tamiru : Base-n number representations.
Triangle geometry and elementary trigonometry.
9 : Chris : Number systems, infinity, countability of sets.
10 : Peter : Pascal's triangle, (p+q)^n, probability theory.
Fast multiplication, binomial distribution, Pascal's tetrahedron.
11+12: David : Pi-sided dice, Buffon's needle, Catalan numbers.
CCSE : Josh + : AI for games with kaggle, Halite game, distance.
Term 3 --- Week 5
8+9 : Zoltan : Geometric series, existence of limits, 1+2+4+8+16 = -1?
10 : Peter : Continued with outline of Karatsuba multiplication (& fast arithmetic)
Binomial (p + q)^n, multinomial (p_1 + p_2 + ... + p_5)^n,
elementary symmetric fns (x + a_1)(x + a_2)(...)(x+a_5) etc (Pascal's triangle)
Counting / summing weighted paths in Pascal's triangle, hint of EM for HMMs
11+12: Ralph : Topology in 0-dim (not much going on here),
1-dim ... elementary knot theory and invariants,
2-dim ... cylinder, sphere, torus, Moebius band, Klein bottle,
cross-cap, MB+MB=KB, classification of all surfaces.
CCSE : Cassy + : Introduction to functional programming using CodeWorld for Haskell
Josh
Term 3 --- Week 6
8 : David + : Game theory with NIM and other games.
Zoltan
9 : Chris : Function spaces and sampling.
10 : Ralph : Greatest common divisor of two integers, Euclidean algorithm.
Probability that two natural numbers are coprime.
Peano proof that 1+1=2.
11+12: Peter : Groups, rings fields, and prime ideals.
CCSE : Artem + : Computer networking and on monitoring and diagnostic tools.
Josh (See networking github)
Term 3 --- Week 7
8 : Ralph : Moebius bands, Klein bottles and topology.
Banach-Tarski paradox.
Harmonic sum card stack trick.
9 : Tamiru : We discussed Numerical Semigroups.
A numerical semigroup is a subset S ⊆ N containing 0,
stable under addition and with finite complement in N,
where N= { 0,1,2,3, ... }. Some examples and proofs.
10 : David : The game of Nim and some generalisations.
11+12: Peter : Vector spaces, rings, modules, ideals, prime ideals. Examples in Z, R[x], C[x].
Algebra <---> Geometry via Ring <---> prime ideals of ring.
Fundamental theorem of algebra/arithmetic. Inverses unit groups e.g. Z*, R*, C*.
Localisation of rings, e.g. Z --> Z_3. Algebraic geometry.
CCSE : Artem + : Computer networking and attacks against networks including IP spoofing.
Josh