2023 Term 1
Term 1 --- Week 1
8 : Zoltan : Chocolate game, Nim with 2 piles.
Horrible game y=8x-41
Proof of Thales theorem.
9 : Ralph : Computed perfect, abundant and deficient numbers between 1 and 30.
Studied Euler's theorem of even perfect numbers.
Considered amicable numbers 220 and 284.
10 : Peter : Q1 & Q3 Junior Ordinary Spring 2003 ToT.
11 : Angus : Started Senior Ordinary Spring 2003 ToT.
Also worked on "polite chocolate game".
12 : Michael : Q1 and Q2 Senior Ordinary Spring 2003 ToT.
Term 1 --- Week 2
8 : Zoltan : Pigeonhole Principle
Explained ToT a little and some notation (element of Z, ceiling function).
9 : Elizabeth : Q1 Junior Ordinary Spring 2003 ToT.
10 : Peter : Q3 & Q2 (Started Q4) Junior Ordinary Spring 2003 ToT.
11 : Angus : Solved Q1 Senior Ordinary Spring 2003 ToT together on board.
12 : Michael : Discussed nature of "proof", axioms, and zero-knowledge proofs.
Group discussion on various approaches to Q3 Senior Ordinary Spring 2003 ToT.
Term 1 --- Week 3
8 : Zoltan : Numberphile video shoelaces.
Horrible game y=x(x+1)/2
T_n+T_(n+1) = (n+1)^2 by picture and algebra.
Challenge 8T_n+1 = (2n+1)^2
Difference table useful ... but not for nth prime.
Prime deserts
Notation 9|72 means 72 = 9k for some k in Z.
Headway on Junior ToT 2003 Spring Q4.
9 : Elizabeth : Discussed Q1 Junior Ordinary Spring 2003 ToT.
Proof by contradiction using sqrt{2} irrational as example.
Individual work on other problems.
10 : Peter : Finished ToT JO Spring Q3. Started Q4.
11 : Angus : Worked on Senior Ordinary Spring 2003 ToT.
Some solutions to Q2.
12 : Michael : CC = R[x]/(x^2+1), DD = R[x]/(x^2), HH = R[x]/(x^2-1).
Term 1 --- Week 4
8 : Tryon : Headway on Junior ToT 2003 Spring Q5.
9 : Zoltan : Horrible game y=400-x^2.
Individual work.
Special case of Q3 2003 JO ToT when AK=LC.
10 : Elizabeth : Went through Q4 JO ToT 2003 Spring on the board.
Individual work on Q2 and Q5.
11 : Peter : SO 2003 ToT Spring. Revised Q1 and Q2
12 : Angus : SO 2003 ToT Spring Q5.
Term 1 --- Week 5
8 : Tryon : Junior ToT 2003 Spring Q1.
9 : Zoltan : Horrible game : largest prime factor of x
Numberphile Shoelaces.
Ramble a) what are pi and e?
b) Z, Q, R, C, H, O
c) e^(i*pi)+1=0
d) What is 3^sqrt(2) ?
ToT 2003 spring Q3 completed.
10 : Tamiru : Went through Q5 JO ToT 2003 Spring on the board.
11 : Peter : SO 2003 ToT Spring. Worked on Q5 and Q2, Q4
12 : Angus : SA 2003 ToT Spring Q1.
Term 1 --- Week 6
8 : Ralph : Preparation for Junior ToT 2003 Spring Q1.
Monomials, polynomials, complete the square, quadratic formula proof.
9 : Zoltan : Theory vs Theorem vs Lemma
Horrible game : y=ord_2(x)
Q3 JA 2003 ToT Spring.
10 : Michael : Started Q1 JA ToT 2003 Spring.
11 : Peter : SA 2003 ToT Spring. Q6 and Q5
12 : Angus : SA 2003 ToT Spring presentations on Q1 and Q5. Worked on Q6.
Term 1 --- Week 7
8 : Zoltan : Worked on Junior advanced ToT 2003 Spring Q1.
9 : Andrew : Worked on Q1 JA 2003 ToT Spring.
10 : Tamiru : Solved Q1 JA ToT 2003 Spring.
11 : Michael : SA ToT 2003 Q1 on quadratics with rational solutions.
Derived the quadratic formula.
12 : Ralph : Solving linear and quadratics in non-integral domains.
Completion of the square.
Using rings Z/6Z, Z/8Z, as counteraxamples for
cancellation property and Gauss' thorem (#roots of a degree n poly).