8&9 : Zoltan : Horrible game y=400-x^2, y=2^x mod 99.
& Srinivasa : JO 2004 Fall Q1 progress
10,11,12 : Ralph : 2004 SO Fall Q1 completed. Ryan gave an awesome proof to the class.
Q2 and Q3 started.
8&9 : Zoltan : Careful proof of JO 2004 Fall Q1.
Horrible game y=pi(x)
Individual work.
10,11,12 : Ralph : 2004 SO Fall Q2 lots of competing answers.
We showed that 65 was too small via an example.
However, we have not completed this question.
8&9 : Zoltan : JO 2004 Fall solved Q2, Mentioned Q4.
Horrible game y=least prime factor of x+21
Individual work.
10,11,12 : Ralph : 2004 SO Fall Q2 and Q3 proofs given on board.
Discussed degree 2 polynomial fitting at 1,2,3 points.
8&9 : Elizabeth : Proof techniques --- explained the pigeonhole principle and then
used it to solve two problems from "Parabolic Problems".
10 : Michael : 2004 SO Fall Q4 and Q5.
11,12 : Peter : 2004 SO Fall Q4 (plus a chance to collect and discuss some free math books)..
8&9 : Zoltan : Horrible game y = x^2+x+1, JO 2004 Fall Q4 after explaining "ruler & compass".
+ Srinivasa JO 2004 Fall Q5. (almost)
10 : Elizabeth : 2004 JA Fall Q1 --- solution shown on board after individual work.
11,12 : Toby : 2004 SO Fall Q5 solved.
and Peter
8 : Zoltan : Horrible game y = Ceiling(sqrt(x))^2 - x
+ Srinivasa Complete the square
JO 2004 Fall Q5. proof.
New Mersenne prime, perfect numbers.
"Don't be the turkey."
9 : Peter : Mathematical structures, groups, rings, fields also CC.
Matrix multiplication.
Z[sqrt(-5)] : 6=2.3 = (1+sqrt(-5))(1-sqrt(-5)).
10 : Ralph : Computed iterated roots sqrt(n+sqrt(n+sqrt(n+... )))
for n=1, n=2, n=3 and a general formula for n.
Asked for what values of k is the iterated root an integer.
Answered this question.
11,12 : Toby : Induction and strong induction followed by mathematical games.
and Paul
8 : Zoltan : Horrible game y = (x-2)(x+4)
+ Srinivasa Pencil and paper games.
Torus.
9 : Peter : Aside on general and special relativity, G=8piT.
More on rings. When is Z/NZ a field?
10 : Paul : Continued fractions (golden and silver ratio)
Combinatorial proofs (counting things two different ways)
Convergent and divergent series (proof that sum 1/n^2 converges)
11,12 : Toby : Model d12 from two d6's.
Define injective, surjective, bijective and show
N-->> Z, N -->> Q, N -/->> R.
Stable homotopy theory at the end.
8 : Zoltan : A ToT puzzle,
Student run horrible game (3^2024+7^2025) mod 10.
9 : Peter : Rings and Z/NZ continued.
When is Z/NZ a field?
(Z/pZ)[x]/(f(x)) ... when is this a field?
(Z/2Z)[x]/(1+x+x^2)
10 : Paul : Subtle mistakes in proofs and how to avoid them.
Proofs : number of edges in a tree
No odd cycles in a bi-partite graph
Introduction to strong induction.
11,12 : Toby : Ramsey Theory, addition chains.
For integers m,n show l(mn) <= l(m) +l(n).