The School of Mathematics

Past Workshop Series

Fibonacci numbers and golden ratio
Meetings: April 17 and 24, 2010

What determines the shape of a rectangle? Is there a rectangle which is composed of a square and another rectangle of the same shape as the original? Surprisingly, this question leads to a discussion of Fibonacci numbers and their asymptotic behavior!

Friends and enemies
Meetings: March 6, 2010

Given a group of alliances and enemies (say between nations) what does it mean for this system to be stable? Once this is decided, how can you tell if a system will be stable by looking at it?

A river crosses a road
Meetings: February 20, 2010

How many ways can a river cross a road? That is, if n is any number, then how many ways can it loop back on itself to cross the road exactly n times?

Geometry of the Earth
Meetings: November 7, 2009

What does it mean to be a straight line on the Earth?

Geometry of the plane
Meetings: September Oct 31, 2009

Two points determine a line. But do two points determine anything else interesting?

Logic and circuits
Meetings: September 26, 2009

If a wire carrying current represents a 1, and a wire carrying no current represents a 0, then we can perform binary computation with a circuit. But how do we actually do it?

The size of infinite sets
Meetings: September 12, September 19, 2009

The discussion focused on the following argument:

Bill says that there are more numbers than even numbers, since every even number is a number but not vice versa.

Jane says that there are the same number of numbers as even numbers, since both collections are infinite.

Adding infinitely many numbers
Meetings: August 22, August 29, September 5, 2009

The discussion focused on the following questions:

Suppose I climb a ladder with infinitely many rungs, always climbing the next rung twice as fast as the previous. Will I climb the ladder? In how long?

What does it mean to add infinitely many numbers together?

Is there a number between .99999... and 1?

What is the relationship between lengths and numbers?
Meetings: August 15, 2009

The discussion will begin something like this:

Samuel: How can I measure the length of a line segment?
Avital: Use a unit measure!
Samuel: And what if the line segment isn't an even number of units?

How can we prove things about numbers?
Meetings: Saturdays March 14, March 21, 2009

The discussion will begin something like this:

Avital: How could we explain to an alien that 2 x 4 is equal to 4 x 2?
Ayal: They are both equal to 8!
Avital: What about 3 x 4 and 4 x 3?
Ayal: Those are both equal to 12!
Avital: What about 342 x 563 and 563 x 342?

Meetings: Saturdays February 7, February 14, February 21, 2009

The discussion will begin something like this:

Sam: What is an odd number?
Moe: It's one more than an even number.
Joe: Then what is an even number?
Moe: It's one more than an odd number.
Sam: Did you answer my question??

What is area?
Meetings: Saturdays January 10, January 17, January 24, 2009

This workshop is vaguely formed around our introduction to area. Some questions we might talk about:

  • What does it mean for two shapes to have the same area?
  • How would you go upon measing the area of a certain shapes?
  • Why are the formulas for the are of a rectangle, triangle, circle correct? (or: more accurately, how could someone have come up with them?)

Patterns in multiples of 9
Meetings: Wednesdays, December 17, January 7, January 14, 2008-9

The discussion began something like this:

Avital: Let's write down the first few multiples of 9. Each row will be 9 more than the previous one.


Samuel: That looks nice.

Avital: Do we notice some pattern?

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