Pure Mathematics Mathematical Techniques, Proof, Mathematical Thinking

Pure Mathematics

Mathematical Techniques,Proof,

Mathematical Thinking

The Kangaroo Problem

PRIZE

Mathematician Kangaroo’s Solution

,...32

31,

16

15,

8

7,

4

3,

2

1

Engineer Kangaroo’s Solution

0.5, 0.75, 0.875, 0.938, 0.969, 0.984, 0.992, 0.996, 0.998, 0.999, 1.000

DecisionMathematics

Finding techniques for solving problems

Solving Problems Involving Networks

A Beautiful Mind

The story of John Nash

The Handcuffs ProblemThe Handcuffs Problem

Statistics

Reaching conclusions from data

Are girls more intelligent than boys ?

OR

Are boys more intelligent than girls ?

Stage 1

Select a Random Sample of 3 girls

Select a Random Sample of 3 boys

Random Sample

Stage 2

Carry out a suitable test to compare the two samples.

We will use 15 mathematical questions.

Question 1

Make the largest possible three digit number.

Question 2

Make the smallest possible three digit number.

Question 3

Make the largest possible three digit even number.

Question 4

Make the smallest possible three digit odd number.

Question 5

Produce the number zero.

Question 6

Produce the number 3.

Question 7

Produce the number one.

Question 8

Produce a number between zero and one.

Question 9

Produce a number between one and two.

Question 10

Produce the number one without using a fraction.

Question 11

Produce the 13th square number .

Question 12

Produce the 14th square number .

Question 13

Produce the 31st square number .

Question 14

Produce the numbernegative three.

Question 15

Produce the number that is nearest to 200.

Stage 3

Analysis of the results

Can we say that X are more intelligent than Y ?

Assume that males and females are equally intelligent.

Then the probability that a female

answers any question first is .

You could then generate a tree diagram.

2

1

M

M

M

M

M

M

MF

F

F

F

F

F

F

Tree Diagram for Three Questions

Table of Probabilities

P(15) = 0.0000 P(7 or more) = 0.6964P(14 or more) = 0.0005 P(6 or more) = 0.8491P(13 or more) = 0.0037 P(5 or more) = 0.9408P(12 or more) = 0.0176 P(4 or more) = 0.9824 P(11 or more) = 0.0592 P(3 or more) = 0.9963P(10 or more) = 0.1509 P(2 or more) = 0.9995P(9 or more) = 0.3036 P(1 or more) = 1.0000P(8 or more) = 0.5000 P(0 or more) = 1.0000

So on the basis of this sample we conclude that ...

Mechanics

Applying mathematics to statics and dynamics in the real world

Which way will the bike move ?

Which way will the drum move ?