Pure Mathematics Mathematical Techniques, Proof, Mathematical Thinking.

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Presentation transcript:

Pure Mathematics Mathematical Techniques, Proof, Mathematical Thinking

The Kangaroo Problem PRIZE

Mathematician Kangaroo’s Solution 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

Decision Mathematics Finding techniques for solving problems

Solving Problems Involving Networks

A Beautiful Mind The story of John Nash

The 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 number negative 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.

M M M M M M M F F F F F F F Tree Diagram for Three Questions

Table of Probabilities P(15)= P(7 or more) = P(14 or more)= P(6 or more) = P(13 or more)= P(5 or more) = P(12 or more)= P(4 or more) = P(11 or more)= P(3 or more) = P(10 or more)= P(2 or more) = P(9 or more)= P(1 or more) = P(8 or more)= P(0 or more) = 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 ?