Mathematics In Schools
Professor Geoffrey Brooks has been the guest Mathematician at Victorian Secondary Schools, as part of the “Mathematicians in Schools” program.
Geoff was brought up in the outer Eastern suburbs, where he attended Ferntree Gully and Vermont High Schools. He is currently the Professor of Mathematics at Swinburne University of Technology. Previously, he was a Senior Principal Research Scientist at CSIRO, and an Associate Professor in Engineering at McMaster University.
Geoff’s expertise is in applying mathematics to improving the production of metals and he has published over a hundred papers on that topic and delivered invited lectures around the world on his work, including at Cambridge and Columbia Universities. A lot of Geoff’s work is concentrated on trying reduce the environmental impact of metal production, which is a big challenge facing Australia as we tackle climate change and developing sustainable industries.
Geoff loves mathematics and particularly enjoys explaining to young people (or anybody willing to listen!) how useful mathematics is to solving practical problems.
This year he will be involved in several tutorials, workshops and lectures focused on engaging Year 9 students in mathematics, as part of the Mathematicians in School program.
Geoff is also happy to offer any general advice to students or parents about careers involving mathematics,
You can checkout Geoffs Blog about mathematics at Imagining Archimedes
A Day in the life of a Mathematician
Teaching Machines How to Count
A Maths Presentation for year 9 students
Questions for the Teaching Machines how to Count Session
Quiz by Geoff Brooks
1. Which great mathematician invented binary? A. Issac Newton B. Gottfried Leibniz C. Alan Turing D. Brendon Fevola
2. In the land where people have eight digits on their hands (and count in eights), what would a sign showing 40 km/hr translate into decimal?
3. Convert 5 into its binary equivalent.
4. Adding in binary is very simple, there are only two rules. What are they?
5. Charles Babbage invented the world’s first programmable computer in the 1830s. What makes it very different from modern computers?
6. A very simple code, involves moving the alphabet to the right by one position (e.g. “A” is coded as “B”). Using this code, de-code the following message: HP CVMMEPHT
7. Which great mathematician developed the concept of the Universal Machine? A. Issac Newton B. Gottfried Leibniz C. Alan Turing D. Brendon Fevola
8. During World War II, Alan Turing, working with many thousands of people at Bletchley Park, developed machines for breaking which code?
9. The “ENIAC” was one of the very first electronic computers, how much did it weigh?
10. Digital images are commonly converted into three channels labelled RBG. What does “RBG” stand for?
Answers 1.B 2. 32 3. 101 4. 1 + 0 = 1 and 1 + 1 = 10 5. It was entirely mechanical 6. Go Bulldogs 7. C 8. Enigma 9.30 tonnes 10. Red Blue Green
A Maths Presentation for year 9 students
Geoff's Brain Teasers
Problem 1Imagine you are building a storage room in a warehouse. The room must be 60 m3. The architect has specified that the room must be 1m higher than its width and 1m longer than its height. What are the dimensions of the room? Would you need to have less or more floorboards if the room (of the same volume) was a simple cube?
Special bonus marks for any students who can answer correctly the question: Is there is only one solution to this problem?
Problem 2Imagine there are three cars travelling down a straight stretch of road. One car (Car A) takes of from dead stop in a nice regular way (speed has a linear relationship with time) and reaches a maximum speed of 60 km/hr after one minute and holds this speed. At exactly the same time, another car (Car B) takes of slowly but speeds up (speed has a parabolic relationship with time) as it approaches it maximum speed of 60 km/hr after one minute. Like the first car, it holds this speed. Car C also takes off at the same time but starts quickly and than gradually builds up speed (speed follows a square root relationship with time) until it reaches it maximum speed of 60 km/hr after one minute. It also holds it's maximum speed after one minute.
A) After five minutes, which car has travelled the most distance?
B) Assuming that rapid de-acceleration is bad for brakes, which car has worn their brakes the most from the five minutes of driving?
C) What is the difference between the distance travelled by Car A and Car B after five minutes?
Note: Question A and B can be solved through looking at a graph and a little intuition (always handy in mathematics!). Question C can be solved graphically but a bit of calculus will help (Year 10 and below are excused).
The Mathematics of Football
The Mathematics of Football Quiz
Resources - Links
High School Partners
OtherAustralasian Problem Solving Mathematical Olympiads
Wikipedia - Enigma Machine
The Amazing Alan Turing - Richard Buckland (extension lecture) UNSW 2008
Alan Turing: Codebreaker and AI Pioneer
CIA - kids home page
The enigma machines