This is a series of workshops intended to introduce contemporary areas
of mathematics and applications. Initially the topics will parallel the 4
component parts of the ANU secondary college course, see Introduction
to Contemporary Mathematics
for details.
Future Workshops
In 2008, 2009 there will be two workshops each year on topics chosen
to provide contemporary applications and extensions to the material
taught in college level mathematics.
Mathematics and Envirinmental Modelling.
Tentative date: mid November, 2007.
Mathematics and the Universe.
Wednesday 25 June, 2007. Lecturers: Lilia Ferrario, John Hutchinson, Dayal Wickramasinghe.
Here is the Flyer.
The following were used during the workshop.
From Newton to Hubble and Beyond (LF)
The Cosmic Ladder (JH) (These are the notes which go through the computations. They should be suitable for use in a class which has done some very basic trigonometry)
The Cosmic Ladder (TT) These are from a lecture given by Professor Terry Tao to high school teachers in Sydney and UCLA. Or go to the links from his website .
Curved Spaces and the Nature of the Universe (DW)
Geometry and Topology.
Friday 9 November, 2007. Lecturers: John Hutchinson, Adam Rennie, Bryan
Wang.
Here is the Flyer.
Optional Preliminary Reading: The material treated is from Chapter
5 of Introduction to Contemporary Mathematics (big
download, 10 MB).
Here are some preliminary comments ,
and some relevant notes from
the "Teachers Manual" for the
book "Heart
of Mathematics".
The following overheads were used during the workshop. Most of the material is presented in more detail in Introduction to Contemporary Mathematics .
Overview (JH)
Euclid's Elements, Platonic Solids (AR)
Fourth Dimension, Topology, Knot Theory (BW)
Classification of Surfaces, of 3D manifolds (JH)
Chaos and Fractals.
Friday 18 May, 2007. Lecturers: Michael Barnsley, Florica Cirstea, John
Hutchinson.
Here is the Preliminary
Information.
Optional Preliminary Reading: The material treated is from Chapter
4 of Introduction to Contemporary
Mathematics (big download, 10 MB).
The laboratory session used applets from the following websites. Note also
the information provided there for each of the applets.
Iterating
the Logistic Map
Bifurcation
for the Logistic Map
The Chaos
Game
Infinity: History, Philosophy, Mathematics.
Friday 3 November, 2006. Lecturers: Ben Andrews,
John Hutchinson,Chris Wetherell.
For Mathematics and Other Teachers, ACT and
Local Region, Secondary Colleges & High Schools.
Here is the Flyer.
Optional Preliminary Reading: The material treated is in Chapter 3
from Introduction to Contemporary Mathematics and Chapter
3 (big download, 28 MB !!) from [HM]. The latter is independent
of the material in the remainder of [HM].
This was the approximate schedule.
And here are some additional notes for the talks on Sections
3.1, 3.2 and Section
3.3 of the above
references.
Internet Security, Number Theory & RSA
Cryptography.
Friday 2 June, 2006. Lecturers: Jim Borger, John Hutchinson, Jonathan
Manton.
For Mathematics and IT Teachers, ACT Secondary
Colleges & High Schools.
Here is the Flyer.
The material treated is in Chapter 2.3--5 from [ICM] above and Chapter
2.3--5 from [HM]. The latter is independent
of the material in the remainder of [HM].
The following Lecture Overheads and Maple Worksheets were
provided (see also [ICM] for some further details). If you have trouble
downloading the Maple worksheets in the
correct format, try to save them to the desktop as .mw files.
Arithmetic
Background
RSA
Cryptography
Introduction
to Maple Worksheet, Introduction
to Maple (pdf version)
RSA
Cryptography Worksheet, RSA
Cryptography (pdf version)
Mod
Arithmetic Worksheet, Mod
Arithmetic (pdf version)
A
Taste of Cryptography and Number Theory
Other Handouts:
First
Year ANU Maths Courses and College prerequisites. See also the Department
of Maths website. Go
to Undergraduate study / First (Second, or Third) Year Courses and download
the pdf file noted there.
Majors
which involve Mathematics This can be useful for students with mathematical
abilities who want to know "why I should study mathematics" and
how to structure a science degree. Apart from these majors, many degrees
other than science require mathematics (engineering, economics, commerce,
IT, and increasingly
the
social sciences.)
