CHRISTOPHER COOPER’S WEB PAGES

You can contact me at chris@maths.mq.edu.au

These are predominately PDF files for which you need Acrobat Reader on your computer.  If you don’t have it you can download it for free by going to the Adobe website http://www.adobe.com/products/acrobat/main.html and click on the button “Get Adobe Reader”

 

LITERARY WEB PAGES

The Australian Brontė Association

The Australian Brontė Association is a local organization, based in Sydney, devoted to promoting the study and enjoyment of the Brontės.  Its role is to complement the Brontė Society’s activities within Australia by organising Brontė events in the Sydney area.  It also produces a newsletter twice a year and a journal, The Thunderer, at the end of each year.  Past copies are available here.

http://www.maths.mq.edu.au/bronte

 

Other Literary Societies in Sydney: http://www.maths.mq.edu.au/bronte/litcoc.htm

 

The Brontė Society

The Brontė Society is the worldwide society, based in Haworth.  It maintains the Haworth parsonage and its collection of Brontė “treasures”, organises activities within the UK and produces the journal Brontė Studies (previously the Brontė Society Transactions).  The Australian Representative of the Brontė Society is the President of the Australian Brontė Association.

http://www.bronte.org.uk

 

MATHEMATICS NOTES

These notes have been used over many years for various courses at Macquarie University.  We have been quite innovative with course content at Macquarie and, while we teach material that’s widely taught in undergraduate courses, we also include an elementary account of quite a bit of material that’s only taught elsewhere in advanced postgraduate courses.

Though mathematically rigorous, the style in these notes is informal and they includes numerous “stories” to illustrate the concepts.  There are many exercises with solutions.

Feedback can be sent to chris@maths.mq.edu.au.

 

MATH123 Concepts of Calculus

This is an introductory course on calculus for those who haven’t studied it before.  It emphasises the concepts rather more than the technicalities and contains many examples and illustrations.  It’s particularly suitable for economics students and hence includes an elementary chapter on Lagrange Multipliers, something not normally done at this introductory level.  It also contains a numerical technique for finding areas under curves that’s superior to Simpson’s Rule.  This is the Cubic Fit Method and it’s not found elsewhere.  

http://www.ics.mq.edu.au/~chris/calculus

 

MATH237 Languages and Machines

This is a course on discrete mathematics that discusses the mathematics behind computing science.  It includes chapters on logic, set theory and strings and languages.  There are some chapters on finite-state machines, some chapters on Turing machines and computability, and a couple of chapters on codes.

http://www.ics.mq.edu.au/~chris/langmach

 

MATH300 Geometry and Topology

This geometry part of this course includes an introductory course on projective geometry (using the linear algebra approach rather than the axiomatic one) and some chapters on symmetry.  The topology part of this course consists of geometric and combinatorial topology and includes material on the classification of surfaces, embedding graphs on surfaces, map colouring and knot theory.  This latter topic includes material on the group of a knot, published here for the first time.  A chapter is devoted to providing a background in abelian groups for those who have never studied group theory.

http://www.ics.mq.edu.au/~chris/geometry

http://www.ics.mq.edu.au/~chris/topology

 

MATH337 Groups: Presentations and Representations

This is a first course on group theory but is more suitable to a third year student than a first year one.  It attempts to motivate group theory with many illustrative examples such as shuffling of cards, bell ringing and permutation puzzles.  As well as the usual introductory theory there’s an elementary introduction to representation theory, to the Todd-Coxeter algorithm and to free groups.

http://www.ics.mq.edu.au/~chris/groups

 

MATH338 Galois Theory

This follows the usual path through to Galois groups, but just for subfields of the complex numbers.  It takes as its goal the insolubility of polynomials by radicals.  This is as far as we normally reach, though there is an additional chapter that gives an algebraic proof of the Fundamental Theorem of Algebra, using Sylow theory.

http://www.ics.mq.edu.au/~chris/galois

 

Mathematics at the Edge of the Rational Universe

Mathematics is the art of logical story-telling and its creations exist only in the mind.  Yet it’s amazing how useful scientists have found these imaginative constructs in trying to understand the material universe.  This book will take you on a journey to the extreme regions, just before the point where logic breaks down.  It discusses the impossible, the infinite, the unimaginable, the uncomputable and the undecidable.  While a little high-school algebra wouldn’t go astray, the emphasis will be more on the imaginative and philosophical aspects than on the computational.

http://www.ics.mq.edu.au/~chris/beyond