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There are a lot of interesting web-pages out there about material in SMA,
covering many of the topics in the course and much more. For some of
them you'll need to have some sort of pdf reader (eg acrobat) installed.
Click
here
for the Single Maths A module page
and here
for duo.
-
An inductive
proof that all horses are the same colour (and why it's wrong).
-
Ninety-eight proofs
of Pythagoras's theorem (including this
neat animation).
-
Probably the best proof
of Pythagoras in the world (further discussed in Terry Tao's blog).
-
Some mathematical discussions,
written by Tim Gowers, who has a (higher-level) blog here.
-
The first chapter of
John Derbyshire's
book
has some discussion of the card-stacking problem; see also
this
link.
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More on the catenary.
-
The Wikipedia entry on the Gamma function
goes well beyond material covered in this course, but might still be
of interest to you.
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The mathworld entry on
complex numbers.
-
A Radio 4 In Our Time
discussion of imaginary numbers - the Related Links down the page are
also worth checking out.
-
Who wants to be a (dollar) millionaire: the Riemann
hypothesis, one of the
millennium
problems.
-
John Derbyshire's
book
explains the history, and some of the mathematics, of the Riemann Hypothesis in
a very accessible way.
-
Some pictures
and a biography
of Riemann.
-
The Riemann Hypothesis also featured in an American
TV show.
-
A short biography
of de Moivre (from the MacTutor website).
-
A little on the history of complex numbers and the
fundamental theorem of algebra. Some more about the fundamental theorem of
algebra can be found in Wikipedia,
and a very colourful explanation is in this paper.
- Four suggestions for further reading on complex numbers:
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Complex numbers too easy? Try
quaternions, invented
by Hamilton
on the 16th of
October 1843 (a Monday). See here
for some pictures of Hamilton's bridge. Quaternions are now
used in iPhones.
- Some information about Pythagoras is
here
and
here, while the story that
Hippasus' (re)discovery of the irrationality of the square root of two resulted in his
being thrown into the sea is reported
here and
here.
-
Pythagoras was also the subject of an episode of In Our Time on
Radio 4.
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Cantor's diagonal argument shows that there are "more" irrational
numbers than rational numbers; the Wikipedia entry for this topic
is here.
- You can find more about Bhaskara here
and here. For
some general discusion of Indian mathematics, try this
episode of In Our Time.
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A final
puzzle
from Terry Tao's blog, and two
more from Gil Kalai's blog.
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