Mathematical Links
The internet has an abundance of mathematics sites and the purpose of this page is to get you to explore them. There are so many site that I have had to cheat and subdivide the ten slots. In addition, there are lots of links on the other pages of this site.
Try these links:
1. Video Lectures
- You'll need Real
Player
, a sound card, a fast computer and a good internet connection to
watch these.
Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas
- This is a series of talks and songs devoted to the history and
proof of Fermat's
Last Theorem, given at a level that is accessible to everyone.
Although the video is long you should watch it to find out all about
the result that had mathematicians puzzled for hundreds of years.
- Do find out about Tom Lehrer as well and have a look at his song lyrics.
- What's Problematic in Undergraduate Mathematics Education?
- Teachers and lecturers may like to compare experience in US education with their own. Don't forget the first year of undergraduate education is comparable with sixth-form education in England and Wales.
- This is a discussion about undergraduate mathematical experience in America, particularly with elementary calculus. The video is, unfortunately, not exactly professionally produced.
- Mathematics in the Broadcast Media
- Do watch Keith Devlin's introduction which includes a few minutes of an excellent and very amusing BBC radio series "The Square on the Pythagoras" broadcast in 1995. If you know anyone with a copy of this then do listen to it.
- There are lots more videoed lectures at Mathematical Sciences Research Institute though many are aimed at postgraduate level and beyond.
- Do find out about Tom Lehrer as well and have a look at his song lyrics.
2. Ian Stewart's Royal Institution Christmas Lectures
- In December 1997 Ian Stewart gave a series of televised lectures
called The Magical Maze: The Natural World and the Mathematical Mind.
These lectures made mathematics come alive and should be watched by
anyone interested in mathematics. If you can get hold of the videos
then you are in for a treat. You'll find details of how to buy the
videos at The
Royal Institution of Great Britain and a summary of the lectures
at RIGB 1997 Christmas Lectures.
- "The Christmas Lectures are an opportunity for young people to learn directly from scientists who are recognised as among the best in the world. The lectures are broadcast not only in Britain, but also in Europe, Japan and the USA, demonstrating the ability of the lecturers to explain their fascination with science and their own work to young people of all backgrounds."
- There have only been two Christmas lectures about mathematics, Ian Stewart's in 1997 and Christopher Zeeman's sometime in the seventies. The fact that they were both mathematics professors at Warwick University tells you something about the status of the Mathematics Institute.
- "The Christmas Lectures are an opportunity for young people to learn directly from scientists who are recognised as among the best in the world. The lectures are broadcast not only in Britain, but also in Europe, Japan and the USA, demonstrating the ability of the lecturers to explain their fascination with science and their own work to young people of all backgrounds."
3. The Most Common Errors In Undergraduate Mathematics
- This is an excellent page giving all the errors we all see time
and time again, along with explanations of what's gone wrong. There's
a great opening sentence:
- "I am tired of seeing these same old errors over and over again. (I would rather see new, original errors!)"
- See note above about undergraduate.
- "I am tired of seeing these same old errors over and over again. (I would rather see new, original errors!)"
4. Proof
- One of the complaints of university mathematics lecturers is that students don't seem to appreciate the nature of, or indeed the necessity for proof in maths. This page, The Origins of Proof, explains all about proof in an easy to follow manner. Oh yes, it also includes my all-time favourite puzzle. Go there and find out what it is.
5. Cryptography
- One of the most recent and surprising applications of mathematics
is to cryptography. I say surprising, because the underlying number
theory was developed without any idea that it would be so useful. The
browser you are using may well use these techniques to connect to
secure sites. Read all about it at the RSA site.
- I particularly recommend reading What is public-key cryptography? which has become an extremely secure way of encrypting messages, and is the reason why both the British and American governments are worried about its use Secrecy.
- Recently a school student made a significant contribution to cryptography called The Cayley-Purser Algorithm.
- Simon Singh, author of Fermat's Last Theorem, has published a fascinating book called The Code Book which details the history of crypography from ancient Egypt to quantum cryptography. Internet Bookshop, Amazon
- See also:
- I particularly recommend reading What is public-key cryptography? which has become an extremely secure way of encrypting messages, and is the reason why both the British and American governments are worried about its use Secrecy.
6. Unsolved Mathematics Problems
- Fermat's Last Theorem may have been solved but there are plenty of other unsolved problems, one of the most famous being Goldbach's Conjecture (made in 1742) that every even integer greater than two can be expressed as the sum of two primes. Unsolved Mathematics Problems gives this amongst many other such problems.
7. Understanding Mathematics
- Many of you may wish that mathematics wasn't so hard to
understand. Well there's no getting away from it, it is hard.
But every so often it clicks and you realise that it was all worth it.
- Understanding Mathematics a study guide by Peter Alfeld is designed to help you study. It starts with questions like:
-
That being lost in mathematics is the natural state of things?
-
That lectures and textbooks are incomprehensible?
-
That the amount of material in any math course is so overwhelming that you (or anybody else) could not possibly absorb it?
Do you feel
- and so on.
- If you experience any of these feelings then Peter Alfeld will help you to overcome them. It will also teach you about Powers, Logs and Quadratic Equations as well as telling you about the beauty of mathematics, something I have attempted to do with my pages.
- Peter Alfeld says "The purpose of this page is to help you learn how to approach mathematics in a more effective way".
- Understanding Mathematics a study guide by Peter Alfeld is designed to help you study. It starts with questions like:
8. Internet Mathematics Library
- The Math Forum Internet Mathematics Library is a collection of maths pages sorted not only by subject but by Grade Levels - Elementary, Middle, Secondary, College, Research. This will give you access to a very large store of pages at your level.
9. POP Mathematics
- "Did you ever wonder what made your teacher get so excited
about some topic in Mathematics? On this page, we will try to collect
items about Mathematics one of which hopefully may explain this weird behavior."
- Beautifully put! Don't waste time, visit POP Mathematics now. Warning - it is the gateway to so many interesting mathematical sites that you may never come back here again!
10. Classic Fallacies
- This is what happens when you are slapdash in mathematics and you end up showing that 1 = 2 or that every person in Canada is the same age. Classic Fallacies shows you the fallacy then helps you to spot the flaw.
11. Eric Weisstein's World of Mathematics.
Yes, I know there should only be ten links, but I just can't leave this one out. It is a comprehensive online encyclopedia of mathematics which has recently reappeared after a bruising copyright dispute; it contains explanations on almost every part of mathematics. If you want to find out about any mathematical topic this is very definitely the first place to look.
As I've said, there are so many good mathematics sites that I can barely do justice to them. I hope that the sites that I have given, and the links elsewhere on this site, will start you on a journey of exploration during which you'll find much to marvel at.