What's a theorem? An assertion you can prove is true, at least that's what I'm asserting following yesterday's seminar at an Oxford University Continuing Education (OUCE) day.
If you've seen the Theorem of the Day web site you'll get a flavour of what the discussion was about. The presenter was the author of that site. Now that site is not easy, not the best way to get to learn about theorems, if you know nothing to start with. Theorems are challenging. But if you like thinking, then you'd have enjoyed the day. And it did help to have some maths.
The participants included relative amateurs like myself, retired maths teachers, chemists, physicists, an eminent professor of biology, a couple of sixth former, a member of the Institute of Mathematics and her husband who'd done a PhD in maths - but not this field she hastened to assure me.
Showing posts with label maths. Show all posts
Showing posts with label maths. Show all posts
Wednesday, August 29, 2018
Sunday, October 18, 2009
Guided tour to theorem country
What's a theorem? An assertion you can prove is true, at least that's what I'm asserting following yesterday's seminar at an Oxford University Continuing Education (OUCE) day.
If you've seen the web site Theorem of the Day, then you'll get a flavour of the day, created by the presenter, Robin Whitty. That web site is challenging though and so was the day. However, if you like thinking, and thinking in good like minded company, then you'd have enjoyed it too. The company included physicists, sixth formers, an eminent professor of biology, chemists, a member of the society of mathematics and her husband who had a PhD in maths, though not in the same area she hastened to assure me, and retired maths teachers.
Starting with some maths language and shorthand helped me remember some of the maths I used to know, and others in the audience were equally forthcoming with questions, which made for a relaxed atmosphere. Theorems covered included:
Finally we had a discussion about whether computers 'do' maths. There's a Faustian battle between mathematicians: you have a choice between geometry and algebra. If we use computers, then we turn to algebra to compute rather than geometry that allows our intuition.
For example, someone had been presenting partitions from using the Pascal's triangle. At the end of the lecture, one person, Corteel, saw a bijection along the rth diagonal within the binomial expansion that matched the rth row of the partitioning - a computer couldn't have seen that!
I might go to another OUCE maths day - like the one next year on the history and consequences of calculus.
If you've seen the web site Theorem of the Day, then you'll get a flavour of the day, created by the presenter, Robin Whitty. That web site is challenging though and so was the day. However, if you like thinking, and thinking in good like minded company, then you'd have enjoyed it too. The company included physicists, sixth formers, an eminent professor of biology, chemists, a member of the society of mathematics and her husband who had a PhD in maths, though not in the same area she hastened to assure me, and retired maths teachers.
Starting with some maths language and shorthand helped me remember some of the maths I used to know, and others in the audience were equally forthcoming with questions, which made for a relaxed atmosphere. Theorems covered included:
- Euclid's Infinity of Primes
- Ramsey's Theorem (I can see how to relate that to how many people you know)
- Contraction Mapping Theorem
- Hardy-Ramanujan Asymptotic Partition Formula - partitioning is so simple that you teach it to infant school children - it's how many different ways can you add up a number, like 5 is 2+3, and also 4+1, and 1+1+3 and so on
- Erdos-K-Rado Theorem on intersecting permutations - we got a bit confused on this one because Robin initially told us to think of Rubik's cube, but it isn't quite the same.
- The Robbins problem - I like Boolean algebra
- Morley's Miracle - that was an amusing story of a school teacher who discovered this by accident. If you tri-sect the angles of a triangle then at the intersections of the trisection lines, you can make the vertices's of a triangle. The miracle is that no-one ever noticed before Morley did, but then drawing a trisection isn't very easy.
Finally we had a discussion about whether computers 'do' maths. There's a Faustian battle between mathematicians: you have a choice between geometry and algebra. If we use computers, then we turn to algebra to compute rather than geometry that allows our intuition.
For example, someone had been presenting partitions from using the Pascal's triangle. At the end of the lecture, one person, Corteel, saw a bijection along the rth diagonal within the binomial expansion that matched the rth row of the partitioning - a computer couldn't have seen that!
I might go to another OUCE maths day - like the one next year on the history and consequences of calculus.
Tuesday, August 11, 2009
Maths
If you like maths, then look at the site that gives a theorem for the day, here: http://www.theoremoftheday.org/. If you were a maths teacher, you could collect all the pdf files in a folder, ready for use.
Wednesday, March 25, 2009
Ada Lovelace Day
Ada Lovelace blogging happened yesterday.
Adele Goldberg and Grace Hopper were important computer scientists who've been blogged.
At least five other people wrote about Emmy Noether. Here's one. I really like the Gin and Comment blog on Honorary Men.
I like it that some people wrote about their mothers as inspiration but isn't it wonderful that fathers are writing about their daughters programming? And there's two posts on grandmothers.
And there's a map of where we blogged at here.
Adele Goldberg and Grace Hopper were important computer scientists who've been blogged.
At least five other people wrote about Emmy Noether. Here's one. I really like the Gin and Comment blog on Honorary Men.
I like it that some people wrote about their mothers as inspiration but isn't it wonderful that fathers are writing about their daughters programming? And there's two posts on grandmothers.
And there's a map of where we blogged at here.
Tuesday, March 24, 2009
Emmy Noether
Einstein couldn't have proved the conservation of energy without the work of Emmy Noether. This was a German woman born 1882, so of my grandmother's generation. My grandmother was the daughter of a Scottish carpenter. Emmy Noether was the daughter of a German mathematician. When my grandmother was 14, her father died, so she had to leave school though she'd intended to train as a teacher, and go to work. Emmy Noether's father taught her maths, and in 1907, she was awarded a doctorate - only the second doctorate awarded to a woman by a German university.
In the same decade, Einstein was working out his theory of general relativity but had more problems to solve. He presented his theory and problems in 1915, convincing Hilbert and Klein of the merits of his work. They involved Emmy Noether, who within months produced a brilliant paper that resolved one of the issues of general relativity.
In 1915, my grandmother had her first child, my much loved aunty. Both Emmy Noether and my grandmother have impacted on my life. It's people like Emmy Noether beating the way through prejudices against women and Jews that mean my grandmother's children, grandchildren and great grand-daughters can recognise and use their mathematical talents.
But achievement is not due only to women on their own. Emmy Noether had a skilled father who recognised and nurtured her talents. Women need reliable, caring fathers who respect and encourage their daughters to realise their potential to contribute to our world so men and womens' work complement each other, as did Einstein and Noether.
Source: Derbyshire, J, Unknown Quantity: a real and imaginary history of algebra, 2006
In the same decade, Einstein was working out his theory of general relativity but had more problems to solve. He presented his theory and problems in 1915, convincing Hilbert and Klein of the merits of his work. They involved Emmy Noether, who within months produced a brilliant paper that resolved one of the issues of general relativity.
In 1915, my grandmother had her first child, my much loved aunty. Both Emmy Noether and my grandmother have impacted on my life. It's people like Emmy Noether beating the way through prejudices against women and Jews that mean my grandmother's children, grandchildren and great grand-daughters can recognise and use their mathematical talents.
But achievement is not due only to women on their own. Emmy Noether had a skilled father who recognised and nurtured her talents. Women need reliable, caring fathers who respect and encourage their daughters to realise their potential to contribute to our world so men and womens' work complement each other, as did Einstein and Noether.
Source: Derbyshire, J, Unknown Quantity: a real and imaginary history of algebra, 2006
Thursday, January 31, 2008
Visiting Bath
Daughter and I went to visit Bath University where she had an interview in the maths department. There was the usual milling around of enthusiastic youngsters, the pleasant experience of finding someone else who is as interested in maths as you are, and the almost-always-male lecturer who provides an explanation of the course and eulogises on the department and the university.
Unfortunately, they did seem to emphasise Bath's great sporting facilities, and there were a lot of very sporty looking people bouncing around with their kit - probably because it's Wednesday afternoon when many universities take the time off studying for sport. This didn't go down too well with daughter, even though they apparently have a good tae kwondo club too.
Two other things put her off:
She quite liked the city; we spent a happy hour exploring the shops in the centre, including a magic shop where we found a birthday present for small cousin, and a chocolate shop...
We got back to the station in time to catch a train just after 5 o'clock.
Unfortunately, they did seem to emphasise Bath's great sporting facilities, and there were a lot of very sporty looking people bouncing around with their kit - probably because it's Wednesday afternoon when many universities take the time off studying for sport. This didn't go down too well with daughter, even though they apparently have a good tae kwondo club too.
Two other things put her off:
- the university doesn't have arts or social science faculties and she would like to meet other than scientists, mathematicians and technologists.
- after first year you have to live on the other side of the city and it takes 40-50 minutes to get across to the university
She quite liked the city; we spent a happy hour exploring the shops in the centre, including a magic shop where we found a birthday present for small cousin, and a chocolate shop...
We got back to the station in time to catch a train just after 5 o'clock.
Subscribe to:
Posts (Atom)
