Astronauts in orbit are still strongly attracted to the Earth by gravity. So why do they float about as if they were in deep space, far from any big masses?
Here is a nice simple blog post which gets across the basics. For a more general/detailed explanation…I have tutorial sheets available!
The ancient Babylonians and Greeks knew about equations, though they wrote them using words and pictures. For the past 500 years, mathematicians and scientists have used symbols, the crucial one being the equals sign. Unusually, we know who invented it, and why. It was Robert Recorde, who in 1557 wrote in his treatise The Whetstone of Witte: “To avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a paire of paralleles, or gemowe lines of one lengthe: bicause noe .2. thynges, can be moare equalle.”
It’s not surprising that some people learn to hate maths.
Here is an article which talks about how poor teaching can sometimes cause ongoing problems. It’s just not fair that artistic people are frequently denied good explanations of mathematical concepts.
The young Gauss was so smart and mathematically intuitive, he must have been a nightmare to have in class…take a look here.
The explanation you are looking for is here.
If you fancy making some simulations of lots of interacting software agents, this is a great place to start playing about with large numbers of ‘turtles’.
StarLogo even includes a graphical programming interface.
The answer is a surprise.
Online teaching, when done just to cut costs, seems to have limited success.
Here is another New York Times article about the US’s attempts to educate their nation economically.
The central limit theorem is pretty cool and is outlined here.
So
toss a coin 100 times
count 1 for each head and 0 for each tail
add these numbers up ->sum
now repeat all of the above say 200 times
the 200 sum values will be distributed normally
eg
Sum/ Number of occurrences
2 /…3
10 /…..5
15 /……..8
23 /…………12
32 /……………………23
41 /……………………………..35
52 /…………………………………………….50
65 /………………………..29
73 /……………15
75 /……….10
82 /….4
93 /….4
95 /.1
100 /.1
Patrick Andrews has a PhD in Mechanical Engineering from Heriot-Watt University and an MSc in Neuroscience from the University of Cambridge.
A former Chartered Engineer and Chartered Mathematician, Patrick has worked in management consultancies and high-tech startups, and in academia as a postdoc in Applied Mathematics at Cambridge and a maths lecturer at De Montfort University.
Patrick is the father of three delightful (but not uniformly mathematical!) daughters.