Running a U3A group is very different from school or college teaching. Our members vary from those whose school maths has been gently rusting away for fifty years to retired engineers and scientists, but we have some great advantages. What our members have in common are lively minds , and the desire to learn. We meet fortnightly , which is a long time for our tired old memories. So we begin each session with a recap.
We began our meetings in 2013, with a historical approach; stone age notched bones, Sumerian bags of counters, the beginnings of place value, Greek logic and reasoning, irrational numbers and Euclid. Our members were intrigued by Roman multiplication; why does it work? We made polyhedral, leading to more geometry, Fibonacci and the golden ratio and plant growth; and a beautiful quilt made by a member. We investigated plane and spherical geometry, tinkering with mirrors, cameras, a globe and bits of string; what is a straight line? We learned about the great Bedford level uproar and the Flat Earth Society. We studied the development of astronomy and navigation, Newtons discoveries and determinism. By contrast, we rigged up a double pendulum as an example of chaos. we encountered infinity as the Greeks attempted to tackle it, and got as far as Cantor's  revolutionary ideas. There's more than one kind of infinity!
We did some algebra, studying polynomial functions  and their Cartesian graphs with little models. we developed function theory as far as logarithmic, exponential and trig functions. these last are periodic and repeating functions which led us to Simple Harmonic Motion; approximately what an oscillating system does. We listened to a tuning fork and a members guitar as examples and saw a little Lego gadget which drew a sine wave as it rolled along. We investigated the problem of musical tuning known as Pythagorean comma. A lot of musicians don't know about that.
We went further into the understanding of calculus that most A level students do and got as far as the Fundamental Theorem of Analysis. We found the minimum surface area of a fixed volume cylinder by calculus ; rather surprisingly a result which Archimedes knew! (how?)
We have studied the concept of proof and recently complex numbers. we explored probability and statistics, always relevant in todays world. for 2017, we have agreed to use Tony Crilly's "50 Mathematical Ideas you Really Need to Know" as a course book. This will be the framework, not a cage and will give us a fresh approach to the extended revision our members want. We have a mixed group of twelve members and I am impressed by their enthusiasm and achievements
Ian Spey  

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