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This is our collection of resources on the theme of Population Dynamics. It will take you through the fascinating mathematics of creating mathematical models to describe the changes in populations of living creatures. This is an advanced set of material, taking you right through to university-level mathematical modelling.
If you have ambitions to become a famous and successful scientist or applied mathematician, this is a good place to start!
We made these resources with the help of two undergraduate Cambridge mathematicians and a postgraduate mathematical ecologist, who had often used many of these concepts throughout their studies, and we all hope that you enjoy this challenging and stimulating collection. Good luck!
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?