This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Match the descriptions of physical processes to these differential equations.
Get further into power series using the fascinating Bessel's equation.
Was it possible that this dangerous driving penalty was issued in error?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Explore the properties of matrix transformations with these 10 stimulating questions.
The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?
Invent scenarios which would give rise to these probability density functions.
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Formulate and investigate a simple mathematical model for the design of a table mat.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which pdfs match the curves?
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Who will be the first investor to pay off their debt?
Build up the concept of the Taylor series
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Are these estimates of physical quantities accurate?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore how matrices can fix vectors and vector directions.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Explore the relationship between resistance and temperature
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Can you sketch these difficult curves, which have uses in mathematical modelling?
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Can you find the volumes of the mathematical vessels?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Can you match the charts of these functions to the charts of their integrals?
Looking at small values of functions. Motivating the existence of the Taylor expansion.