Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in error?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get further into power series using the fascinating Bessel's equation.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which units would you choose best to fit these situations?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How much energy has gone into warming the planet?
Work out the numerical values for these physical quantities.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Invent scenarios which would give rise to these probability density functions.
When you change the units, do the numbers get bigger or smaller?
Get some practice using big and small numbers in chemistry.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Match the descriptions of physical processes to these differential equations.
How would you go about estimating populations of dolphins?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you find the volumes of the mathematical vessels?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Can you match these equations to these graphs?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
This problem explores the biology behind Rudolph's glowing red nose.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you work out what this procedure is doing?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the relationship between resistance and temperature
Go on a vector walk and determine which points on the walk are closest to the origin.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore how matrices can fix vectors and vector directions.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.