Are these statistical statements sometimes, always or never true? Or it is impossible to say?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Was it possible that this dangerous driving penalty was issued in error?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which units would you choose best to fit these situations?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you find the volumes of the mathematical vessels?
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
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.
This problem explores the biology behind Rudolph's glowing red nose.
Match the descriptions of physical processes to these differential equations.
Can you work out which processes are represented by the graphs?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
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?
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.
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Which of these infinitely deep vessels will eventually full up?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Who will be the first investor to pay off their debt?