Which of these infinitely deep vessels will eventually full up?

Use vectors and matrices to explore the symmetries of crystals.

How would you go about estimating populations of dolphins?

Can you make matrices which will fix one lucky vector and crush another to zero?

Explore the shape of a square after it is transformed by the action of a matrix.

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Explore the properties of matrix transformations with these 10 stimulating questions.

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Explore the meaning of the scalar and vector cross products and see how the two are related.

How do you choose your planting levels to minimise the total loss at harvest time?

This problem explores the biology behind Rudolph's glowing red nose.

Was it possible that this dangerous driving penalty was issued in error?

Can you match the charts of these functions to the charts of their integrals?

Get further into power series using the fascinating Bessel's equation.

Analyse these beautiful biological images and attempt to rank them in size order.

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Go on a vector walk and determine which points on the walk are closest to the origin.

Match the descriptions of physical processes to these differential equations.

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Look at the advanced way of viewing sin and cos through their power series.

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Looking at small values of functions. Motivating the existence of the Taylor expansion.

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

Can you draw the height-time chart as this complicated vessel fills with water?

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?

Invent scenarios which would give rise to these probability density functions.

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Build up the concept of the Taylor series

Can you sketch these difficult curves, which have uses in mathematical modelling?

Can you work out which processes are represented by the graphs?

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Formulate and investigate a simple mathematical model for the design of a table mat.

Which line graph, equations and physical processes go together?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Why MUST these statistical statements probably be at least a little bit wrong?

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Explore the relationship between resistance and temperature

Can you construct a cubic equation with a certain distance between its turning points?