Go on a vector walk and determine which points on the walk are
closest to the origin.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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.
Which line graph, equations and physical processes go together?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the meaning of the scalar and vector cross products and see how the two are related.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
How much energy has gone into warming the planet?
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Was it possible that this dangerous driving penalty was issued in
Explore the shape of a square after it is transformed by the action
of a matrix.
Analyse these beautiful biological images and attempt to rank them in size order.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the properties of matrix transformations with these 10 stimulating questions.
Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Why MUST these statistical statements probably be at least a little
Invent scenarios which would give rise to these probability density functions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
Match the descriptions of physical processes to these differential
How would you go about estimating populations of dolphins?
When you change the units, do the numbers get bigger or smaller?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
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?
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which units would you choose best to fit these situations?
This problem explores the biology behind Rudolph's glowing red
Can you sketch these difficult curves, which have uses in