Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
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
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
Which units would you choose best to fit these situations?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
How much energy has gone into warming the planet?
Formulate and investigate a simple mathematical model for the design of a table mat.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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 physical contexts.
Invent scenarios which would give rise to these probability density functions.
Build up the concept of the Taylor series
Why MUST these statistical statements probably be at least a little bit wrong?
Was it possible that this dangerous driving penalty was issued in error?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
Which pdfs match the curves?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Who will be the first investor to pay off their debt?
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?
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
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?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore how matrices can fix vectors and vector directions.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Can you work out what this procedure is doing?