Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
Work out the numerical values for these physical quantities.
Look at the advanced way of viewing sin and cos through their power series.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which units would you choose best to fit these situations?
How would you go about estimating populations of dolphins?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Build up the concept of the Taylor series
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the relationship between resistance and temperature
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Invent scenarios which would give rise to these probability density functions.
Explore the shape of a square after it is transformed by the action of a matrix.
Which pdfs match the curves?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
Was it possible that this dangerous driving penalty was issued in error?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Match the descriptions of physical processes to these differential equations.
Which dilutions can you make using only 10ml pipettes?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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?
Who will be the first investor to pay off their debt?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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 make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the properties of perspective drawing.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Go on a vector walk and determine which points on the walk are closest to the origin.