Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
How would you go about estimating populations of dolphins?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which line graph, equations and physical processes go together?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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 biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which units would you choose best to fit these situations?
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?
Which pdfs match the curves?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
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.
Use vectors and matrices to explore the symmetries of crystals.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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
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?
When you change the units, do the numbers get bigger or smaller?
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the relationship between resistance and temperature
Which dilutions can you make using only 10ml pipettes?
Explore the properties of perspective drawing.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
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.
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you make matrices which will fix one lucky vector and crush another to zero?
Was it possible that this dangerous driving penalty was issued in error?
Can you find the volumes of the mathematical vessels?
This problem explores the biology behind Rudolph's glowing red nose.