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.
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 physical contexts.
Work out the numerical values for these physical quantities.
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
How much energy has gone into warming the planet?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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?
When you change the units, do the numbers get bigger or smaller?
Was it possible that this dangerous driving penalty was issued in error?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
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.
Match the descriptions of physical processes to these differential equations.
Explore the relationship between resistance and temperature
Use vectors and matrices to explore the symmetries of crystals.
Can you find the volumes of the mathematical vessels?
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Which dilutions can you make using only 10ml pipettes?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Who will be the first investor to pay off their debt?
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
This problem explores the biology behind Rudolph's glowing red nose.
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?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you work out what this procedure is doing?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
Can you draw the height-time chart as this complicated vessel fills with water?
Formulate and investigate a simple mathematical model for the design of a table mat.
How would you go about estimating populations of dolphins?