Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
When you change the units, do the numbers get bigger or smaller?
How much energy has gone into warming the planet?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Get some practice using big and small numbers in chemistry.
Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Formulate and investigate a simple mathematical model for the design of a table mat.
Build up the concept of the Taylor series
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?
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?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Get further into power series using the fascinating Bessel's equation.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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 relationship between resistance and temperature
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which dilutions can you make using only 10ml pipettes?
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?
Look at the advanced way of viewing sin and cos through their power series.
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Is it really greener to go on the bus, or to buy local?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore how matrices can fix vectors and vector directions.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which pdfs match the curves?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Simple models which help us to investigate how epidemics grow and die out.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?