Get further into power series using the fascinating Bessel's equation.
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.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Was it possible that this dangerous driving penalty was issued in error?
Work out the numerical values for these physical quantities.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Build up the concept of the Taylor series
Get some practice using big and small numbers in chemistry.
Match the descriptions of physical processes to these differential equations.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Why MUST these statistical statements probably be at least a little bit wrong?
Analyse these beautiful biological images and attempt to rank them in size order.
Use vectors and matrices to explore the symmetries of crystals.
Formulate and investigate a simple mathematical model for the design of a table mat.
Which of these infinitely deep vessels will eventually full up?
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?
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
How would you go about estimating populations of dolphins?
When you change the units, do the numbers get bigger or smaller?
Which units would you choose best to fit these situations?
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
Explore the properties of matrix transformations with these 10 stimulating questions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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 how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you work out what this procedure is doing?
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Which pdfs match the curves?
Can you construct a cubic equation with a certain distance between its turning points?
Who will be the first investor to pay off their debt?