By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Which pdfs match the curves?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How would you go about estimating populations of dolphins?
Use vectors and matrices to explore the symmetries of crystals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Who will be the first investor to pay off their debt?
Why MUST these statistical statements probably be at least a little bit wrong?
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
How do you choose your planting levels to minimise the total loss at harvest time?
Match the descriptions of physical processes to these differential equations.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
Explore the properties of perspective drawing.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
Match the charts of these functions to the charts of their integrals.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the relationship between resistance and temperature
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?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
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?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you construct a cubic equation with a certain distance between its turning points?