Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Build up the concept of the Taylor series
Work out the numerical values for these physical quantities.
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.
Get some practice using big and small numbers in chemistry.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Formulate and investigate a simple mathematical model for the design of a table mat.
Why MUST these statistical statements probably be at least a little bit wrong?
How do you choose your planting levels to minimise the total loss at harvest time?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you match the charts of these functions to the charts of their integrals?
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you make matrices which will fix one lucky vector and crush another to zero?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Can you work out what this procedure is doing?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use vectors and matrices to explore the symmetries of crystals.
Was it possible that this dangerous driving penalty was issued in error?
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?
Are these estimates of physical quantities accurate?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How would you go about estimating populations of dolphins?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate areas using random grids
Who will be the first investor to pay off their debt?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
When you change the units, do the numbers get bigger or smaller?
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?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the relationship between resistance and temperature