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.
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Build up the concept of the Taylor series
Use vectors and matrices to explore the symmetries of crystals.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the properties of matrix transformations with these 10 stimulating questions.
How would you go about estimating populations of dolphins?
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
Explore how matrices can fix vectors and vector directions.
Which of these infinitely deep vessels will eventually full up?
Invent scenarios which would give rise to these probability density functions.
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which pdfs match the curves?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Match the descriptions of physical processes to these differential equations.
Work out the numerical values for these physical quantities.
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?
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?
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Get some practice using big and small numbers in chemistry.
Formulate and investigate a simple mathematical model for the design of a table mat.
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 the relationship between resistance and temperature
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of perspective drawing.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you match these equations to these graphs?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?