See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Build up the concept of the Taylor series
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Look at the advanced way of viewing sin and cos through their power series.
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Invent scenarios which would give rise to these probability density functions.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
How much energy has gone into warming the planet?
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the shape of a square after it is transformed by the action of a matrix.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Was it possible that this dangerous driving penalty was issued in error?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the properties of matrix transformations with these 10 stimulating questions.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Can you construct a cubic equation with a certain distance between its turning points?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Which units would you choose best to fit these situations?
Explore the relationship between resistance and temperature
Who will be the first investor to pay off their debt?
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Explore the properties of perspective drawing.
Match the descriptions of physical processes to these differential equations.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Analyse these beautiful biological images and attempt to rank them in size order.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which dilutions can you make using only 10ml pipettes?
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?
This problem explores the biology behind Rudolph's glowing red nose.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Can you work out what this procedure is doing?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore how matrices can fix vectors and vector directions.