Get further into power series using the fascinating Bessel's equation.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Why MUST these statistical statements probably be at least a little bit wrong?
How would you go about estimating populations of dolphins?
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?
Invent scenarios which would give rise to these probability density functions.
Can you find the volumes of the mathematical vessels?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
How much energy has gone into warming the planet?
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Work out the numerical values for these physical quantities.
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.
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the descriptions of physical processes to these differential equations.
Get some practice using big and small numbers in chemistry.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
This problem explores the biology behind Rudolph's glowing red nose.
Who will be the first investor to pay off their debt?
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Explore the relationship between resistance and temperature
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 physical contexts.
Which units would you choose best to fit these situations?
Which dilutions can you make using only 10ml pipettes?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the shape of a square after it is transformed by the action of a matrix.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?