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.
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
Looking at small values of functions. Motivating the existence of the Taylor expansion.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Who will be the first investor to pay off their debt?
Was it possible that this dangerous driving penalty was issued in error?
Which pdfs match the curves?
Match the descriptions of physical processes to these differential equations.
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you find the volumes of the mathematical vessels?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Work out the numerical values for these physical quantities.
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you match the charts of these functions to the charts of their integrals?
Explore how matrices can fix vectors and vector directions.
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?
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Which units would you choose best to fit these situations?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Are these estimates of physical quantities accurate?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which dilutions can you make using only 10ml pipettes?
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 work out what this procedure is doing?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?