Build up the concept of the Taylor series
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.
How would you go about estimating populations of dolphins?
Was it possible that this dangerous driving penalty was issued in error?
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.
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Who will be the first investor to pay off their debt?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Invent scenarios which would give rise to these probability density functions.
Use vectors and matrices to explore the symmetries of crystals.
Can you make matrices which will fix one lucky vector and crush another to zero?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
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?
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?
Can you match the charts of these functions to the charts of their integrals?
Explore the properties of matrix transformations with these 10 stimulating questions.
Which pdfs match the curves?
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?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Which units would you choose best to fit these situations?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Explore the relationship between resistance and temperature