Get some practice using big and small numbers in chemistry.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Work out the numerical values for these physical quantities.
Which line graph, equations and physical processes go together?
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which units would you choose best to fit these situations?
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?
Was it possible that this dangerous driving penalty was issued in error?
Use vectors and matrices to explore the symmetries of crystals.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Invent scenarios which would give rise to these probability density functions.
Which pdfs match the curves?
Match the descriptions of physical processes to these differential equations.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Who will be the first investor to pay off their debt?
When you change the units, do the numbers get bigger or smaller?
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 make matrices which will fix one lucky vector and crush another to zero?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you work out what this procedure is doing?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Can you sketch these difficult curves, which have uses in mathematical modelling?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you match the charts of these functions to the charts of their integrals?
Explore the relationship between resistance and temperature
Which dilutions can you make using only 10ml pipettes?
How would you go about estimating populations of dolphins?