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.
Get further into power series using the fascinating Bessel's equation.
Match the descriptions of physical processes to these differential equations.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
When you change the units, do the numbers get bigger or smaller?
How much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Was it possible that this dangerous driving penalty was issued in error?
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
Work out the numerical values for these physical quantities.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Build up the concept of the Taylor series
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 calculate various quantities in biological contexts.
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?
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Can you find the volumes of the mathematical vessels?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Use vectors and matrices to explore the symmetries of crystals.
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Who will be the first investor to pay off their debt?
This problem explores the biology behind Rudolph's glowing red nose.
Explore the properties of perspective drawing.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Which dilutions can you make using only 10ml pipettes?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Explore the shape of a square after it is transformed by the action of a matrix.