This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Get further into power series using the fascinating Bessel's equation.
Which pdfs match the curves?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Who will be the first investor to pay off their debt?
Look at the advanced way of viewing sin and cos through their power series.
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
Invent scenarios which would give rise to these probability density functions.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Build up the concept of the Taylor series
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?
How would you go about estimating populations of dolphins?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work out the numerical values for these physical quantities.
Which units would you choose best to fit these situations?
Was it possible that this dangerous driving penalty was issued in error?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
When you change the units, do the numbers get bigger or smaller?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
Explore the relationship between resistance and temperature
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Match the descriptions of physical processes to these differential equations.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Can you make matrices which will fix one lucky vector and crush another to zero?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Which dilutions can you make using only 10ml pipettes?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Match the charts of these functions to the charts of their integrals.
Are these estimates of physical quantities accurate?
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.