Match the descriptions of physical processes to these differential equations.
Was it possible that this dangerous driving penalty was issued in error?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Look at the advanced way of viewing sin and cos through their power series.
Get some practice using big and small numbers in chemistry.
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Which line graph, equations and physical processes go together?
Who will be the first investor to pay off their debt?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
Use vectors and matrices to explore the symmetries of crystals.
Work out the numerical values for these physical quantities.
Which pdfs match the curves?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Invent scenarios which would give rise to these probability density functions.
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.
Build up the concept of the Taylor series
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which of these infinitely deep vessels will eventually full up?
Formulate and investigate a simple mathematical model for the design of a table mat.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Can you work out what this procedure is doing?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the shape of a square after it is transformed by the action of a matrix.
Can you find the volumes of the mathematical vessels?
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Are these estimates of physical quantities accurate?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the properties of perspective drawing.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How would you go about estimating populations of dolphins?
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?