Which line graph, equations and physical processes go together?
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
When you change the units, do the numbers get bigger or smaller?
Which units would you choose best to fit these situations?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Get some practice using big and small numbers in chemistry.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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?
How much energy has gone into warming the planet?
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Work out the numerical values for these physical quantities.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
Get further into power series using the fascinating Bessel's equation.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Simple models which help us to investigate how epidemics grow and die out.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Explore the properties of perspective drawing.
Which dilutions can you make using only 10ml pipettes?
Can you work out which processes are represented by the graphs?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Explore the properties of matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Which of these infinitely deep vessels will eventually full up?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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?
Which pdfs match the curves?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Match the charts of these functions to the charts of their integrals.
Match the descriptions of physical processes to these differential equations.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
How would you go about estimating populations of dolphins?
Are these estimates of physical quantities accurate?
Build up the concept of the Taylor series