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.
Look at the advanced way of viewing sin and cos through their power series.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the properties of matrix transformations with these 10 stimulating questions.
Invent scenarios which would give rise to these probability density functions.
Was it possible that this dangerous driving penalty was issued in error?
Formulate and investigate a simple mathematical model for the design of a table mat.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
When you change the units, do the numbers get bigger or smaller?
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?
Match the descriptions of physical processes to these differential equations.
Can you make matrices which will fix one lucky vector and crush another to zero?
Why MUST these statistical statements probably be at least a little bit wrong?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the shape of a square after it is transformed by the action of a matrix.
Can you work out what this procedure is doing?
Explore the relationship between resistance and temperature
Which dilutions can you make using only 10ml pipettes?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which of these infinitely deep vessels will eventually full up?
Are these estimates of physical quantities accurate?
Can you find the volumes of the mathematical vessels?