Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Use vectors and matrices to explore the symmetries of crystals.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Explore the properties of matrix transformations with these 10 stimulating questions.
Which of these infinitely deep vessels will eventually full up?
Explore the shape of a square after it is transformed by the action of a matrix.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you construct a cubic equation with a certain distance between its turning points?
Can you find the volumes of the mathematical vessels?
How much energy has gone into warming the planet?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Was it possible that this dangerous driving penalty was issued in error?
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.
Which line graph, equations and physical processes go together?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you match these equations to these graphs?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Match the descriptions of physical processes to these differential equations.
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.
This problem explores the biology behind Rudolph's glowing red nose.
When you change the units, do the numbers get bigger or smaller?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How do you choose your planting levels to minimise the total loss at harvest time?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
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
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Work out the numerical values for these physical quantities.
Why MUST these statistical statements probably be at least a little bit wrong?
How would you go about estimating populations of dolphins?
Which dilutions can you make using only 10ml pipettes?
Can you match the charts of these functions to the charts of their integrals?
Explore the relationship between resistance and temperature
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?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
Are these estimates of physical quantities accurate?