Match the descriptions of physical processes to these differential equations.
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Invent scenarios which would give rise to these probability density functions.
Who will be the first investor to pay off their debt?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Was it possible that this dangerous driving penalty was issued in error?
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which line graph, equations and physical processes go together?
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?
Can you find the volumes of the mathematical vessels?
Which of these infinitely deep vessels will eventually full up?
Can you make matrices which will fix one lucky vector and crush another to zero?
How much energy has gone into warming the planet?
Can you match the charts of these functions to the charts of their integrals?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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.
Can you match these equations to these graphs?
Why MUST these statistical statements probably be at least a little bit wrong?
Explore how matrices can fix vectors and vector directions.
When you change the units, do the numbers get bigger or smaller?
This problem explores the biology behind Rudolph's glowing red nose.
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 physical contexts.
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
Which units would you choose best to fit these situations?
Which dilutions can you make using only 10ml pipettes?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Go on a vector walk and determine which points on the walk are closest to the origin.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Get some practice using big and small numbers in chemistry.
Have you ever wondered what it would be like to race against Usain Bolt?