Advanced problems in the mathematical sciences.
Which line graph, equations and physical processes go together?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Look at the calculus behind the simple act of a car going over a
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
Find out some of the mathematics behind neural networks.
Work in groups to try to create the best approximations to these
PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics
A look at different crystal lattice structures, and how they relate
to structural properties
Find out how to model a battery mathematically
chemNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of chemistry, designed to help
develop the mathematics required to get the most from your study. . . .
See how the motion of the simple pendulum is not-so-simple after
Read all about electromagnetism in our interactive article.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
A look at the fluid mechanics questions that are raised by the
A look at a fluid mechanics technique called the Steady Flow
How fast would you have to throw a ball upwards so that it would
An introduction to a useful tool to check the validity of an equation.
Get some practice using big and small numbers in chemistry.
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
How does the half-life of a drug affect the build up of medication
in the body over time?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the rates of growth of the sorts of simple polynomials
often used in mathematical modelling.
Explore the power of aeroplanes, spaceships and horses.
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?
Show that even a very powerful spaceship would eventually run out
of overtaking power
When you change the units, do the numbers get bigger or smaller?
Ever wondered what it would be like to vaporise a diamond? Find out
Which units would you choose best to fit these situations?
Where will the spaceman go when he falls through these strange planetary systems?
Problems which make you think about the kinetic ideas underlying
the ideal gas laws.
How high will a ball taking a million seconds to fall travel?
Can you work out the natural time scale for the universe?
Investigate why the Lennard-Jones potential gives a good
approximate explanation for the behaviour of atoms at close ranges
Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.
Have you got the Mach knack? Discover the mathematics behind
exceeding the sound barrier.
Can you match up the entries from this table of units?
What is an AC voltage? How much power does an AC power source
Explore the Lorentz force law for charges moving in different ways.
Investigate the effects of the half-lifes of the isotopes of cobalt
on the mass of a mystery lump of the element.
Investigate some of the issues raised by Geiger and Marsden's
famous scattering experiment in which they fired alpha particles at
a sheet of gold.
A ball whooshes down a slide and hits another ball which flies off
the slide horizontally as a projectile. How far does it go?
An article about the kind of maths a first year undergraduate in
physics, engineering and other physical sciences courses might
encounter. The aim is to highlight the link between particular
maths. . . .
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.
Can you arrange a set of charged particles so that none of them
start to move when released from rest?
Explore the energy of this incredibly energetic particle which struck Earth on October 15th 1991
Work out the numerical values for these physical quantities.
Explore how can changing the axes for a plot of an equation can
lead to different shaped graphs emerging
Derive an equation which describes satellite dynamics.