This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.

Which units would you choose best to fit these situations?

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

How does the half-life of a drug affect the build up of medication in the body over time?

When you change the units, do the numbers get bigger or smaller?

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 step.

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. . . .

PhysNRICH is the area of the StemNRICH site devoted to the mathematics underlying the study of physics

engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering

Get some practice using big and small numbers in chemistry.

A look at different crystal lattice structures, and how they relate to structural properties

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

An introduction to a useful tool to check the validity of an equation.

See how the motion of the simple pendulum is not-so-simple after all.

Dip your toe into the world of quantum mechanics by looking at the Schrodinger equation for hydrogen atoms

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?

Things are roughened up and friction is now added to the approximate simple pendulum

Ever wondered what it would be like to vaporise a diamond? Find out inside...

Which line graph, equations and physical processes go together?

Work out the numerical values for these physical quantities.

Derive an equation which describes satellite dynamics.

Problems which make you think about the kinetic ideas underlying the ideal gas laws.

Where will the spaceman go when he falls through these strange planetary systems?

Investigate why the Lennard-Jones potential gives a good approximate explanation for the behaviour of atoms at close ranges

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 look at a fluid mechanics technique called the Steady Flow Momentum Equation.

Explore the Lorentz force law for charges moving in different ways.

Look at the units in the expression for the energy levels of the electrons in a hydrogen atom according to the Bohr model.

Can you work out the natural time scale for the universe?

What is an AC voltage? How much power does an AC power source supply?

Show that even a very powerful spaceship would eventually run out of overtaking power

A look at the fluid mechanics questions that are raised by the Stonehenge 'bluestones'.

Can you match up the entries from this table of units?

How high will a ball taking a million seconds to fall travel?

Work in groups to try to create the best approximations to these physical quantities.

How fast would you have to throw a ball upwards so that it would never land?

Can you arrange a set of charged particles so that none of them start to move when released from rest?

Use trigonometry to determine whether solar eclipses on earth can be perfect.

A think about the physics of a motorbike riding upside down

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. . . .