Advanced problems in the mathematical sciences.
This is the area of the advanced stemNRICH site devoted to the core applied mathematics underlying the sciences.
Explore the rates of growth of the sorts of simple polynomials
often used in mathematical modelling.
Find out some of the mathematics behind neural networks.
How does the half-life of a drug affect the build up of medication
in the body over time?
Can you break down this conversion process into logical steps?
Investigate the mathematics behind blood buffers and derive the
form of a titration curve.
In this question we push the pH formula to its theoretical limits.
Use the interactivity to practise your skills with concentrations
See how differential equations might be used to make a realistic
model of a system containing predators and their prey.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
At what temperature is the pH of water exactly 7?
Dip your toe into the fascinating topic of genetics. From Mendel's
theories to some cutting edge experimental techniques, this article
gives an insight into some of the processes underlying. . . .
Which line graph, equations and physical processes go together?
Can you work out how to produce the right amount of chemical in a
Can you fill in the mixed up numbers in this dilution calculation?
Use the logarithm to work out these pH values
Which dilutions can you make using 10ml pipettes and 100ml
Which exact dilution ratios can you make using only 2 dilutions?
When you change the units, do the numbers get bigger or smaller?
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. . . .
This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.
Fifth in our series of problems on population dynamics for advanced students.
Second in our series of problems on population dynamics for advanced students.
Sixth in our series of problems on population dynamics for advanced students.
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Fourth in our series of problems on population dynamics for advanced students.
Third in our series of problems on population dynamics for advanced students.
First in our series of problems on population dynamics for advanced students.
A brief introduction to PCR and restriction mapping, with relevant
Which units would you choose best to fit these situations?
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Which dilutions can you make using only 10ml pipettes?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
Is the age of this very old man statistically believable?
Can you work out the parentage of the ancient hero Gilgamesh?
How would you massage the data in this Chi-squared test to both
accept and reject the hypothesis?
STEM students at university often encounter mathematical
difficulties. This articles highlights the 8 key problems for
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
Use combinatoric probabilities to work out the probability that you
are genetically unique!
How efficiently can various flat shapes be fitted together?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Several graphs of the sort occurring commonly in biology are given.
How many processes can you map to each graph?
Test your skills at this light-absorbance calculation.
bioNRICH is the area of the stemNRICH site devoted to the
mathematics underlying the study of the biological sciences,
designed to help develop the mathematics required to get the most
from your. . . .
Scientists often require solutions which are diluted to a
particular concentration. In this problem, you can explore the
mathematics of simple dilutions
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.