Biology

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Mathematical issues for biologists

STEM students at university often encounter mathematical difficulties. This articles highlights the 8 key problems for biologists.

$Advanced \STEM$

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Advanced STEM

This collection of resources is designed for developing STEM at Post-16.

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Core scientific mathematics

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

$\chemNRICH$

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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 of chemistry at A-level and university.

$\bioNRICH$

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bioNRICH

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 study of biology at A-level and university.

problem

Discuss and choose

Age

5 to 11

Challenge level

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

project

Bird watch

Do you know which birds are regular visitors where you live?

problem

Food web

Age

11 to 14

Challenge level

Is this eco-system sustainable?

problem

Food chains

Age

11 to 14

Challenge level

When a habitat changes, what happens to the food chain?

problem

Big and small numbers in the living world

Age

11 to 16

Challenge level

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

project

Terrariums

Build a mini eco-system, and collect and interpret data on how well the plants grow under different conditions.

problem

Maths is everywhere!

Age

11 to 16

Challenge level

Maths is everywhere in the world! Take a look at these images. What mathematics can you see?

problem

Genetics

Age

14 to 16

Challenge level

A problem about genetics and the transmission of disease.

problem

Packing 3D shapes

Age

14 to 16

Challenge level

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

problem

Ratios and dilutions

Age

14 to 16

Challenge level

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

problem

Robot camera

Age

14 to 16

Challenge level

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

problem

Dilution series calculator

Age

14 to 16

Challenge level

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

problem

Exact dilutions

Age

14 to 16

Challenge level

Which exact dilution ratios can you make using only 2 dilutions?

problem

Peas in a pod

Age

14 to 16

Challenge level

What is the chance this pea plant will look like its parents?

$Disease Dynamics - \understanding \the \spread \of \diseases$

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Disease dynamics - understanding the spread of diseases

Age

14 to 16

A chance to explore the mathematics of networks as applied to epidemics and the spread of disease.

problem

Big and small numbers in biology

Age

14 to 16

Challenge level

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

problem

Mixed up mixture

Age

14 to 16

Challenge level

Can you fill in the mixed up numbers in this dilution calculation?

problem

The genes of Gilgamesh

Age

14 to 16

Challenge level

Can you work out the parentage of the ancient hero Gilgamesh?

problem

Bigger or smaller?

Age

14 to 16

Challenge level

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

problem

Bio graphs

Age

14 to 16

Challenge level

What biological growth processes can you fit to these graphs?

problem

Alternative record book

Age

14 to 18

Challenge level

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

problem

Time to evolve

Age

14 to 16

Challenge level

How many generations would link an evolutionist to a very distant ancestor?

problem

Natural shapes

Age

14 to 16

Challenge level

How does shape relate to function in the natural world?

problem

Biology measurement challenge

Age

14 to 16

Challenge level

Analyse these beautiful biological images and attempt to rank them in size order.

problem

Real-life equations

Age

16 to 18

Challenge level

Here are several equations from real life. Can you work out which measurements are possible from each equation?

problem

Is your DNA unique?

Age

16 to 18

Challenge level

Use combinatoric probabilities to work out the probability that you are genetically unique!

problem

Population dynamics - part 3

Age

16 to 18

Challenge level

Third in our series of problems on population dynamics for advanced students.

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Population dynamics collection

Age

16 to 18

Challenge level

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

problem

Blood buffers

Age

16 to 18

Challenge level

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

problem

Population dynamics - part 2

Age

16 to 18

Challenge level

Second in our series of problems on population dynamics for advanced students.

problem

Population dynamics - part 1

Age

16 to 18

Challenge level

First in our series of problems on population dynamics for advanced students.

$Mixing \pH$

problem

Mixing pH

Age

16 to 18

Challenge level

Use the logarithm to work out these pH values

problem

Population dynamics

Age

16 to 18

Challenge level

This problem opens a major sequence of activities on the mathematics of population dynamics for advanced students.

problem

Very old man

Age

16 to 18

Challenge level

Is the age of this very old man statistically believable?

$\pH temperature$

problem

pH temperature

Age

16 to 18

Challenge level

At what temperature is the pH of water exactly 7?

problem

Population dynamics - part 4

Age

16 to 18

Challenge level

Fourth in our series of problems on population dynamics for advanced students.

problem

Extreme dissociation

Age

16 to 18

Challenge level

In this question we push the pH formula to its theoretical limits.

problem

Branching processes and extinction

Age

16 to 18

Challenge level

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

problem

Population dynamics - part 6

Age

16 to 18

Challenge level

Sixth in our series of problems on population dynamics for advanced students.

problem

Catalyse that!

Age

16 to 18

Challenge level

Can you work out how to produce the right amount of chemical in a temperature-dependent reaction?

problem

Chi-squared faker

Age

16 to 18

Challenge level

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

problem

Population dynamics - part 5

Age

16 to 18

Challenge level

Fifth in our series of problems on population dynamics for advanced students.

problem

Reaction types

Age

16 to 18

Challenge level

Explore the rates of growth of the sorts of simple polynomials often used in mathematical modelling.

problem

Stats statements

Age

16 to 18

Challenge level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

problem

Drug stabiliser

Age

16 to 18

Challenge level

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

problem

Population ecology using probability

Age

16 to 18

Challenge level

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

problem

Whose line graph is it anyway?

Age

16 to 18

Challenge level

Which line graph, equations and physical processes go together?

problem

Bird-brained

Age

16 to 18

Challenge level

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

article

Neural nets

Find out some of the mathematics behind neural networks.

problem

Predator - prey systems

Age

16 to 18

Challenge level

See how differential equations might be used to make a realistic model of a system containing predators and their prey.

article

Genetic intrigue

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 a fundamental biological discipline.