Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Population Dynamics Collection


This is our collection of resources on the theme of Population Dynamics. It will take you through the fascinating mathematics of creating mathematical models to describe the changes in populations of living creatures. This is an advanced set of material, taking you right through to university-level mathematical modelling.

If you have ambitions to become a famous and successful scientist or applied mathematician, this is a good place to start!




We made these resources with the help of two undergraduate Cambridge mathematicians and a postgraduate mathematical ecologist, who had often used many of these concepts throughout their studies, and we all hope that you enjoy this challenging and stimulating collection.  Good luck!

Population Dynamics

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 1

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 2

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 3

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 4

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 5

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Dynamics - Part 6

Age 16 to 18
Challenge Level Yellow starYellow star

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

Population Ecology Using Probability

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

Branching Processes and Extinction

Age 16 to 18
Challenge Level Yellow starYellow starYellow star

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

You may also like

Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo