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# Maths Makes A Difference

### 2 February 2021: Making predictions in an uncertain world

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Age 14 to 18

- Problem
- Student Solutions

**On 2 February 2021, the Mathematics outreach teams at Oxford and Cambridge streamed a webinar aimed at year 12 students, as part of a series of webinars for Maths Makes A Difference.**

**In this interactive webinar we discussed how predictions can be useful in a wide range of situations, and why predicting the future might be difficult!**

Here is a PDF of the slides from the start of the presentation.

Here is a PDF of the slides from during the presentation.

You can watch the recording of the webinar below:

Here is a summary of the ideas from the webinar, with some extra explanations about cobweb diagrams.

**Links to resources used in the webinar**

- Logistic map with one population and slider for k
- Logistic maps with one population and input box for k
- Logistic map with three populations
- Desmos cobweb diagram
- Geogebra cobweb diagram (this wasn't used in the webinar)

**Links to further reading/watching**

- Plus maths article on the logistic map
- BBC weather article on "Beast from the East 2021"
- An article about Mary Cartwright one of the founders of chaos theory
- Royal Institution Christmas lecture by Professor Marcus du Sautoy. At about 17 minutes in there is an example of where small changes in initial conditions can make a big difference, and at about 24 minutes in there is a discussion about lemmings and a demonstration of how the logistic map works with some human-lemmings.
- Numberphile video where Ben Sparks talks about the logistic map and the Feigenbaum constant.
- Two books on Chaos (that Claire read when she was in Yr13) are Chaos by James Gleick and Does God Play Dice? by Ian Stewart. Both of these books contain a section on the Logistic Map.
- This list of books contains recommendations for sixth-formers (and everyone else interested in maths), which covers lots of different maths topics, including Chaos.
- Vicky's book Why Study Mathematics? includes some of the ways in which maths can be used to make a difference.

We encouraged participants to continue exploring after the webinar, and to send us the outcomes of their investigations for others to see. Here are some possibilities we suggested they could explore:

- You could explore the maths of the logistic map further.
- You could research the use of maths in studying population dynamics
- You could research the maths in weather forecasting.
- You could explore other applications where maths is used to make predictions.
- You could explore the mathematical concept of Chaos further.

You can see the responses we received here.

Here are some ways that you can keep in touch with events and information from us!

**Twitter:**Follow @OxUniMaths, @nrichmaths, @stepsupportcam**Facebook:**Oxford Mathematics and Plus Magazine**Instagram:**Oxford Mathematics**YouTube:**Oxford Mathematics and Millennium Maths Project

Here are some websites for other projects that we are involved in:

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