# Mathematical induction games

*This is a template which you can use to help get you started on the wiki submission. It is just intended as a guide and you may modify the structure to suit your project.*

## Contributors

*Name and what department each person was in.**Student or staff partner?**How was each person involved?**What rough dates did they contribute?*

- Mark Wheelhouse, Department of Computing. Staff partner from October 2021.

## Aims & Learning Outcomes

*Explain the motivation for your visualisation.*

*Introduce the subject of your visualisation.**Which module and year is it intended for and which setting (lecture or self study)?**List learning outcomes. E.g.: "After using this visualisation, students should be able to explain that..."*

These two game visualisations will be shown during a lecture of COMP400018 - Discrete Mathematics, Logic and Reasoning. They will also be available for self-study so that students can validate what we have discussed in the lecture.

1. Visualising "The Game of Frogs"

This is a thought experiment to get students thinking about Mathematical Induction. We would like to have a visualisation for this little game that will allow the students to experiment with the idea (number of frogs, starting speeds, etc).

The core learning outcome here is that a student should be able to provide an inductive argument to answer why all of the frogs will eventually fall off of the plank.

2. Visualising "The beetle and the cactus".

This is a thought experiment to get students thinking about Mathematical Induction. We would like to have a visualisation for this scenario that will allow the students to experiment with the idea (e.g. initial cactus set-up and beetle's rules). The core learning outcome here is that a student should be able to provide an inductive argument to show why the beetle can (and will) eventually consume the whole cactus. This thought experiment has also been referred to as "Hercules and the Hydra" and has an existing online visualisation.

## Design Overview

*What the final outcome was, how it looks, how it functions etc.**Include graphics.**Do not include justification or design progression, leave this for later sections.*

## Design Justification

### Assessment Criteria

*List your cohort's assessment criteria. You may want to number the assessment criteria so you can refer to them easily later.*

### Education Design

*What Methods were considered to convey concepts?**Design progression, key choices with justifications.**How has feedback been incorporated.*

### Graphical Design

*How were accessibility issues considered?**How was space used effectively?**Design progression, key choices with justifications.**How has feedback been incorporated.*

*How is the design intuitive?*

### Interaction Design

*Choice of interactive element(s) that fit in organically with the visualisation [inspiration of choice might be from lecture/in-class activity or other sources] - Sliders/Buttons/Cursor (hover/click).**Keeping accessibility of interactive elements in mind during design phase.**Design progression, key choices with justifications.**How has feedback been incorporated.*

## Progress and Future Work

*Is the design finalised?**Which pages have been uploaded to website?**Any ideas for future improvements.*

## Links

*Link to GitHub repository for code in development:**Link to visualisation on ImpVis website (when uploaded):**Link to Collection on ImpVis website (when created):**Any other links to resources (Miro boards / notes pages / Google Docs etc):*