## MATH1210 Maths all Around

### 10 creditsClass Size: 40

Module manager: Prof Paul Martin; Dr Rob Sturman
Email: P.P.Martin@leeds.ac.uk; R.Sturman@leeds.ac.uk

Taught: Semester 2 View Timetable

Year running 2016/17

### Pre-requisite qualifications

Enthusiasm, willingness to contribute and work in a team.

This module is approved as a discovery module

### Module summary

1. Is every voting system unfair? 2. Is there a hotel which has rooms available even when it's full? 3. Why do 5, 8, 13 appear more often in nature than other numbers? 4. How can building a new road create more traffic jams? 5. How do you increase your chances in a quiz show?In this module we will explore various interesting, empowering and surprising facts and thought experiments from a maths perspective. No maths beyond GCSE level is assumed.The above questions are some surprising examples we might consider. Here are some details: 1. When listing natural criteria for a fair voting system, one quickly ends up with criteria that cannot be satisfied simultaneously. 2. This is about a thought experiment: Strange things might happen if a hotel has infinitely many rooms. 3. Various plants have spiral patterns (e.g. pine cones or the grains in sunflowers). How tightly things can be packed in such a pattern depends on the number of spirals in a surprising way. 4. In certain configurations of streets, for each person individually it's better to use the new road, but nevertheless, if everybody does it, the end result is that everybody gets to the goal more slowly than before. 5. Tactical thinking in quiz shows can sometimes be useful in surprising ways.

### Objectives

-To develop studentsâ€™ interest and ability to explore the world around us from a mathematical perspective.
-To help students understand and analyse the mathematical principles behind some phenomena in the world.
-To guide students to explore the usefulness of mathematics in everyday life.
-To encourage students to use their mathematical skills to interrogate published information.
-To guide students to articulate a mathematical viewpoint.

Learning outcomes
The aim is that by the end of the module students will have gained confidence
- using their mathematical skills to question and analyse phenomena around them;
- using their analytical thinking skills, and be more inquisitive about the maths behind everything;
- articulating a mathematical viewpoint in verbal and written form.

### Syllabus

We will explore a number of different topics, not fixed in advance. Some typical examples:
- Networks and social media
- The weird world of infinity
- Big Data
- The Monty Hall problem
- The 2 envelopes problem
- Voting systems
- Gambling Strategies
- Encoding & Encryption
- Estimations
- Global warming
- Weather forecasting
- Chaos
- Patterns in nature
- Fractals
- The parking problem
- Tilings
- The Game of Life
- Packing problems
- The Prisoner's Dilemma

### Teaching methods

 Delivery type Number Length hours Student hours Seminar 6 2.00 12.00 Private study hours 88.00 Total Contact hours 12.00 Total hours (100hr per 10 credits) 100.00

### Private study

Students will be required to work individually and in group to prepare for the teaching sessions and complete a project and presentation.

### Opportunities for Formative Feedback

Feedback during discussions, class activities, and presentations

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Group Project Presentation, report, discussion, activities, peer moderated assessment. 100.00 Total percentage (Assessment Coursework) 100.00

If the module is failed, the resit assessment comprises of an individual project.