# 2015/16 Undergraduate Module Catalogue

## MATH1225 Introduction to Geometry

### 10 creditsClass Size: 180

**Module manager:** Professor R Marsh**Email:** R.J.Marsh@leeds.ac.uk

**Taught:** Semester 1 View Timetable

**Year running** 2015/16

### Pre-requisite qualifications

A-level Mathematics or equivalent.**This module is approved as a discovery module**

### Module summary

Geometry is one of the oldest subjects in mathematics. It is appealing in itself and the emphasis in this introductory course is on using diagrams to understand problems and to help formulate rigorous proofs. The use of low dimensions and hands-on calculations allows you to develop geometric intuition to support problem-solving in other modules. Geometry pervades Mathematics with applications to motions of particles, group theory and shape analysis in Statistics.### Objectives

On completion of this module, students should be able to:a) Prove Pythagoras' theorem.

b) Show when two triangles are similar.

c) Recognise the equations and parametrisations of parabolas, ellipses and hyperbolas, and solve problems about these curves.

d) Classify conics.

e) Classify polyhedra.

### Syllabus

1. Elementary plane geometry. Pythagoras' Theorem and its converse. The angles within a triangle sum to 180 degrees. Trigonometry. Congruence, similarity. Bisectors, distance to a line.

2. Parametrization versus implicit descriptions of curves. Differentiation of vectors and tangents to curves. Parametric and implicit forms of conics and other important curves. Polar form. Tangents to conics. Classification of conics.

3. Polyhedra. Classification and construction of regular polyhedra, Euler characteristic.

4. Introduction to three dimensional geometry, including spheres, planes and introduction to quadrics.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Lecture | 22 | 1.00 | 22.00 |

Tutorial | 5 | 1.00 | 5.00 |

Private study hours | 73.00 | ||

Total Contact hours | 27.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Private study

72 hours:- 20 hours on 5 problem sheets

- 2 hours study per lecture

- 8 hours exam preparation

### Opportunities for Formative Feedback

5 problem sheets.!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

In-course Assessment | . | 15.00 |

Total percentage (Assessment Coursework) | 15.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

**Exams**

Exam type | Exam duration | % of formal assessment |

Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 85.00 |

Total percentage (Assessment Exams) | 85.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

### Reading list

The reading list is available from the Library websiteLast updated: 15/04/2015

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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