## MATH1225 Introduction to Geometry

### 10 creditsClass Size: 260

Module manager: Dr Ben Lambert
Email: b.s.lambert@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### Pre-requisite qualifications

Grade B in 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

84 hours:
- 20 hours on 5 problem sheets
- 5 hours study per lecture
- 9 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

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

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