# 2021/22 Undergraduate Module Catalogue

## MATH1055 Numbers and Vectors

### 10 creditsClass Size: 220

**Module manager:** Dr Oleg Chalykh**Email:** o.chalykh@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2021/22

### Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.### This module is mutually exclusive with

MATH1005 | Core Mathematics |

MATH1010 | Mathematics 1 |

MATH1012 | Mathematics 2 |

MATH1026 | Sets, Sequences and Series |

**This module is approved as a discovery module**

### Module summary

This module introduces students to three outstandingly influential developments from 19th century mathematics: - complex numbers- vectors- and the rigorous notion of limit. Complex numbers are the natural setting for much pure and applied mathematics, and vectors provide the natural language to describe mechanics, gravitation and electromagnetism, while the rigorous notion of limit is fundamental to calculus. Along the way, students will go beyond the straightforward calculation and problem solving skills emphasized in A-level Mathematics, and learn to formulate rigorous mathematical proofs.### Objectives

On completion of this module, students should be able to:a) perform algebraic calculations with complex numbers and solve simple equations for a complex variable;

b) determine whether simple sequences and series converge;

c) perform calculations with vectors, write down the equations of lines, planes and spheres in vector language, and, conversely, describe the geometry of the solution sets of simple vector equations;

d) construct rigorous mathematical proofs of simple propositions, including proofs by mathematical induction.

### Syllabus

1. Proof by induction.

2. Complex numbers: modulus, argument; de Moivre's Theorem; geometry of the complex plane; complex roots.

3. Sequences: definition of convergence; algebra of limits; squeeze rule; monotone convergence theorem (statement only).

4. Series: definition of convergence; divergence test, comparison tests, ratio test.

5. Vector geometry: parallelogram law; scalar product, norm; vector product.

triple product; equations of lines, planes and spheres.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Delivery type | Number | Length hours | Student hours |

Lecture | 11 | 1.00 | 11.00 |

Tutorial | 5 | 1.00 | 5.00 |

Private study hours | 84.00 | ||

Total Contact hours | 16.00 | ||

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

### Private study

Studying and revising of course material.Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular example sheets.!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

**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 |

Open Book exam | 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

There is no reading list for this moduleLast updated: 02/11/2021

## Browse Other Catalogues

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

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