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2011/12 Undergraduate Module Catalogue

MATH1055 Numbers and Vectors

10 creditsClass Size: 220

Module manager: Dr Charles Harris
Email: charlie@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2011/12

Pre-requisite qualifications

A-Level Pure Mathematics, or equivalent.

This module is mutually exclusive with

MATH1010Mathematics 1
MATH1012Mathematics 2
MATH1026Sets, Sequences and Series
MATH1035Analysis

This module is approved as an Elective

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

Delivery typeNumberLength hoursStudent hours
Lecture221.0022.00
Tutorial101.0010.00
Private study hours68.00
Total Contact hours32.00
Total hours (100hr per 10 credits)100.00

Opportunities for Formative Feedback

Regular example sheets and in-class quizzes.

Methods of assessment


Coursework
Assessment typeNotes% of formal assessment
In-course Assessment.20.00
Total percentage (Assessment Coursework)20.00

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


Exams
Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 00 mins80.00
Total percentage (Assessment Exams)80.00

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 module

Last updated: 27/02/2012

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