2012/13 Undergraduate Module Catalogue

MATH1026 Sets, Sequences and Series

15 creditsClass Size: 200

Module manager: Prof Martin Speight
Email: J.M.Speight@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2012/13

Pre-requisites

MATH1025

Number Systems

This module is mutually exclusive with

MATH1055

Numbers and Vectors

This module is approved as an Elective

Module summary

This module introduces students to the mathematics of sequences, series and power series. Students will explore examples using a computer package. The sizes of infinite sets (such as sets of sequences, rationals, reals) are explored. The Mandelbrot Set is introduced in the context of sequences of complex numbers.

Objectives

On completion of this module, students should:
- be able to state and prove properties of sequences, series, and power series, and be familiar with examples of these;
- have strengthened their skills in:
> constructing, writing (using LateX) and communicating proofs;
> presenting mathematical ideas using precise language in written and verbal form;
> manipulating and exploring sequences and series confidently.

Syllabus

1. Sequences. Definition of convergence. Sums and products. Subsequences, the Bolzano-Weierstrass theorem.
2. Supremum and Infimum.
3. Sizes of infinite sets (sets of sequences, rationals, reals), (un)countability.
4. Series. Absolute & conditional convergence. Standard tests.
5. Power series. Radius of convergence.
6. Complex sequences, the Mandelbrot Set.

Teaching methods

Delivery type	Number	Length hours	Student hours
Workshop	6	1.00	6.00
Lecture	33	1.00	33.00
Tutorial	11	1.00	11.00
Private study hours			100.00
Total Contact hours			50.00
Total hours (100hr per 10 credits)			150.00

Private study

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

Opportunities for Formative Feedback

Assessed coursework with written and oral presentations throughout the semester with feedback.

Methods of assessment

Coursework

Assessment type	Notes	% 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 type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	80.00
Total percentage (Assessment Exams)		80.00

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

Reading list

The reading list is available from the Library website

Last updated: 11/02/2013

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