2011/12 Undergraduate Module Catalogue
MATH1026 Sets, Sequences and Series
15 creditsClass Size: 200
Module manager: Dr Martin Speight
Email: speight@maths.leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2011/12
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 Maple and Excel. 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.
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. 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 websiteLast updated: 27/02/2012
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