2019/20 Undergraduate Module Catalogue

MATH1026 Sets, Sequences and Series

15 creditsClass Size: 290

Module manager: Professor Alexander Strohmaier
Email: A.Strohmaier@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2019/20

Pre-requisites

MATH1025

Number Systems

This module is mutually exclusive with

MATH1055

Numbers and Vectors

This module is not approved as a discovery module

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. Some fundamental results in real analysis are precisely formulated and proved.

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. Supremum and Infimum.
2. Sizes of infinite sets (rationals, reals), (un)countability.
3. Sequences. Definition of convergence. Sums and products. Subsequences, the Bolzano-Weierstrass Theorem.
4. Series. Absolute & conditional convergence. Standard tests.
5. Sequential continuity. The Extreme Value Theorem. The Intermediate Value Theorem.
6. Complex sequences and series. Power series. Radius of convergence.

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.



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

Methods of assessment

Coursework

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

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 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: 30/04/2019

Disclaimer

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