## MATH1026 Sets, Sequences and Series

### 15 creditsClass Size: 290

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

Taught: Semester 2 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