Module manager: Prof Martin Speight
Email: J.M.Speight@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2013/14
| MATH1025 | Number Systems |
| MATH1055 | Numbers and Vectors |
This module is approved as an Elective
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.
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.
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.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 6 | 1 | 6 |
| Lecture | 33 | 1 | 33 |
| Tutorial | 11 | 1 | 11 |
| Private study hours | 100 | ||
| Total Contact hours | 50 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Assessed coursework with written and oral presentations throughout the semester with feedback.
!!! In order to pass the module, students must pass the examination. !!!
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 20 |
| Total percentage (Assessment Coursework) | 20 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 30 Mins | 80 |
| Total percentage (Assessment Exams) | 80 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 2/13/2014
Errors, omissions, failed links etc should be notified to the Catalogue Team