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 | Delivery type 6 | Number 1 | Length hours 6 |
| Lecture | Delivery type 33 | Number 1 | Length hours 33 |
| Tutorial | Delivery type 11 | Number 1 | Length hours 11 |
| Private study hours | Delivery type 100 | ||
| Total Contact hours | Delivery type 50 | ||
| Total hours (100hr per 10 credits) | Delivery type 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 |
|---|---|---|
| Assessment type In-course Assessment | Notes . | % of formal assessment 20 |
| Total percentage (Assessment Coursework) | Assessment type 20 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Exam type Standard exam (closed essays, MCQs etc) | Exam duration 2.0 Hrs 30 Mins | % of formal assessment 80 |
| Total percentage (Assessment Exams) | Exam type 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