Module manager: Dr O Chalykh
Email: o.chalykh@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2010/11
A-Level Pure Mathematics, or equivalent.
| MATH1035 | Analysis |
This module is approved as an Elective
This module introduces students to three outstandingly influential developments from 19th century mathematics: - complex numbers - vectors - and the rigorous notion of limit. Complex numbers are the natural setting for much pure and applied mathematics, and vectors provide the natural language to describe mechanics, gravitation and electromagnetism, while the rigorous notion of limit is fundamental to calculus. Along the way, students will go beyond the straightforward calculation and problem solving skills emphasized in A-level Mathematics, and learn to formulate rigorous mathematical proofs.
On completion of this module, students should be able to:
a) perform algebraic calculations with complex numbers and solve simple equations for a complex variable;
b) determine whether simple sequences and series converge;
c) perform calculations with vectors, write down the equations of lines, planes and spheres in vector language, and, conversely, describe the geometry of the solution sets of simple vector equations;
d) construct rigorous mathematical proofs of simple propositions, including proofs by mathematical induction.
1. Proof by induction.
2. Complex numbers: modulus, argument; de Moivre's Theorem; geometry of the complex plane; complex roots.
3. Sequences: definition of convergence; algebra of limits; squeeze rule; monotone convergence theorem (statement only).
4. Series: definition of convergence; divergence test, comparison tests, ratio test.
5. Vector geometry: parallelogram law; scalar product, norm; vector product.
triple product; equations of lines, planes and spheres.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Tutorial | 10 | 1 | 10 |
| Private study hours | 68 | ||
| Total Contact hours | 32 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Regular example sheets and in-class quizzes.
| 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 Mins | 80 |
| Total percentage (Assessment Exams) | 80 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
There is no reading list for this module
Last updated: 4/1/2011
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