Unit name | Further Topics in Analysis |
---|---|
Unit code | MATH11521 |
Credit points | 10 |
Level of study | C/4 |
Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
Unit director | Professor. van den Berg |
Open unit status | Not open |
Pre-requisites |
Normally and A at A level Maths or equivalent |
Co-requisites |
MATH11006 Analysis 1 |
School/department | School of Mathematics |
Faculty | Faculty of Science |
The unit starts by extending some of the basic ideas concerning sets and functions which will have been introduced by this stage in the Analysis element of Core Mathematics, and goes on to such new topics as Russell's Paradox, equivalence relations, and countability and cardinality. Then some further topics in analysis are covered, including additional material on dequences, series, and continuous fractions.
Aims:
This unit aims to develop students' ability to think and express themselves in a clear logical fashion, and to develop some of the material on set theory which will have been introduced in Analysis 1, and some additional topics in analysis.
Syllabus
Further Set Theory: finite and countable sets, equivalence relations, cardinality, examples of uncountable sets, a set and its power set have different cardinalities, Russell's Paradox. [6 lectures]
Further Analysis: construction of the real numbers, subsequences, limit superior and limit inferior, Cauchy sequences, uniformly continuous functions, sequences and series of functions, the Riemann integral. [16 lectures]
Relation to Other Units
This unit complements the Analysis 1 material, and is a prerequisite for analysis units in later years.
After taking this unit students should:
The ability to express intuitive ideas in a precise mathematical fashion and to produce clear logical arguments.
The final mark for Further Topics in Analysis is calculated from one 1½ -hour written examination in May/June. This examination paper is in two sections.
Calculators may NOT be used.
The following are useful but not essential: