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# Sequences And Series

4CCM115A

4

Autumn

15

## Module description

Syllabus:

An introduction to sets and functions: defining sets, subsets, intersections and unions; injections, surjections, bijections. Compositions and inverses of functions. An introduction to mathematical logic and proof: logical operations, implication, equivalence, quantifiers, converse and contrapositive; proof by induction and contradiction, examples of proofs. Then these ideas will be applied in the context of the real numbers to make rigorous arguments with sequences and series and develop the notions of convergence and limits.

## Assessment details

Written examination and class tests.

Exercises or quizzes will be set each week to be handed in the following week. These problems will be discussed in the tutorials and solutions will be available.

Semester 1 only students will be set an alternative assessment in lieu of in-person exams in January.

Full year students will complete the standard assessment.

## Educational aims & objectives

This module aims to introduce the ideas and methods of university level pure mathematics. In particular, the module aims to show the need for proofs, to encourage logical arguments and to convey the power of abstract methods. This will be done by example and illustration within the context of a connected development of the following topics: real numbers, sequences, limits, series.

## Learning outcomes

Understand and be able to apply basic definitions and concepts in set and function theory. Understand the nature of a logical argument and a mathematical proof and be able to produce examples of these. Understand the definitions of limits and convergence in the context of sequences and series of real numbers. Be able to compute limits of sequences involving elementary functions. Be able to prove simple statements involving convergence arguments.

## Teaching pattern

Three hours of lectures and one hour of tutorial per week throughout the term

## Suggested reading list

Indicative reading list - link to Leganto system where you can search with module code for lists

#### Department

##### Module description disclaimer

King’s College London reviews the modules offered on a regular basis to provide up-to-date, innovative and relevant programmes of study. Therefore, modules offered may change. We suggest you keep an eye on the course finder on our website for updates.

Please note that modules with a practical component will be capped due to educational requirements, which may mean that we cannot guarantee a place to all students who elect to study this module.

Please note that the module descriptions above are related to the current academic year and are subject to change.