Module: Sequences & Series

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Sequences & Series
Module Code	MS114 (ITS) / MTH1015 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Abraham Harte
Module Teachers	Brien Nolan, Paul Razafimandimby
NFQ level	6	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination

Description

This module introduces students to the principles and practice of mathematical analysis via the study of sequences and series. There will be an emphasis on constructing rigorous mathematical proofs of results from analysis. Students will also learn how to use diagrams and informal ideas to develop their knowledge and skills in this area of mathematics. Students will attend interactive lectures in which the class build some definitions of mathematical constructs, and engage in creating convincing mathematical arguments and proofs to support given statements.

Learning Outcomes

1. apply the epsilon-X formulation of statements involving convergence of sequences and series;
2. construct rigorous arguments using the epsilon-X formulation and be able to distinguish between rigorous and informal arguments;
3. construct and analyse their own examples and counterexamples of mathematical objects arising in analysis;
4. use different structured approaches to solve problems in mathematical analysis.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	Inquiry based study of course material
Tutorial	12	Student work on exercises with tutor support.
Independent Study	89	Independent study of course material and work on exercise sheets.
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Sequences
Introduction to sequences. Null sequences. Convergent and divergent sequences. Monotone sequences and the Weierstrass-Bolzano theorem. Cauchy's criterion for convergence.

Series
Introduction to series. Series with non-negative terms. Tests for convergence. Series with positive and negative terms and absolute convergence. Rearranging series.

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	n/a	10%	Week 27
Assignment	Biweekly homework	10%	n/a

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

D Brannan: 2006, A First Course in Mathematical Analysis, OUP/CUP,
S Abbott: 2001, Understanding Analysis, Springer: SUMS,

Other Resources

None