Module: Sequences & Series

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Sequences & Series
Module Code	MTH1015 (ITS: MS114)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

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

Section Breakdown
CRN	20781	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Abraham Harte	Module Teacher	Brien Nolan, Paul Razafimandimby

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	n/a	10%	Week 27
Assignment	Biweekly homework	10%	n/a
Formal Examination	End-of-Semester Final Examination	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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.

Indicative Reading List

Books:

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

Articles:
None

Other Resources

None