Module: Analysis

Module Specifications

Academic Year 2026 - 2027

Module Title	Analysis
Module Code	MTH1099
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	8	Credit Rating	7.5

Description

This module serves as a rigorous introduction to the fundamentals of analysis, particularly focusing on sequences and series, limits and continuity, and the concepts of differentiation and integration.

Learning Outcomes

1. Understanding the foundations of mathematical analysis
2. Developing literacy skills: understanding written mathematics and writing mathematics
3. Developing communication skills: presenting and explaining complex mathematical concepts and results

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	12 weeks, 3 hours of lectures per week
Workshop	16	Two hours workshop per week over 8 weeks
Independent Study	75	No Description
Total Workload: 127

Section Breakdown
CRN	21501	Part of Term	Semester 2
Coursework	100%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Thorsten Neuschel	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Participation	Active participation in weekly workshops can contribute up to 10% of the final grade.	10%	n/a
In Class Test	Midterm and final exam.	90%	n/a

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

Number sets
Natural, integer, rational and real numbers.

Sequences of real numbers
Convergence, monotonicity, boundedness, cluster points, Cauchy sequences

Series
Convergence and absolute convergence, Cauchy condensation, Dirichlet test, Leibniz test, comparison test, root test, ratio test, Cauchy product, power series

Limits and Continuity
Limit points of sets, limits of functions and their properties, continuity, uniform continuity and main theorems

Differentiation
Main properties and theorems for differentiation, Generalised Mean Value Theorem, L'Hospital's rule, Taylor's Theorem, real-analytic functions

Integration
Main properties and theorem of Riemann integration, Fundamental Theorem of Calculus, Integration by Parts, Change of Variables, improper integrals, comparison test

Indicative Reading List

Books:

Abbott, Stephen: 2015, Understanding Analysis, 2nd ed. 2015, Springer New York,

Articles:
None

Other Resources

None