Registry

Module Specifications

Archived Version 2020 - 2021

Module Title
Module Code
School
Online Module Resources
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module introduces students to the formal and rigorous approach to mathematics which underpins mathematical analysis.The students will develop the skills necessary to make the transition from a formulaic understanding of mathematics to constructing their own formal mathematical arguments, and to promote advanced mathematical thinking through the use of guided inquiry and example generation. Students will participate in the following learning activities: Lectures: There will be a weekly lecture introducing material. Group discussions and problem solving: students will spend the equivalent of two lectures a week on guided group discussions in order to derive results or tests for solving problems, generating examples or counterexamples, and so on. Presentations: students will present their approach to solving particular problems to the class for analysis and critique. Portfolio: students will make regular contributions to a portfolio of written assignments examining more general aspects of the module. Reading: students are expected to fully use the lecture notes and textbooks listed below.

Learning Outcomes

1. interpret the formal mathematical definitions and statements which arise in analysis.
2. classify and describe the main components of the definitions or statements, and the motivation behind them.
3. give examples or counterexamples of important phenomena which are studied in mathematical analysis.
4. critique and explain the logical steps which are required to apply definitions or theorems to the phenomena which occur in mathematical analysis.
5. critique and explain the main logical arguments which occur in the proofs of a selection of theorems.
6. calculate important quantities which arise in mathematical analysis e.g. bounds of sets or sequences, convergence of sequences or series.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	12	Weekly lecture
Lecture	24	Supervised enquiry and problem based student learning
Assignment Completion	22	Portfolio assignment
Independent Study	67	Recommended time for self-study
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

Numbers and sets
The real numbers. Archimedean property of the reals. Least upper bounds and greatest lower bounds.

Sequences and series
Monotone and bounded sequences. Alternating series. Tests for convergence of series. Power series. Move Up

Assessment Breakdown
Continuous Assessment	%	Examination Weight	%

Type	Description	% of total	Assessment Date
Course Work Breakdown

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
Unavailable

Indicative Reading List

David Alexander Brannan: 0, A first course in mathematical analysis, Cambridge University Press, 978-0521684248
J. and P. Mikusinski: 0, An introduction to analysis, Wiley,
C. H. Edwards: 0, The historical development of the calculus, Springer-Verlag,

Other Resources

None

Programme or List of Programmes

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