Registry

Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Introduction to Analysis
Module Code	MS212
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Brien Nolan Semester 2: Brien Nolan Autumn: Brien Nolan
Module Teacher	Brien Nolan
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, limits of series or functions, derivatives and integrals of functions.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	12	Weekly lecture
Lecturer-supervised learning (contact)	24	Supervised enquiry and problem based student learning
Assignment	11	Portfolio assignment
Independent learning time	78	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..

Limits.
Definition of a limit..

Properties of functions.
Continuity. Differentiability. Proof of rules of differentiation. Mean value theorem..

Integration.
Riemann sums. Riemann integral. Fundamental theorem of calculus..

Assessment Breakdown
Continuous Assessment	40%	Examination Weight	60%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Portfolio	Weekly exercise to be completed in students own time	20%	Every Week
Presentation	Group presentation of solutions to exercises during weekly tutorial	20%	Every Week

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
This module is category 3

Indicative Reading List

David Brannan: 0, A first course in mathematical analysis, Cambridge,
Anita E. Solow.: 0, Learning by discovery: A Lab manual for Calculus, in Classroom Resource Material series,
J. and P. Mikusinski: 0, An introduction to analysis, Wiley,
W. R. Wade: 0, An introduction to analysis, Pearson,
C. H. Edwards: 0, The historical development of the calculus, SpringerVerlag,
Felix Klein: 0, Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis, Dover Publications,

Other Resources

None

Array

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