Registry

Module Specifications

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

Module Title	The Mathematical Experience
Module Code	MS108
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Eabhnat Ni Fhloinn Semester 2: Eabhnat Ni Fhloinn Autumn: Eabhnat Ni Fhloinn
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module introduces students to some different general aspects of mathematics, including its history, the nature and use of mathematical language, the role and construction of proofs and problem solving in mathematics.Students will attend lectures on the course material. They will participate in group-work tutorials to work on exercises and problems related to the course material. As part of the assessment for the module, students will undertake a project on a topic from the history of mathematics, and make a poster presentation - as well as a brief oral presentation - on their work.

Learning Outcomes

1. Discuss key historical milestones in the development of mathematics;
2. Analyse the role of definitions and proofs in formal mathematics;
3. Study the construction and properties of the real numbers as an example of the deductive nature of mathematics;
4. Construct their own proofs of elementary mathematical statements;
5. Apply structured problem solving techniques to mathematical problems.
6. Work in a group to collate and present material on a given topic from the history of mathematics.

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	24	Lectures on course material.
Tutorial	12	Student work on exercise sheets, with tutor support.
Independent learning time	89	Independent work on course material and exercises.
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

Introduction.
What is mathematics and where does it come from? How much maths can there be? A brief chronologyof mathematics. Applications of mathematics. The classification of mathematics..

Mathematical problem solving..
Structured approaches to problem solving in mathematics: Mason's Rubric Writing..

Mathematical language and mathematical proof..
The role of definitions in mathematics; mathematical statements; the need for mathematical proof; different types of proof: induction, working forwards-backwards, proof by contradiction, proof by contrapositive argument; nomenclature: conjectures, lemmas, propositions, theorems, corollaries etc; the philosophy of mathematical proof; the creation of new mathematics..

The real numbers..
The real numbers as infinite decimal expansions. The axiomatic approach. The density property and the Archimedean property of the reals. Least upper bounds and greatest lower bounds. Completeness of the reals..

History of mathematics..
An overview of the history of mathematics and its role in the natural and human world, from pre-history to the 21st century..

Assessment Breakdown
Continuous Assessment	50%	Examination Weight	50%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Assignment	Tutorial participation	5%	Every Week
Assignment	Take home work.	10%	Week 4
Assignment	Take home work	10%	Week 8
Project	Group project: preparation of an essay, a poster and an oral presentation on a topic from the history of mathematics.	25%	Week 11

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 1

Indicative Reading List

Philip J. Davis and Reuben Hersh: 1981, The Mathematical Experience, Penguin,
W.S Anglin: 1994, Mathematics: A Concise History and Philosophy, Springer-Verlag,
DA Brannan: 1996, A First Course in Mathematical Analysis, CUP, 9780511573200
Reuben Hersh: 1997, What is Mathematics, Really?, OUP,

Other Resources

1093, Website, 0, St Andrew's History of Mathematics Website, http://www-groups.dcs.st-andrews.ac.uk/~history/,

Array

Programme or List of Programmes

ACM

BSc Actuarial Mathematics

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

CAFM

Common Entry into Mathematical Sciences