Title:  Mathematical Explorations 
Long Title:  Mathematical Explorations 
Field of Study: 
Mathematics

Valid From: 
Semester 2  2013/14 ( February 2014 ) 
Module Delivered in 
no programmes

Module Coordinator: 
David Goulding 
Module Author: 
MICHAEL BRENNAN 
Module Description: 
The objective of this module is to capture the beauty and power of mathematics through various explorations. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
demonstrate skills in mathematical reasoning and presentation 
LO2 
describe the way in which mathematics is used in various areas of human endeavour 
LO3 
develop and understand mathematical arguments 
LO4 
identify the cultural role that mathematics has played throughout history 
LO5 
appreciate how mathematics can be used as a learning resource 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 
No recommendations listed 
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section. 
No requirements listed 
Corequisites

No Co Requisites listed 
Module Content & Assessment
Indicative Content 
The Logic of Discovery
The familiar Suduko puzzle provides a nice introduction to problem solving using some basic logical reasoning. Other topics that reinforce the different steps necessary in the problem solving process include Tower of Hanoi, Magic Squares and Algebraic gems.

History and Culture
The concept of conjecture and proof are fundamental to mathematics. This section develops these from a historical viewpoint with emphasis on elementary mathematics (e.g. primes and geometry).

Pleasures of Probability
Illustrate how lots of everyday life occurrences can be analysed via probability. Examples include games, National lottery, betting/gambling.

Applications
The power of mathematics is in its practical application to science, engineering and the world of business. This section uses a variety of examples to highlight this.

Assessment Breakdown  % 
Course Work  100.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Practical/Skills Evaluation 
Computer Lab and In class Worksheets 
1,2,3,4,5 
50.0 
Every Second Week 
Other 
Written final exam 
1,2,3,4 
50.0 
Sem End 
No End of Module Formal Examination 
Reassessment Requirement 
Repeat the module
The assessment of this module is inextricably linked to the delivery. The student must reattend the module in its entirety in order to be reassessed.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Conventional Lecture 
2.0 
Every Week 
2.00 
Lab 
Lab/Discussion 
2.0 
Every Week 
2.00 
Independent & Directed Learning (Noncontact) 
Outside Class Workload 
3.0 
Every Week 
3.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
This module has no Part Time workload. 
Module Resources
Recommended Book Resources 

 Anne Rooney 2009, The story of mathematics, Arcturis [ISBN: 9781841939407]
 Theoni Pappas 1989, The joy of mathematics, World Wide Publishers Tetra [ISBN: 0933174659]
 Tony Crilly, 50 Mathematical Ideas You Really Need to Know [ISBN: 9781847241474]
 Supplementary Book Resources 

 David Flannery 2006, The square root of 2, Praxis [ISBN: 9780387202204]
 Underwood Dudley 2008, Is mathematics inevitable?, Mathematical Association of America Washington, D.C. [ISBN: 9780883855669]
 George Polya 1990, How to solve it, Penguin [ISBN: 9780140124996]
 John Stillwell 1989, Mathematics and its history, Springer Verlag [ISBN: 3540969810]
 Devi Shakuntala, Figuring [ISBN: 0233965912]
 Recommended Article/Paper Resources 

 Martin Gardner A Quarter Century of Recreational Mathematics, Scientific American, August 1998, 6875
 Michael Kleber The Best Card Trick Ever, The Mathematical Intelligencer, vol 24, no. 1 Winter 2002, 911
 Other Resources 

 Website: Wolfram's MathWorld
 Website: Maple Application Centre
 Website: Tower of Hanoi Applet
 Website: Wikipedia Mathematics
 Website: Koch's Curve Fractal
 Website: Susan HolmesBirthday Problem
 