MATH6028 - Mathematical Explorations

Title:Mathematical Explorations
Long Title:Mathematical Explorations
Module Code:MATH6028
Duration:1 Semester
Credits: 5
NFQ Level:Fundamental
Field of Study: Mathematics
Valid From: Semester 2 - 2019/20 ( January 2020 )
Module Delivered in no programmes
Module Coordinator: David Goulding
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
Pre-requisite 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 MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).

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
Co-requisite Modules
No Co-requisite modules listed

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

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.
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 Work100.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Practical/Skills Evaluation Computer lab and in-class assessments. 1,2,3,4,5 50.0 Every Second Week
Other Written in-class exam. 1,2,3,4 50.0 Week 13
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 (Non-contact) 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 2007, 50 Mathematical Ideas You Really Need to Know [ISBN: 9781847241474]
Supplementary Book Resources
  • David Flannery 2006, The square root of 2, Praxis [ISBN: 978-0387-20220-4]
  • John Stillwell 2010, Mathematics and its history, Third Ed., Springer Verlag [ISBN: 9781441960535]
  • 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]
  • Devi Shakuntala 1977, Figuring, The Joy of Numbers [ISBN: 0233965912]
Recommended Article/Paper Resources
  • Martin Gardner A Quarter Century of Recreational Mathematics, Scientific American, August 1998, 68-75
  • Michael Kleber The Best Card Trick Ever, The Mathematical Intelligencer, vol 24, no. 1 Winter 2002, 9-11
Other Resources