MTH0003 - Exploring Mathematics (2023)

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MODULE TITLEExploring Mathematics CREDIT VALUE15
MODULE CODEMTH0003 MODULE CONVENERDr Houry Melkonian (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 0
Number of Students Taking Module (anticipated) 30
DESCRIPTION - summary of the module content
This module is designed to develop an understanding of the nature of mathematics and mathematical thinking. It takes you on a voyage of exploration of how mathematics was invented and developed. For millennia BC, mathematics was used for various purposes such as in the study of planets and their motions as well as in construction and trading, and since then the study of mathematics was expanded and new branches were explored. The module aims to enhance your ability to use mathematical reasoning, abstraction and logic while enjoying the process of learning and performing mathematical procedures. In its first theme, it focuses on the  concept of number sets and cardinality, where notions like, ‘infinity’ are discussed and explored through examples and simple proofs. The second theme develops an understanding of the mathematical language through an illustration of symbolic representations, patterns and relationships, such as the relationship between the number of spirals in a pine cone (a natural pattern) and the famous Fibonacci sequence (a number pattern), showing how those patterns are linked to other parts of mathematics such as geometry, arithmetic and probability. This is followed by a third theme about Euclidean geometry featuring some of its intriguing theorems and properties  including simple geometrical proofs, it also covers some aspects of coordinate geometry and transformations.
 
Students are expected to have knowledge of Principles of Pure Mathematics (MTH0001) as a co-requisite.
 
 

 

AIMS - intentions of the module

This module aims to develop your knowledge and understanding of core mathematical skills, including the ability to use abstract ideas; formulate accurate and rigour justifications; provide concise and logical proofs; generalise concepts; form examples that demonstrate understanding of a topic. By studying a number of topics you will become familiar with the development stages of mathematics, and you will learn how to communicate ideas and solutions. The module is designed to broaden your horizon by exploring a number of divisions of mathematics and the connections between them.

 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Module Specific Skills and Knowledge:
1. Demonstrate a general appreciation of the development of key mathematical concepts explored in this module 
2. Reveal awareness of a selection of topics in mathematics and the connections between them
 
Discipline Specific Skills and Knowledge:
3. Demonstrate a basic knowledge and understanding of fundamental concepts necessary for progression to further studies in mathematics or in other quantitative degree pathways
4. Develop skills to reason and solve problems using abstract ideas, critique mathematical claims, test concepts by creating examples, understand the importance of logic in proofs, recognize underlying simple ideas common to many areas of mathematics
 
Personal and Key Transferable/ Employment Skills and Knowledge:
5. Acquire ability to: perform symbolic representation of concepts and generalise ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing and oral presentation
6. Work in groups and learn to analyse and evaluate solutions
7. Demonstrate appropriate use of learning resources, demonstrate ability to use library resources
8. Demonstrate self-management and time management skills
 
 
SYLLABUS PLAN - summary of the structure and academic content of the module

Theme A: Numbers and  cardinality of sets; mathematical logic [3 weeks]

 

Theme B: Patterns such as special numbers; mathematical proofs  [3 weeks]

 

Theme C: Geometry: Euclidean geometry and geometrical proofs: transformations and symmetry [3 weeks]

 
LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33.00 Guided Independent Study 117.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning & teaching activities 22 Lectures
Scheduled learning & teaching activities 11 Tutorials, in-class tests
Guided independent study 117 Further reading and preparation

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
In-class worked examples  10 x 1 hour 1-8 Provided solutions, exercises discussed in class

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 50 Written Exams 50 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
3 tests 3 x 10 40 mins 1-8
Annotated scripts 
 
Coursework 15 800 words 1-8 Written feedback
Presentation 5
5-10 mins 
 1-8 Written feedback
Written exam 50 1½  hours  1-8 Annotated scripts/feedback sheet

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
3 tests 3 tests (3 x 10%) 1-8 August Ref/Def period
Coursework Coursework (15%) 1-8 August Ref/Def period
Presentation Presentation (5%) 1-8 August Ref/Def period
Written exam Written exam (50%) 1-8 August Ref/Def period

 

RE-ASSESSMENT NOTES
Deferral – if you have been deferred for any assessment, you will be expected to complete relevant deferred assessments as determined by the Mitigation Committee. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.
 
Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to undertake re-assessments as described in the table above for any of the original assessments that you failed. The mark given for a re-assessment taken as a result of referral will be capped at 40%.
 
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener
Basic reading/Web-based and electronic resources: 
 
• ELE – College to provide hyperlink to appropriate pages
 
Other resources: 
 
• ‘Exploring mathematics : problem-solving and proof’ by Daniel Grieser, Springer ,2018

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Liebeck, M. A Concise Introduction to Pure Mathematics 3rd Chapman & Hall/CRC Press 2010 978-1439835982 [Library]
Set Houston, K. How to Think Like a Mathematician: A Companion to Undergraduate Mathematics 1st Cambridge University Press 2009 978-0521719780 [Library]
Set McGregor, C., Nimmo, J. & Stothers, W. Fundamentals of University Mathematics 2nd Horwood, Chichester 2000 000-1-898-56310-1 [Library]
Set Finney, R.L., Maurice, D., Weir, M. and Giordano, F.R. Thomas' Calculus based on the original work by George B. Thomas, Jr. 10th or later Addison-Wesley 2003 000-0-321-11636-4 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES MTH0001
CO-REQUISITE MODULES MTH0001
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 29 July 2021 LAST REVISION DATE Monday 05 June 2023
KEY WORDS SEARCH Problem Solving, Critical Thinking, Logic, Geometry, Number Sets, Number Patterns