Exploring Mathematics - 2024 entry

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.

 

Theme A: Numbers and cardinality of sets; mathematical logic

Theme B: Patterns such as special numbers; mathematical proofs

Theme C: Geometry: Euclidean geometry and geometrical proofs: transformations and symmetry 

 

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%.

 

Basic reading

• ‘Thomas' Calculus Based on the Original Work by George B. Thomas, Jr.’ by Finney, R.L, Maurice, D., Weir, M. and Giordano, F.R, 10th edition or later, Addison-Wesley, 2003.
• ‘Exploring mathematics : problem-solving and proof’ by Daniel Grieser, Springer , 2018.
• ‘Fundamentals of University Mathematics’ by McGregor, C., Nimmo, J. & Stothers, W., 2nd edition, Horwood, Chichester, 2000.
• ‘How to Think Like a Mathematician: A Companion to Undergraduate Mathematics’ by Houston, K., 1st edition, Cambridge University Press, 2009.
• ‘A Concise Introduction to Pure Mathematics’ by Liebeck, M., 3rd edition, Chapman & Hall/CRC Press, 2010.
   

Web-based and electronic resources:

ELE

 

Other resources: 

 

• ‘Exploring mathematics : problem-solving and proof’ by Daniel Grieser, Springer, 2018.