MA4055 - Mathematical Proofs (2023/24)
| Module specification | Module approved to run in 2023/24 | ||||||||||||
| Module title | Mathematical Proofs | ||||||||||||
| Module level | Certificate (04) | ||||||||||||
| Credit rating for module | 15 | ||||||||||||
| School | School of Computing and Digital Media | ||||||||||||
| Total study hours | 150 | ||||||||||||
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| Assessment components |
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| Running in 2023/24(Please note that module timeslots are subject to change) |
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Module summary
This module develops the skills necessary to support academic study at degree level. It will also develop reflective learning and action planning via the Personal Development Planning (PDP) process. The first term topics will look into history of mathematics, development of modern number system and introduce idea of mathematical proofs. Different proof techniques will be covered using examples from Set Theory and Number Theory.
Prior learning requirements
None.
Available for Study Abroad? NO
Syllabus
• Origins of mathematics (Babylonian Mathematics; Egyptian Mathematics; the ancient Greeks and the introduction of proof); (LO1)
• Development of the modern number system; non-traditional approaches to mathematics (e.g., Vedic mathematics). (LO2)
• Proof Techniques in Mathematics. Various proof methods will be introduced: deduction, induction, direct proof, contradiction, contrapositive, well-ordered principle via topics in Set and Number Theory below. (LO2-3)
• Number theory topics. Divisibility, Prime decomposition, Quotient- Remainder Theorem, Euclid’s Algorithm, Modular arithmetic. (LO2-3)
Balance of independent study and scheduled teaching activity
This module will be delivered through a mixture of lectures and tutorials.
The lectures will develop theory, explain the methods and techniques and demonstrate them by going through examples. The tutorials will provide students with the opportunity of reviewing their lecture notes and working through the problems designed for their practice, which will underpin the skills and techniques demonstrated in the lectures. Students will be encouraged to construct valid and precise mathematical arguments and will be expected to produce solutions using appropriate notational and stylistic conventions. Self-study exercises will enable students to monitor their own progress.
A set of lecture notes will be provided to students and answers for exercise questions will be put on the VLE.
Blended learning is incorporated by using online resources as a medium for communication (both peer and tutor-led) and will also provide additional materials to stimulate the student interest and broaden their horizons.
Learning outcomes
LO1: Be familiar with the historical developments of mathematics from the origin to modern times.
LO2: Understand different proof techniques and be able to apply them.
LO3: Be familiar with the basic results from the Number Theory, Set Theory.
Assessment strategy
The assessment for this module consists of two courseworks.
The coursework will require students to:
Produce an account of students’ learning so far, experience on the course, the feedback received in modules and reflection on formative feedback. (LO1)
Solve problem sheets on different proof techniques covering. (LO2-3)
Bibliography
Core Text:
Johnson, D. L.(1998), Elements of Logic via Numbers and Sets, Springer-Verlag
Velleman, D(1994), How to Prove It, (Cambridge University Press
Recommended Reading:
Houston, K.(2009), How to Think Like a Mathematician, Cambridge University Press