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| Module Availability |
| Semester 1 |
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| Assessment Pattern |
Assessment Pattern
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: 1 class test
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25
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Exam, 2 hours
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75
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.
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| Module Overview |
This module is an introduction to methods of proof and some standard topics in algebra. |
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| Prerequisites/Co-requisites |
| None. |
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| Module Aims |
| The aim of this module is firstly to introduce the standard techniques of mathematical proof, and then to develop the theory and methods of a number of key algebraic systems. |
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| Learning Outcomes |
At the end of the module the student should:
• Understand and be able to formulate simple proofs, selecting an appropriate method.
• Know properties of prime numbers and be able to apply the Euclidean algorithm.
• Understand complex numbers and be able to calculate with them.
• Know how to find the dot product and cross product of two vectors.
• Understand matrices and determinants, and use them to solve systems of linear equations.
• Understand the concepts and notation associated with permutations.
• Solve simple congruences and understand the concept of arithmetic modulo n.
• Know the definition of a group and recognise basic examples.
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| Module Content |
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• Proof by deduction, induction, contraposition and contradiction.
• Prime numbers, prime factorisation.
• The Euclidean algorithm. Greatest common divisor, lowest common multiple.
• Complex numbers. Modulus, argument, polar form, de Moivre's theorem. • Scalar and vector products.
• Matrices and their use in solving simultaneous linear equations.
• Permutations.
• Determinants and inverse matrices.
• Equivalence relations, congruences and modular arithmetic.
• Introduction to groups.
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| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and tests: 4 hours per week for 11 weeks.
Learning takes place through lectures, tutorials, tests and exercise sheets.
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| Selected Texts/Journals |
Recommended:
J. Gilbert and C. Jordan: Guide to Mathematical Methods, Palgrave Macmillan, 2002, ISBN 978-0333794449
K. Houston: How to Think Like a Mathematician, CUP, 2009. ISBN 978-0521719780
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| Last Updated |
| 21 April 2011 |
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