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Can we square a circle? Can we trisect an angle? These two questions were studied by the Ancient Greeks and were only solved in the 19th century using algebraic structures such as rings, fields and polynomials. In this module, we introduce these ideas and concepts and show how they generalise well-known objects such as integers, rational numbers, prime numbers, etc. The theory is then applied to solve problems in Geometry and Number Theory. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography.
Total contact hours: 42
Private study hours: 108
Total study hours: 150
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 Hours 60%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.
R. Allenby, Rings, fields and groups: an introduction to abstract algebra, Oxford: Butterworth/Heinemann, Second edition, 1991 (reprinted 2003).
J. Howie, Fields and Galois Theory, Springer, 2006.
A. Knapp, Basic Algebra, Birkhäuser, 2006
See the library reading list for this module (Canterbury)
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within abstract algebra and its applications;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the
following areas: rings, fields and polynomials;
3 apply the concepts and principles in basic abstract algebra in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically
the appropriateness of different tools and techniques.
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