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An introduction to fields and rings, including applications to coding theory and the impossibility of constructions such as ‘squaring the circle’.
This course formally introduces rings and fields, which have been encountered at 100- and 200-level in special situations, and investigates their algebraic structure. It gives a deeper understanding of these algebraic concepts and thus provides a thorough grounding in the algebraic theory which underpins modern applications like cryptography, error-correcting codes, number theory or finite mathematics. If you are interested in any of these subjects or if you want to see how algebraic theory can be applied to solve certain geometric construction problems or prove their impossibility, then this is the course to take.The topics covered by this course are:• fundamentals of ring theory: subrings, ideals, factor rings, ring homomorphisms; • special rings: integral domains and polynomial rings and factorizations of elements therein; • fundamentals of field theory: field extensions, constructions of fields, in particular finite fields, and their uses, like the impossibility of certain geometric constructions such as trisecting the angle.
Students successfully completing this course should:understand a range of basic algebraic concepts.have developed a high level of competence at core algebraic skills.be able to confidently apply algebraic concepts in practical settings.be able to present clear and logical mathematical arguments.
One of MATH203, MATH220, MATH240, orEMTH211, and a further 15 points from MATH201-294.
Students must attend one activity from each section.
and Gunter Steinke
To obtain a pass (C- or better), you must obtain at least 40% in the exam.
Recommended text:J.A. Gallian: Contemporary Abstract Algebra, Houghton Mifflin, 8th ed or later.Earlier editions of the text are also suitable.
General information for students
Domestic fee $780.00
International fee $4,250.00
* Fees include New Zealand GST and do not include any programme level discount or additional course related expenses.
For further information see
Mathematics and Statistics.