units

MTH3150

Faculty of Science

18 September 2017
18 February 2020

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## 6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSLRefer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.
## SynopsisRings, fields, ideals, algebraic extension fields. Coding theory and cryptographic applications of finite fields. Gaussian integers, Hamilton's quaternions, Chinese Remainder Theorem. Euclidean Algorithm in further fields. ## ObjectivesAt the completion of this unit, students will be able to demonstrate understanding of advanced concepts, algorithms and results in number theory; the use of Gaussian integers to find the primes expressible as a sum of squares, Diophantine equations, primitive roots; the quaternions, the best known skew field; many of the links between algebra and number theory; the most commonly occurring rings and fields: integers, integers modulo n, rationals, reals and complex numbers, more general structures such as algebraic number fields, algebraic integers and finite fields; and will have developed skills in the use of the Chinese Remainder Theorem to represent integers by their remainders; performing calculations in the algebra of polynomials; the use of the Euclidean algorithm in structures other than integers; constructing larger fields from smaller fields (field extensions); applying field theory to coding and cryptography. ## Assessment
Examination (3 hours): 70% ## Chief examiner(s)## Contact hoursThree 1-hour lectures and an average of one 1-hour support class per week ## PrerequisitesMTH2122, MTH2121, MTH3121 or MTH3122 ## Co-requisites |