units
MTH3150
Faculty of Science
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6 points, SCA Band 0 (NATIONAL PRIORITY), 0.125 EFTSL
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 1hour lectures and an average of one 1hour support class per week PrerequisitesMTH2122, MTH2121, MTH3121 or MTH3122 Corequisites 