Last modified: 22 May 2019 17:07
This course concerns the integers, and more generally the ring of algebraic integers in an algebraic number field. The course begins with statements concerning the rational integers, for example we discuss the Legendre symbol and quadratic reciprocity. We also prove a result concerning the distribution of prime numbers. In the latter part of the course we study the ring of algebraic integers in an algebraic number field. One crucial result is the unique factorisation of a nonzero ideal as a product of primes, generalising classical prime factorisation in the integers.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
Number theory is the study of integers and has three main branches: Elementary, Analytical and Algebraic. This course consists of a selection of topics from these branches. The topics will include some of the following: the theory of quadratic congruences, continued fractions, pseudo-primes, primitive roots, Diophantine equations, the distribution of prime numbers, algebraic integers in quadratic number fields.
Information on contact teaching time is available from the course guide.
1st Attempt: 1 two-hour examination (80%) and in-course assessment (20%).
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination. Students undertake practice questions in tutorials allowing formative assessment and feedback from tutors.
In-course assessment will be marked and feedback provided to the students.