Last modified: 31 May 2022 13:05
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.
| Study Type | Undergraduate | Level | 4 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
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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.
Syllabus
Information on contact teaching time is available from the course guide.
Alternative Assessment
3x Standard Course Assessments - 30%, 30% and 40%
Alternative Resit Assessment
Resubmission of failed elements (pass marks carried forward)
There are no assessments for this course.
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Factual | Remember | ILO’s for this course are available in the course guide. |
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