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MX4545: NUMBER THEORY (2023-2024)

Last modified: 14 Dec 2023 14:46


Course Overview

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.



Course Details

Study Type Undergraduate Level 4
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Simona Paoli

Qualification Prerequisites

  • Programme Level 4

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

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

  • Polynomial Congruences.
  • Quadratic Residues and Quadratic Reciprocity.
  • Bertrand’s postulate.
  • Algebraic number fields.
  • Algebraic integers.
  • Quadratic number fields and their rings of algebraic integers.
  • Cyclotomic number fields and their rings of algebraic integers.
  • The factorisation of ideals in rings of algebraic integers.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 2 Lectures during University weeks 26 - 35, 39
  • 1 Tutorial during University weeks 27 - 35, 39

More Information about Week Numbers


Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Homework

Assessment Type Summative Weighting 15
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Homework

Assessment Type Summative Weighting 15
Assessment Weeks Feedback Weeks

Look up Week Numbers

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Exam

Assessment Type Summative Weighting 70
Assessment Weeks Feedback Weeks

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2-hour Exam (on campus)

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting
Assessment Weeks Feedback Weeks

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Feedback

Best of (resit exam mark) or (resit exam mark with carried forward CA marks).

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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