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MATH2617: Elementary Number Theory II

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Type Open
Level 2
Credits 10
Availability Available in 2024/2025
Module Cap
Location Durham
Department Mathematical Sciences

Prerequisites

  • Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Linear Algebra I (Maths Hons) (MATH1091) or Linear Algebra I (MATH1071).

Corequisites

  • None.

Excluded Combinations of Modules

  • None.

Aims

  • To provide and introduction to the basics of number theory.

Content

  • Review of basic features of integers.
  • Congruences and modular arithmetic
  • Quadratic reciprocity
  • Diophantine equations

Learning Outcomes

Subject-specific Knowledge:

  • By the end of the module students will: be able to solve a range of predictable and unpredictable problems in Number Theory.
  • have an awareness of the abstract concepts of theoretical mathematics in the field of Number Theory.
  • have a knowledge and understanding of fundamental theories of these subjects demonstrated through one or more of the following topic areas: Fundamental theorem of arithmetic, modular arithmetic and chinese remainder theorem.
  • Diophantine equations.

Subject-specific Skills:

  • In addition students will have the ability to undertake and defend the use of alternative mathematical skills in the following areas with minimal guidance: Abstract reasoning.

Key Skills:

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

  • Lecturing demonstrates what is required to be learned and the application of the theory to practical examples.
  • Weekly/Fortnightly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills.
  • Tutorials provide active engagement and feedback to the learning process.
  • The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

ActivityNumberFrequencyDurationTotalMonitored
Lectures222 per week in Michaelmas and in first week of Easter1 Hour22 
Tutorials5Fortnightly in Michaelmas and one in Easter1 Hour5Yes
Problems Classes4Fortnightly in Michaelmas1 Hour4 
Preparation and Reading69 
Total100 

Summative Assessment

Component: ExaminationComponent Weighting: 100%
ElementLength / DurationElement WeightingResit Opportunity
End of year written examination2 hours100Yes

Formative Assessment

Fortnightly or Weekly written assignments.

More information

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