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Module

MAS1702 : Number Systems

  • Offered for Year: 2020/21
  • Module Leader(s): Dr James Waldron
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

To develop concepts and techniques of mathematical proof, illustrated by results in algebra. To stimulate logical thinking and to develop students' skills at constructing mathematical arguments.

Module summary

This module introduces one of the two principal branches of pure mathematics: algebra via number systems. Integer arithmetic has always provoked fascination in mathematicians and has been a source of many famous theorems, for example Fermat's Last Theorem. The module will cover areas such as prime numbers and modular arithmetic, before concluding by presenting properties of the real numbers, including proofs of irrationality of numbers like the square root of 2 and e. However, the principal aim of the module is to develop students' understanding of proof and their ability to construct valid mathematical arguments, with examples from number systems providing the objects of study.

Outline Of Syllabus

Cardinality and countability.

Number theory including the Division Algorithm and the Euclidean algorithm.

Modular arithmetic.

Relations.

Rational and irrational numbers.

Teaching Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Assessment Methods

Module leaders are revising this content in light of the Covid 19 restrictions.
Revised and approved detail information will be available by 17 August.

Reading Lists

Timetable