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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

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture41:004:00Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Synchronous On Line Material
Structured Guided LearningLecture materials181:0018:00Non Synchronous Activities
Guided Independent StudyAssessment preparation and completion151:0015:00N/A
Structured Guided LearningStructured non-synchronous discussion91:009:00N/A
Scheduled Learning And Teaching ActivitiesDrop-in/surgery21:002:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study471:0047:00N/A
Total100:00
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Student should consult their timetable for up-to-date delivery information.

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

The format of resits will be determined by the Board of Examiners

Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M20N/A
Written exercise2M20N/A
Written exercise2A60Alternative Assessment
Assessment Rationale And Relationship

The course assessments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable