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MAS1702 : Number Systems

  • Offered for Year: 2024/25
  • Module Leader(s): Dr James Waldron
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 2 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System


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.


Rational and irrational numbers.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Structured Guided LearningStructured non-synchronous discussion531:0053:00Preparation time for lectures, background reading, coursework review
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00n/a
Guided Independent StudyIndependent study115:0015:00Completion of in-course assessments
Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

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

Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem-solving exercises
Prob solv exercises2M5Problem-solving exercises
Prob solv exercises2M5Problem-solving exercises
Prob solv exercises2M5Problem-solving exercises
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments 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