MAS1702 : Number Systems
- Offered for Year: 2025/26
- Module Leader(s): Dr James Waldron
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
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 | |
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
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Structured Guided Learning | Structured non-synchronous discussion | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, coursework review |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 5 | 1:00 | 5:00 | n/a |
| Guided Independent Study | Independent study | 1 | 15:00 | 15:00 | Completion of in-course assessments |
| Total | 100:00 |
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. Module drop-in sessions allow students to receive learning support in areas where they may need additional guidance.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Digital Examination | 120 | 2 | A | 80 | NUMBAS exam, both digital and written questions |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises |
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises |
| Prob solv exercises | 2 | M | 5 | Problem-solving exercises |
| Prob solv exercises | 2 | M | 5 | Problem-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
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1702's Timetable