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 Activities | Lecture | 4 | 1:00 | 4:00 | Present in Person |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Synchronous On Line Material |
| Structured Guided Learning | Lecture materials | 18 | 1:00 | 18:00 | Non Synchronous Activities |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | N/A |
| Structured Guided Learning | Structured non-synchronous discussion | 9 | 1:00 | 9:00 | N/A |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 2 | 1:00 | 2:00 | Office Hour or Discussion Board Activity |
| Guided Independent Study | Independent study | 47 | 1:00 | 47:00 | N/A |
| Total | 100:00 |
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
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 240 | 2 | A | 60 | 24 hour take home exam. Students get the full 24 hours. |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Written exercise | 2 | M | 20 | N/A |
| Written exercise | 2 | M | 20 | N/A |
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
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS1702's Timetable