MAS1614 : Real Analysis
- Offered for Year: 2024/25
- Module Leader(s): Dr Christian Bönicke
- 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 introduce students to rigorous analysis through the study of properties of the Real Numbers and to put some of the results they have seen in MAS1612 on a firmer footing.
Module Summary
Calculus, as enlightenment thinkers such as Newton and Leibniz thought of it, was very successful at solving problems involving elementary functions. However, as mathematicians began to consider more sophisticated and complicated functions in the 18th and 19th centuries, they needed methods of ensuring that the results they needed still held true. This module introduces students to ways of thinking about the Real Numbers that allow them to prove rigorously some of the results they will have seen at school and in MAS1612 as well as laying the foundation for doing analysis and calculus with mathematical objects other than Real Numbers (e.g. Complex Numbers).
Outline Of Syllabus
Properties and constructions of the Real Numbers
Sequences and convergence
Series
Functions and limits
Continuity and its consequences
Differentiability and its consequences
Power series
The Riemann integral
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Class |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Scheduled Learning And Teaching Activities | Practical | 5 | 2:00 | 10:00 | Teaching labs for in-course assessment |
| Guided Independent Study | Independent study | 63 | 1:00 | 63:00 | Preparation time for lectures, background reading, coursework review |
| 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.
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 and written exam (hybrid) |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 7 | Assignment Lab |
| Prob solv exercises | 2 | M | 7 | Assignment Lab |
| Prob solv exercises | 2 | M | 6 | Assignment Lab |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Prob solv exercises | 2 | M | Assignment Lab |
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/
- MAS1614's Timetable