Real Analysis
| Code | School | Level | Credits | Semesters |
| MATH2102 | Mathematical Sciences | 2 | 10 | Spring UK |
- Code
- MATH2102
- School
- Mathematical Sciences
- Level
- 2
- Credits
- 10
- Semesters
- Spring UK
Summary
This course builds upon the experience of limits of sequences and properties of real numbers gained in first year Core Mathematics. Topics covered include:
- Convergence of sequences of functions.
- Interchange of limit processes.
- Differentiation and integration and application to properties of functions.
Target Students
Single Honours and Joint Honours students from the School of Mathematical Sciences, Mathematical Physics students, Natural Sciences students, Liberal Arts students.
Classes
- One 2-hour lecture
- One 1-hour lecture
Teaching will be through a variety of methods, with the delivery tailored to the material on a week-by-week basis.
Assessment
- 40% Coursework 1: Summative assessment based on tasks distributed through the semester.
- 60% Exam 1 (2-hour): 2 hour written examination – Spring
Assessed by end of spring semester
Educational Aims
The aim of this course is to introduce the main notions and methods of proof in analysis through a mathematically rigorous approach. It follows on from the core module MATH1101, where properties of real numbers were introduced and knowledge of calculus was extended. This course is a key prerequisite for modules in Analysis in later years.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - Demonstrate knowledge and understanding of the theory and applications of real analysis.
L2 – Construct examples of sets, sequences, or functions with required properties.
L3 – Reason logically and work analytically to construct rigorous mathematical proofs of key theorems and basic (unseen) propositions in real analysis.
L4 – Present conclusions and solutions to problems verbally or in writing, using structured and mathematically rigorous arguments and contextually appropriate language.
L5 – Summarise complex ideas clearly and concisely, taking due consideration of the target audience, which may include influencing, educating and/or persuading different audiences using their arguments and/or results.