MT2502 Analysis
Academic year
2025 to 2026 Semester 1
Curricular information may be subject to change
Further information on which modules are specific to your programme.
Key module information
SCOTCAT credits
15
SCQF level
SCQF level 8
Planned timetable
11.00 am Mon (weeks 2, 4, 7, 9, 11), Tue and Thu
Module Staff
Dr Natalia Jurga; Dr Stephen Cantrell
Module description
The main purpose of this module is to introduce the key concepts of real analysis: limit, continuity and differentiation. Emphasis will be placed on the rigorous development of the material, giving precise definitions of the concepts involved and exploring the proofs of important theorems. This module forms the prerequisite for all later modules in mathematical analysis.
Relationship to other modules
Pre-requisites
BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED, ADVANCED HIGHER MATHEMATICS (AT GRADE A) OR A-LEVEL FURTHER MATHEMATICS (AT GRADE A).
Assessment pattern
2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%
Re-assessment
2-hour Written Examination = 100%
Learning and teaching methods and delivery
Weekly contact
2.5 hours lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)
Scheduled learning hours
35
Guided independent study hours
115
Intended learning outcomes
- Understand the concepts maximum, minimum, supremum, infimum, and completeness, especially in the context of the real numbers
- Appreciate the rigorous definitions of convergence, continuity and derivative and be able to apply the definitions to basic examples
- Understand convergence of series and various tests for convergence including the comparison and root tests
- Understand Cauchy sequences and be able to use this concept to prove convergence via the The General Principle of Convergence
- Understand and apply various results relying on differentiation of functions, including the Mean Value Theorem and Taylor's Theorem
Additional information from school
For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/
MT2502 Analysis
Academic year
2026 to 2027 Semester 1
Curricular information may be subject to change
Further information on which modules are specific to your programme.
Key module information
SCOTCAT credits
15
SCQF level
SCQF level 8
Planned timetable
11.00 am Mon (weeks 2, 4, 7, 9, 11), Tue and Thu
Module Staff
TBD
Module description
The main purpose of this module is to introduce the key concepts of real analysis: limit, continuity and differentiation. Emphasis will be placed on the rigorous development of the material, giving precise definitions of the concepts involved and exploring the proofs of important theorems. This module forms the prerequisite for all later modules in mathematical analysis.
Relationship to other modules
Pre-requisites
BEFORE TAKING THIS MODULE YOU MUST PASS MT1002,IF MT1002 HAS NOT BEEN PASSED, ADVANCED HIGHER MATHEMATICS (AT GRADE A) OR A-LEVEL FURTHER MATHEMATICS (AT GRADE A).
Assessment pattern
2-hour Written Examination = 70%, Coursework (including class test 15%) = 30%
Re-assessment
2-hour Written Examination = 100%
Learning and teaching methods and delivery
Weekly contact
2.5 hours lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 weeks)
Scheduled learning hours
35
Guided independent study hours
115
Intended learning outcomes
- Understand the concepts maximum, minimum, supremum, infimum, and completeness, especially in the context of the real numbers
- Appreciate the rigorous definitions of convergence, continuity and derivative and be able to apply the definitions to basic examples
- Understand convergence of series and various tests for convergence including the comparison and root tests
- Understand Cauchy sequences and be able to use this concept to prove convergence via the The General Principle of Convergence
- Understand and apply various results relying on differentiation of functions, including the Mean Value Theorem and Taylor's Theorem
Additional information from school
For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.
Syllabus
- The rationals and the reals: maximum & minimum, supremum & infimum, completeness.
- Sequences, series and convergence: the Bolzano-Weierstrass Theorem, tests for convergence - the ratio test, the root test, the comparison test, Cauchy sequences.
- Continuous functions: algebraic properties of continuous functions, the Intermediate Value Theorem.
- Differentiable functions: the chain rule, Rolle’s Theorem, the Mean Value Theorem, Taylor polynomials.
These topics will be introduced from a rigorous point of view, giving precise definitions, applying an ε-δ approach and giving examples.