Undergraduate Course: Fundamentals of Pure Mathematics (MATH08064)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This is a first course in real analysis and a concrete introduction to group theory and the mathematics of symmetry. |
| Course description |
Analysis:
Real Numbers; Inequalities; Least Upper Bound; Countable and Uncountable Sets; Sequences of Real Numbers; Subsequences; Series of Real Numbers; Integral, Comparison, Root, and Ratio Tests; Continuity; Intermediate Value Theorem; Extreme Values Theorem; Differentiability; Mean Value Theorem; Inverse Function Theorem.
Algebra:
Symmetries of squares and circles; Permutations; Linear transformations and matrices; The group axioms; Subgroups; Cyclic groups; Group actions; Equivalence relations and modular arithmetic; Homomorphisms and isomorphisms; Cosets and Lagrange's Theorem; The orbit-stabiliser theorem; Colouring problems.
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Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2025/26, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 2 |
| Course Start Date |
12/01/2026 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 22,
Seminar/Tutorial Hours 11,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
160 )
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| Additional Information (Learning and Teaching) |
Students must pass exam and course overall.
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| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Minutes |
|
| Main Exam Diet S2 (April/May) | Fundamentals of Pure Mathematics | 00 | | | Resit Exam Diet (August) | Fundamentals of Pure Mathematics | 00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate a conceptual understanding of fundamental concepts of Analysis (completeness, epsilon-N, continuity, epsilon-delta) and be able to derive basic results from them.
- Demonstrate a conceptual understanding of fundamental concepts of Group Theory (groups, group actions, symmetries) and be able to derive basic results from them.
- Explain their reasoning about Algebra and Analysis clearly and precisely using appropriate technical language.
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Reading List
Groups, by C. R. Jordan and D. A. Jordan
Kenneth Ross, Elementary Analysis.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | FPM |
Contacts
| Course organiser | Dr Nikolaos Bournaveas
Tel: (0131 6)50 5063
Email: |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: |
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