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 2020/21, Available to all students (SV1)
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Quota: None |
Course Start |
Semester 2 |
Timetable |
Timetable |
Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 11,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
138 )
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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
60 %,
Coursework
40 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Coursework 40%, Examination 60% |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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Main Exam Diet S2 (April/May) | Fundamentals of Pure Mathematics | 2:00 | | Resit Exam Diet (August) | Fundamentals of Pure Mathematics | 2:00 | |
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
Group theory: Students are expected to have a personal copy of:
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: N.Bournaveas@ed.ac.uk |
Course secretary | Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk |
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