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:
Week 1-2: Real numbers and sets (including inequalities, supremum, and countability)
Week 3-4: Real sequences (from limits to Bolzano-Weierstrass theorem including Cauchy sequences)
Week 5-6: Continuity (from limits for real-valued functions to continuity, including extreme value and intermediate value theorems)
Week 7-9: Differentiability (from the definition to the mean value theorem and inverse function theorem)
Week 10-11: Series (including the definition, integral (without proof), comparison, and ratio tests).
Group theory:
Week 1: Symmetries of squares and circles (Chapter 1)
Week 2: Permutations (Chapter 2)
Weeks 3-4: Linear transformations and matrices. The group axioms. Subgroups. (Chapters 3-5)
Week 5: Cyclic groups (Chapter 6)
Week 6: Group actions (Chapter 7)
Week 7: Equivalence relations and modular arithmetic (Chapter 8)
Week 8: Homomorphisms and isomorphisms (Chapter 9)
Week 9: Cosets and Lagrange's Theorem (Chapter 10)
Week 10: The orbit-stabiliser theorem (Chapter 11)
Week 11: Colouring problems (Chapter 12)
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
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| Academic year 2015/16, 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
85 %,
Coursework
15 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Coursework 15%, Examination 85% |
| 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 | 3:00 | | | Resit Exam Diet (August) | Fundamentals of Pure Mathematics | 3:00 | |
Learning Outcomes
1. Perform basic set manipulation and to distinguish between common countable and uncountable sets
2. Using straightforward epsilon methods to establish convergence/non convergence of sequences and determine whether a given sequence is Cauchy.
3. Verifying limits of functions and check continuity using the epsilon-delta method.
4. Computing derivatives from first principles, and by manipulation rules.
5. Performing simple proofs using epsilon-delta techniques.
6. Using the following tests to check convergence/non-convergence of series: comparison, ratio, root, integral, alternating series and understand absolute convergence.
7. Familiarity with the language and ideas of basic group theory.
8. Ability to calculate in several different sorts of group.
9. Familiarity with the language and ideas of group actions.
10. A knowledge of the basic theorems in group theory mentioned in the syllabus
11. Ability to apply these theorems to solve combinatorial problems involving symmetry.
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Reading List
Analysis: Students are expected to have a personal copy of: An Introduction to Analysis by W. R. Wade. (This book is also relevant for Y3 courses.)
Group theory: Students are expected to have a personal copy of:
Groups, by C. R. Jordan and D. A. Jordan
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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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