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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -
- ARCHIVE as at 1 September 2013 for reference only
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Fundamentals of Pure Mathematics (MATH08064)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) Credits20
Home subject areaMathematics Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionThis is a first course in real analysis and a concrete introduction to group theory and the mathematics of symmetry.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Introduction to Linear Algebra (MATH08057) AND Calculus and its Applications (MATH08058) AND Proofs and Problem Solving (MATH08059)) OR ( Accelerated Algebra and Calculus for Direct Entry (MATH08062) AND Accelerated Proofs and Problem Solving (MATH08071))
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?No
Course Delivery Information
Delivery period: 2013/14 Semester 2, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Course Start Date 13/01/2014
Breakdown of Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 44, Seminar/Tutorial Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 139 )
Additional Notes Students must pass exam and course overall.
Breakdown of Assessment Methods (Further Info) Written Exam 85 %, Coursework 15 %, Practical Exam 0 %
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)Fundamentals of Pure Mathematics3:00
Resit Exam Diet (August)Fundamentals of Pure Mathematics3:00
Summary of Intended 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.
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.
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Analysis:
Week 1-2: Real numbers and sets (including inequalities, supremum, and countability)
Week 3-4: Real sequences (from limits to Bolzano-Weierstrass theorem)
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)
Transferable skills Not entered
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
Study Abroad Not entered
Study Pattern Not entered
KeywordsFPM
Contacts
Course organiserDr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk
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