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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2022/2023

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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
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryThis 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.
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
Information for Visiting Students
Pre-requisitesVisiting 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
Academic year 2022/23, Available to all students (SV1) Quota:  0
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 )
Additional Information (Learning and Teaching) Students must pass exam and course overall.
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
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
Learning Outcomes
On completion of this course, the student will be able to:
  1. Demonstrate a conceptual understanding of fundamental concepts of Analysis (completeness, epsilon-N, continuity, epsilon-delta) and be able to derive basic results from them.
  2. Demonstrate a conceptual understanding of fundamental concepts of Group Theory (groups, group actions, symmetries) and be able to derive basic results from them.
  3. Explain their reasoning about Algebra and Analysis clearly and precisely using appropriate technical language.
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.
Additional Information
Graduate Attributes and Skills Not entered
KeywordsFPM
Contacts
Course organiserDr Nikolaos Bournaveas
Tel: (0131 6)50 5063
Email: N.Bournaveas@ed.ac.uk
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk
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