# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Fundamentals of Pure Mathematics (MATH08064)

 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; Supremum; Countable and Uncountable Sets; Sequences of Real Numbers; The Bolzano-Weierstrass Theorem; Cauchy sequences; 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.
 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
 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
 Academic year 2018/19, Available to all students (SV1) 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 ) 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 Mathematics 3:00 Resit Exam Diet (August) Fundamentals of Pure Mathematics 3:00
 On completion of this course, the student will be able to: Understand the notion of completeness of the Real Number System and appreciate its importance in Analysis.Understand the rigorous theory of limits, continuity and differentiability and use epsilon-delta techniques.Understand the language and ideas of basic group theory.Understand group actions and apply the theory to solve combinatorial problems involving symmetry.Explain their reasoning about Algebra and Analysis clearly and precisely using appropriate technical language.
 Group theory: Students are expected to have a personal copy of: Groups, by C. R. Jordan and D. A. Jordan Kenneth Ross, Elementary Analysis.
 Graduate Attributes and Skills Not entered Keywords FPM
 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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