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 orbitstabiliser theorem; Colouring problems.

Information for Visiting Students
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2019/20, 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  
Learning Outcomes
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 epsilondelta 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.

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 
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 

