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 12: Real numbers and sets (including inequalities, supremum, and countability)
Week 34: Real sequences (from limits to BolzanoWeierstrass theorem including Cauchy sequences)
Week 56: Continuity (from limits for realvalued functions to continuity, including extreme value and intermediate value theorems)
Week 79: Differentiability (from the definition to the mean value theorem and inverse function theorem)
Week 1011: 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 34: Linear transformations and matrices. The group axioms. Subgroups. (Chapters 35)
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 orbitstabiliser theorem (Chapter 11)
Week 11: Colouring problems (Chapter 12)

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2015/16, 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
85 %,
Coursework
15 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 15%, Examination 85% 
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
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 epsilondelta method.
4. Computing derivatives from first principles, and by manipulation rules.
5. Performing simple proofs using epsilondelta techniques.
6. Using the following tests to check convergence/nonconvergence 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.

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

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 

