Undergraduate Course: Fundamentals of Pure Mathematics (MATH08064)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 8 (Year 2 Undergraduate) 
Credits  20 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  This is a first course in real analysis and a concrete introduction to group theory and the mathematics of symmetry. 
Information for Visiting Students
Prerequisites  None 
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 Mathematics  3:00   Resit Exam Diet (August)  Fundamentals of Pure Mathematics  3:00  
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 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. 
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes' above. 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
Analysis:
Week 12: Real numbers and sets (including inequalities, supremum, and countability)
Week 34: Real sequences (from limits to BolzanoWeierstrass theorem)
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) 
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 
Keywords  FPM 
Contacts
Course organiser  Dr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk 
Course secretary  Mr Martin Delaney
Tel: (0131 6)50 6427
Email: Martin.Delaney@ed.ac.uk 

