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
|Summary||This is a first course in real analysis and a concrete introduction to group theory and the mathematics of symmetry.
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.
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.
Information for Visiting Students
|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?
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 44,
Seminar/Tutorial Hours 11,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||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
|Course organiser||Dr Nikolaos Bournaveas
Tel: (0131 6)50 5063
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427