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.
Week 1-2: Real numbers and sets (including inequalities, supremum, and countability)
Week 3-4: Real sequences (from limits to Bolzano-Weierstrass theorem including Cauchy sequences)
Week 5-6: Continuity (from limits for real-valued functions to continuity, including extreme value and intermediate value theorems)
Week 7-9: Differentiability (from the definition to the mean value theorem and inverse function theorem)
Week 10-11: Series (including the definition, integral (without proof), comparison, and ratio tests).
Week 1: Symmetries of squares and circles (Chapter 1)
Week 2: Permutations (Chapter 2)
Weeks 3-4: Linear transformations and matrices. The group axioms. Subgroups. (Chapters 3-5)
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 orbit-stabiliser theorem (Chapter 11)
Week 11: Colouring problems (Chapter 12)
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 2017/18, 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 15%, Examination 85%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Fundamentals of Pure Mathematics||3:00|
|Resit Exam Diet (August)||Fundamentals of Pure Mathematics||3:00|
| 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 epsilon-delta method.
4. Computing derivatives from first principles, and by manipulation rules.
5. Performing simple proofs using epsilon-delta techniques.
6. Using the following tests to check convergence/non-convergence 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.
|Group theory: Students are expected to have a personal copy of:|
Groups, by C. R. Jordan and D. A. Jordan
|Graduate Attributes and Skills
|Course organiser||Dr Nikolaos Bournaveas
Tel: (0131 6)50 5063
|Course secretary||Mr Martin Delaney
Tel: (0131 6)50 6427