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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Combinatorics and Graph Theory (MATH10072)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryA first course in combinatorics and graph theory: Graphs, Euler's V-E+F=2 Theorem, Kuratowski's Theorem, Counting sets, Generating functions, Matching, Hall's Marriage Theorem, Polya counting, Counting paths in graphs.
Course description Graphs (including bipartite, Euler, Hamiltonian, Planar, trees) , Euler's V-E+F=2 Theorem, subdivisions, Kuratowski's Theorem.

Counting sets, subsets, multisets, inclusion/exclusion, applications.
Stirling numbers of first and second kinds, Bell numbers, partitions.
Generating functions, binomial identities.
Matching, Hall's Marriage Theorem, assignment problems.
Polya counting.
Counting paths in graphs, adjacency matrix.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Fundamentals of Pure Mathematics (MATH08064)
Co-requisites
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesEquivalence relations, permutations, set theory, group theory, binomial coefficients. 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 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
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 S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Solve counting problems.
  2. Identify properties of graphs (such as Eulerian/Hamiltonian/Planar/Bipartite/Connectedness).
  3. Solve matching problems using Hall's marriage theorem and equivalent bipartite graph formulations.
  4. Solve counting problems associated to graphs (such as numbers of paths)
Reading List
Reference books which contain some material relevant to the course:
* A First Course in Combinatorial Mathematics by Ian Anderson
* Aspects of Combinatorics by Victor Bryant.
* Graphs An Introductory Approach, by R J Wilson and J J Watkins
* Introduction to Graph Theory, by R J Wilson
Additional Information
Graduate Attributes and Skills Not entered
Study Abroad Not Applicable.
KeywordsCGT
Contacts
Course organiserDr Harry Braden
Tel: (0131 6)50 5072
Email: H.Braden@ed.ac.uk
Course secretaryMiss Sarah McDonald
Tel: (0131 6)50 5043
Email: sarah.a.mcdonald@ed.ac.uk
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