### MAS3216 : Enumeration and Combinatorics

• Offered for Year: 2015/16
• Module Leader(s): Dr Alina Vdovina
• Owning School: Mathematics & Statistics
##### Semesters
 Semester 1 Credit Value: 10 ECTS Credits: 5.0
##### Pre Requisites
Code Title
MAS1041Mathematical Methods A
MAS1042Mathematical Methods B
MAS1241Number Systems
MAS1242The Foundations of Analysis
###### Pre Requisite Comment

MAS2041, MAS2042, MAS2241, MAS2242 acceptable in place of MAS1041, MAS1042, MAS1241, MAS1242 respectively

N/A

#### Aims

To equip students with a range of basic tools and methods for analysing and solving discrete problems, useful in all branches of mathematics. To enable the students to apply these techniques to naturally occuring problems. To reinforce the students’ ability to read, understand and develop mathematical proofs.

Module Summary

The module involves the study of problems involving a finite number of elements, objects or structures; enumeration and counting; relations and functions; algorithmic problems.

#### Outline Of Syllabus

Pigeonhole principle, permutations and cycles, binomial and multinomial coefficients, counting subsets, partitions. Stirling numbers, inclusion-exclusion principle. Graphs, isomorphism, subgraphs, connectedness, Walks and paths. Trees, spanning trees. Travelling salesman problem. Planar graphs and Euler’s formula.

#### Learning Outcomes

##### Intended Knowledge Outcomes

Students will gain an understanding of the nature of discrete problems, particularly those involving enumeration and Graph Theory. They will understand how to apply the techniques of combinatorial mathematics to such problems. They will understand how to apply algorithmic methods when appropriate.

##### Intended Skill Outcomes

Students will be equipped with a range of basic tools and methods for analysing and solving discrete problems. They will be able to use computer programs for solutions to certain combinatorial problems. Students will enhance their ability to read, understand and develop mathematical proofs.

#### Graduate Skills Framework

 Graduate Skills Framework Applicable: Yes
• Cognitive/Intellectual Skills
• Numeracy : Assessed
• Information Literacy
• Use Of Computer Applications : Present
• Self Management
• Personal Enterprise
• Problem Solving : Assessed
• Interaction
• Communication
• Written Other : Assessed

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture61:006:00Problem classes
Guided Independent StudyAssessment preparation and completion111:0011:00Revision for unseen Exam
Guided Independent StudyAssessment preparation and completion11:301:30Unseen Exam
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Guided Independent StudyAssessment preparation and completion55:0025:00Written assignments and CBAs
Scheduled Learning And Teaching ActivitiesPractical21:002:00Computing Practicals
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00Drop-ins in the lecture room
Guided Independent StudyIndependent study51:005:00Assignment review
Guided Independent StudyIndependent study119:3019:30Studying, practising and gaining understanding of course material
Total100:00
##### Jointly Taught With
Code Title
MAS2216Enumeration and Combinatorics
##### Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination901A90unseen
##### Exam Pairings
Module Code Module Title Semester Comment
MAS2216Enumeration and Combinatorics1N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M10Written assignments and computer based assessments
##### Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. Coursework assignments (approximately 5 assignments of approximately equal weight) allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments the deadlines for the two parts will not necessarily be the same.

#### General Notes

N/A

Note: The Module Catalogue now reflects module information relating to academic year 15/16. Please contact your School Office if you require module information for a previous academic year.

Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.