|Semester 1 Credit Value:||10|
|MAS1041||Mathematical Methods A|
|MAS1042||Mathematical Methods B|
|MAS1242||The Foundations of Analysis|
MAS2041, MAS2042, MAS2241, MAS2242 acceptable in place of MAS1041, MAS1042, MAS1241, MAS1242 respectively
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.
The module involves the study of problems involving a finite number of elements, objects or structures; enumeration and counting; relations and functions; algorithmic problems.
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.
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.
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 Applicable:||Yes|
|Guided Independent Study||Assessment preparation and completion||1||1:30||1:30||Unseen Exam|
|Scheduled Learning And Teaching Activities||Lecture||22||1:00||22:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||5||5:00||25:00||Written assignments and CBAs|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||6||1:00||6:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||11:00||11:00||Revision for unseen Exam|
|Scheduled Learning And Teaching Activities||Practical||2||1:00||2:00||Computing Practicals|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Drop-ins in the lecture room|
|Guided Independent Study||Independent study||1||19:30||19:30||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||5||1:00||5:00||Assignment review|
|MAS2216||Enumeration and Combinatorics|
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.
The format of resits will be determined by the Board of Examiners
|Module Code||Module Title||Semester||Comment|
|MAS2216||Enumeration and Combinatorics||1||N/A|
|Prob solv exercises||1||M||10||Written assignments and computer based assessments|
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.
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.