MAS2708 : Groups and Discrete Mathematics
- Offered for Year: 2024/25
- Module Leader(s): Dr Martina Balagovic
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 2 Credit Value: | 10 |
| ECTS Credits: | 5.0 |
| European Credit Transfer System | |
Aims
To introduce the basic concepts, notation, and techniques of discrete mathematics, particularly group theory, graph theory and the theory of algorithms, and the use of these methods in the representation and solutions of problems coming from the real world as well as other parts of mathematics.
Module Summary
Groups will be introduced, and their basic properties will be studied via permutation groups, building on knowledge of mappings and permutations. The concept of an algorithm will be introduced and formally defined, with some discussion on how the complexity of an algorithm can be measured. The basic notation of graphs will be introduced, some well-known problems will be formulated in that language. Solutions to the problem will be discussed, as well as their complexity.
Outline Of Syllabus
Permutations. Groups: definition, properties, examples. Symmetric, alternating and dihedral groups. Subgroups, conjugation, homomorphisms, isomorphisms, cosets, Lagrange's Theorem. Algorithms and growth of functions, comparison of algorithms, P vs NP. Basic concepts of graph theory: examples and problem-solving algorithms such as finite-state automata.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Scheduled Learning And Teaching Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
| Guided Independent Study | Assessment preparation and completion | 15 | 1:00 | 15:00 | Completion of in course assessments |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Drop-in/surgery | 5 | 1:00 | 5:00 | Drop in sessions |
| Guided Independent Study | Independent study | 53 | 1:00 | 53:00 | Preparation time for lectures, background reading, review of coursework |
| Total | 100:00 |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. 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.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 120 | 2 | A | 80 | N/A |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 2 | M | 7 | Problem solving exercises assessment |
| Prob solv exercises | 2 | M | 7 | Problem-solving exercises assessment |
| Prob solv exercises | 2 | M | 6 | Problem-solving exercises assessment |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Prob solv exercises | 2 | M | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The coursework assignments 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; these assessments have a secondary formative purpose as well as their primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS2708's Timetable