Module Catalogue 2024/25

MAS2708 : Groups and Discrete Mathematics

MAS2708 : Groups and Discrete Mathematics

  • Offered for Year: 2024/25
  • Module Leader(s): Dr Thorsten Heidersdorf
  • 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
Pre-requisite

Modules you must have done previously to study this module

Code Title
MAS1606Introductory Algebra
Pre Requisite Comment

MAS1606 can be replaced with MAS1610

Co-Requisite

Modules you need to take at the same time

Co Requisite Comment

N/A

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.

Learning Outcomes

Intended Knowledge Outcomes

Students will be able to demonstrate a reasonable understanding of group theory, graph theory, and algorithms. They will be able to reproduce definitions of elementary notions such as group axioms, group homomorphisms, algorithms, graphs and complexity.

Intended Skill Outcomes

Students should have a reasonable grasp of the knowledge outcomes and perform mathematical arguments with these notions. Students should be able to perform calculations permutations and examples of groups, as well as work with graphs and use them in problem-solving, and compare algorithms based on their complexity.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Drop in sessions
Guided Independent StudyIndependent study531:0053:00Preparation time for lectures, background reading, review of coursework
Total100:00
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.

Reading Lists

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-solving exercises assessment
Prob solv exercises2M5Problem-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.

Timetable

Past Exam Papers

General Notes

N/A

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Disclaimer

The information contained within the Module Catalogue relates to the 2024 academic year.

In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described.

Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2025/26 entry will be published here in early-April 2025. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.