MATHEMATICS FOR COMPUTING

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1I325085 Module Leader Salma Mohamed School School of Computing, Engineering and Built Environment Subject Cyber Security and Networks Trimester A (September start)-B (January start)

Summary of Content

This module introduces elements of discrete mathematics underpinning the study of both hardware and software systems. The techniques developed in this module will be practically based with an emphasis on problem solving. The material will be accessible to students with a limited mathematical background. The percentage of Work Based Learning for this module, as represented by he proportion of the Activity Types which take place off campus, is 79%. The percentage of Work Based Assessment for this module is 0%.

Syllabus

Solving equations: - systems of linear equation; - quadratics; - applying logarithms; - the standard functions; - the graphical method for finding roots; - interpreting equations as mathematical models. Matrices and Vectors: -Definitions, addition, multiplication, matrix inversion; -Modelling: error detection, Hill ciphers, network connectivity. Logic: -709 -Sets: union, intersection, complement, Cartesian products, Venn diagrams; -Relations: order relations, introduction to equivalence relations, composition, inversion; functions. - logic operators: and, or, not, implication and equivalence - truth tables; - examples of proof; - introduction to Formal System Specification Graphs: -Definition, Diagrams, Adjacency and Incidence Matrix, vertex degree, degree sequence, Handshaking Lemma; -Types: Bipartite, Cubic, Complete, Petersen etc.; -Paths, Cycles (including Euler and Hamilton cycles), Connectedness; -Applications: Petri Nets; Gray's codes, Compatibility graphs -709 Trees and Digraphs: - Trees: Definition, Binary, Breadth first search, Depth first search, Stacks; - Directed graphs: Definition, Representations, acyclic and weighted (networks); - In-degree, Out-degree, Handshaking Lemma, Cycles; - weighted digraphs (Networks); - Applications: tournaments, max-flow min-cut. -709 Finite State Automata: - definition; - modelling states and transitions using a digraph; - pattern recognition. Number Modular Arithmetic: the concept and basic operations, applications to cryptography. Number systems: binary, decimal, hexadecimal and changing between bases Bitwise logical operations on binary numbers

Learning Outcomes

On completion of this module, students should be able to:1- Use graphs and digraphs to model and solve problems;2- Apply simple finite state machines and simple algorithms, including recursion;3- Solve simple equations and carry out basic algebraic operations on matrices and vectors, simple mathematical transformations as used in elementary Cryptography;4- Calculate in a range of number systems associated with computer applications;5- Represent statements using logical operators and use them in deductive arguments and work with finite relations.

Teaching / Learning Strategy

Work based Education aims to maximise the direct and digitally mediated contact time with students by practicing teaching and learning strategies that use authentic work based scenarios and encourage action learning, enquiry based learning, problem based learning and peer learning. All these approaches aim to directly involve the students in the process of learning and to encourage sharing of learning between students. The module team will determine the level and accuracy of knowledge acquisition at key points in the delivery, inputting when necessary either directly or with the support of external experts who will add to the authenticity, the credibility and application of the education and learning in the workplace. -1 The course material is delivered through lectures in the form of online presentations which introduce mathematical concepts from discrete mathematics. Discrete mathematics is the study of algebraic structures and relationships that underpin many of the operations in Computing, Mathematics, Engineering and Economics. The online course notes include links to appropriate external material such as videos, literature and exercises to supplement the module content. Students will attend on-campus seminars that involve face-to-face delivery of the course material and provide students with the opportunity to discuss key concepts and issues with their peers and instructors. Students will engage with online tutorial material in the form of traditional exercise sheets and questions implemented in the Maple T. A. software package. This module provides an ideal framework for students to develop their understanding of mathematical concepts in computing, relate these concepts to practical applications and sharpen their problem solving skills. Students are expected to undertake a significant level of independent study in the workplace and will be encouraged to reflect on the theoretical learning and develop their independent learning skills. Students will receive feedback on their performance throughout the module by participating in seminars, attempting the online tutorial exercises and studying the associated solutions Lectures will deliver the module syllabus. Tutorials will be used for developing basic mathematical manipulation skills, and for exploring applications (which can be expected to continue into private study). Directed study will require the undertaking of specified tutorial material; the completion or extension of the applications covered in tutorials; and the opportunity for the student to dig deeper through identified 'advanced' topics (either supplied, or obtainable from identified sources such as the World Wide Web) -'advanced' topics are not assessable. Feedback will be supplied through the marking of the class tests and their associated mocks; in tutorials - through discussion with the tutor; and through supplied solutions and commentary to SAQs.

Indicative Reading

Krantz, S., Discrete Mathematics DeMYSTiFied, McGraw-Hill Professional; 1st edition (2008); ISBN-13: 978-0071549486 Wilson R. Introduction to Graph theory R Wilson Prentice Hall, 5 th edition (2010); ISBN -13: 978-0273728894 R. Huettenmueller, College Algebra DeMYSTiFied McGraw Hill Professional 2ed. (2014); ISBN-13: 978-0071815840

Transferrable Skills

Specialist knowledge and application Critical thinking and problem solving Numeracy Self confidence, self discipline & self reliance (independent working) Appreciating and desiring the need for continuing professional development Ability to prioritise tasks and time management Evaluate current research and technology concepts and their relationship and application to a work based problem.

Module Structure

Activity Total Hours
Assessment (FT) 18.00
Independent Learning (FT) 110.00
Lectures (FT) 24.00
Seminars (FT) 24.00
Practicals (FT) 24.00

Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) 0.75 40.00 35% Class test
Exam (Exams Office) 2.00 60.00 35% Unseen Exam Trimester B