Mathematics for Computing
Run by School of Computer Science and Electronic Engineering
20.000 Credits or 10.000 ECTS Credits
Semester 1 & 2
Organiser: David Evans
Overall aims and purpose
This module aims to provide:
- a grounding in computational thinking.
- an understanding of the fundamental mathematics underlying all computing.
- experience dealing with the mathematical structures under-pinning programming and data structures.
- a revision of and practice with elementary algebra.
Indicative content includes:
- Introduce and use Graphs and Digraphs
- Apply Greedy Algorithms to various graphs
- Look at the fundamental of Sets and how to use them
- Learn to build Venn Diagrams
- Gain the concepts of Boolean algebra and Karnaugh maps to solve logic problems
- Use Lists in relation to algorithms
- Apply the use of Binary Trees for given problems
- Write Linear Difference Equations for various situations
- Gain a foundation in Differentiation both in theory and application.
PART 1. MATRICES 1. Matrices. Definition. Notations. Vector-row and vector-column. Main diagonal of a matrix. Diagonal and square matrices. Symmetric matrix. Identity matrix. Transpose. 2. Operations on matrices. Addition. Multiplication by a scalar. Commutativity of addition. Matrix multiplication. 3. Linear transformations in 2D. Reflections and projections. Contractions, expansions and shear. Rotation matrix. 4. Concept of inverse of a matrix and its use for solving n linear equations with n unknowns. Examples. Inverse of a 2-by-2 matrix. “Express-and-substitute” method for solving 2 simultaneous equations. Matrix method.
PART 2. 2D and 3D SPACES 5. Vectors. Basic definitions and notations. Addition and subtraction. Multiplication by a scalar. Magnitude. Unit vector. Position vector. Coordinate decomposition. 6. Scalar product of vectors. Orthogonality. Euclidean distance between 2 points in the n-dimensional space. 7. Lines in 2D. Generic equation in 2D. Line between two points in 2D. Points on the same/different sides of a line in 2D. 8. Intersection of lines in 2D. Solving by using matrix inverse. Special cases. 9. Planes and lines in 3D. Generic equations. Line between 2 points in 3D. Intersection of a line and a plane in 3D. Plane defined by 3 points in 3D. 10. Special cases of lines and planes in 2D and 3D. Lines parallel to the coordinate axes in 2D. Planes parallel to xy-plane, yz-plan and xz-plane, and parallel to the coordinate axes. 11. Circles and spheres. Generic equations. Intersection between a circle and a line in 2D. Points inside and outside circles and spheres. 12. Vector orthogonal to a line in 2D. Normal and unit normal vector for a line between 2 points. 13. Orthogonality between vector and line/vector and plane. Finding the unit normal vectors for lines and planes given by their generic equations. 14. Collinearity between vectors. Vectors parallel to lines/planes
PART 3. PROBABILITY 15. Counting rule. Permutations. n-factorial. Binomial coefficients. Combinations. 16. Sample space. Elementary events. Compound events. Equiprobable and non-equiprobable elementary events. Probability and its properties. 17. Contingency tables. Joint, marginal and conditional probabilities.
Equivalent to the range 70%+. Assemble critically evaluated, relevent areas of knowledge and theory to constuct professional-level solutions to tasks and questions presented. Is able to cross-link themes and aspects to draw considered conclusions. Presents outputs in a cohesive, accurate, and efficient manner.
Equivalent to 40%. Uses key areas of theory or knowledge to meet the Learning Outcomes of the module. Is able to formulate an appropriate solution to accurately solve tasks and questions. Can identify individual aspects, but lacks an awareness of links between them and the wider contexts. Outputs can be understood, but lack structure and/or coherence.
Equivalent to the range 60%-69%. Is able to analyse a task or problem to decide which aspects of theory and knowledge to apply. Solutions are of a workable quality, demonstrating understanding of underlying principles. Major themes can be linked appropriately but may not be able to extend this to individual aspects. Outputs are readily understood, with an appropriate structure but may lack sophistication.
Understand graph and digraph problems and algorithms for solving them.
Calculate probabilities for elementary and compound events.
Understand polynomial functions, and their derivatives.
Apply elementary algebra.
Perform basic matrix and vector operations.
Graph and set theory, algebra, Boolean Algebra and structures.
Matrix, vector and probability.
|COURSEWORK||Semester 1 - Assignment 1||
Graphs, polynomials and basic algebra
|COURSEWORK||Semester 1 - Assignment 2||
Graphs, Calculus, Boolean Algebra, Advanced Algebra (including Determinant Theory)
|COURSEWORK||Semester 2 - Assignment 1||
Matrix types, operations, vectors. Solving systems of equations using matrix techniques.
|COURSEWORK||Semester 2 - Assignment 2||
Further Matrix methods. Probability Theory.
Teaching and Learning Strategy
Traditional lectures (2hrs x 24 weeks).
Supporting tutorials (1hr x 24 weeks).
Tutor-directed private study, including preparation and revision.
- Numeracy - Proficiency in using numbers at appropriate levels of accuracy
- Computer Literacy - Proficiency in using a varied range of computer software
- Self-Management - Able to work unsupervised in an efficient, punctual and structured manner. To examine the outcomes of tasks and events, and judge levels of quality and importance
- Information retrieval - Able to access different and multiple sources of information
- Critical analysis & Problem Solving - Able to deconstruct and analyse problems or complex situations. To find solutions to problems through analyses and exploration of all possibilities using appropriate methods, rescources and creativity.
Subject specific skills
- Solve problems logically and systematically;
- Knowledge and understanding of facts, concepts, principles & theories
- Problem solving strategies
- Development of general transferable skills
- Knowledge and/or understanding of appropriate scientific and engineering principles
- Knowledge and understanding of mathematical principles
- Knowledge and understanding of computational modelling
- Principles of appropriate supporting engineering and scientific disciplines
Courses including this module
Compulsory in courses:
- G400: BSC Computer Science year 1 (BSC/CS)
- G40B: BSc Computer Science (4 year with Incorporated Foundation) year 1 (BSC/CS1)
- G40F: BSc Computer Science year 1 (BSC/CSF)
- I103: BSc Computer Science with Game Design year 1 (BSC/CSGD)
- I102: BSc Computer Science (with International Experience) year 1 (BSC/CSIE)
- G40P: BSc Computer Science with Industrial Placement year 1 (BSC/CSIP)
- H118: BSc Data Science & Artificial Intelligencetellig year 1 (BSC/DSAI)
- H113: BSc Data Science and Machine Learning year 1 (BSC/DSML)
- H114: BSc Data Science and Visualisation year 1 (BSC/DSV)
- H117: MComp Computer Science year 1 (MCOMP/CS)