CM2104: Computational Mathematics
| School | Cardiff School of Computer Science and Informatics |
| Department Code | COMSC |
| Module Code | CM2104 |
| External Subject Code | 101029 |
| Number of Credits | 10 |
| Level | L5 |
| Language of Delivery | English |
| Module Leader | Professor Paul Rosin |
| Semester | Autumn Semester |
| Academic Year | 2018/9 |
Outline Description of Module
Gives a broad grounding in mathematical programming via MATLAB.
Provides continuous mathematical and programming skills used in Computer Science.
On completion of the module a student should be able to
1. Show a clear understanding of basic MATLAB programming environment and data structures
2. Understand the practical implementation of some general mathematical techniques via MATLAB
3. Demonstrate an awareness of basic Linear Algebra and its application to Computational Geometry concepts with MATLAB
4. Demonstrate an understanding of Discrete Probability Theory
How the module will be delivered
The module will be delivered through a combination of lectures, supervised lab sessions, example classes and tutorials as appropriate.
Skills that will be practised and developed
Practical experience of some general mathematical (including polynomials, calculus, linear algebra and probability theory) using MATLAB
Practical experience of basic MATLAB techniques, including array processing, vectorisation, graph plotting and graphical user interface construction.
How the module will be assessed
Coursework: The coursework will allow the student to demonstrate their knowledge and practical skills and to apply the principles taught in lectures (LO1, LO2, LO3).
Exam: A written exam (2 h) will test the student's knowledge and understanding as elaborated under the learning outcomes (LO1, LO2, LO3, LO4).
The potential for reassessment in this module is a 100% resit examination during the summer.
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Written Assessment | 30 | Individual Project Work | N/A |
| Exam - Autumn Semester | 70 | Computational Mathematics | 2 |
Syllabus content
MATLAB Programming
MATLAB Integrated Development Environment
Basic MATLAB Commands
MATLAB Vectors and Arrays/Matrices. Matrix Operations
Vectorisation
MATLAB functions: built-in and user-defined
MATLAB toolboxes: M-files, paths
MATLAB Graphics: basic plotting and figure commands, 2D/3D plotting
MATLAB GUIS: Dialogs, UIcontrol elements, callbacks, GUIDE.
General Mathematics
Polynomials
Algebra – factorisation
Calculus
Discrete Probability Theory
Discrete probability spaces
Conditional probability and Bayes' theorem
Independence
Random variables and distributions
Expected value and variance
Statistical inference
Linear Algebra
Vectors
Matrices
Linear systems
Geometric Transformations and Warping
Geometric Computing for Computer Graphics
Axes & coordinates in 2D, 3D
Curves in 2D; lines, circles, parametric, implicit
Curves and Surfaces in 3D; lines, planes, parametric
Piecewise shapes; polygons
Intersections
Background Reading and Resource List
Engineering mathematics, K.A. Stroud and Dexter (ISBN 0-8311-3152-7)
Probability and Statistics for Computer Science, J. L. Johnson (ISBN 0-471-32672-0)
Mastering MATLAB, Duane C. Hanselman (Author), Bruce L. Littlefield (Author), Peason, ISBN 013-185-7142
Linear Algebra & its Applications, D Lay, Addison Wesley, ISBN 032-141-7615
An Introduction to the Mathematics & Geometry of Computer Graphics, M Mortenson, Heinemann Newnes, ISBN 083-111-1828
A programmer’s Geometry, A. Bowyer and J. Woodward, Butterworths (1985), ISBN 0-408-01242-0
Discrete Mathematics and its Applications, KH Rosen (ISBN: 0-071-19881-4)