COMP11120 Mathematical Techniques for Computer Science syllabus 2019-2020
This course covers the fundamental maths required by Computer Science students in order to successfully complete the reminder of their courses as well as for a career in computer science. Topics covered include complex numbers, logic, probability, recursion and induction, relations, vectors, matrices and transformations.
This is a full year course that focuses on areas of mathematics required to model and analyse the kind of problems that arise in computer science.
Probabilities are used for example in artificial intelligence, and play a vital role in machine learning, while the combinatorics required here also plays a role in the field of computational complexity. Vectors and matrices are the mathematical model underlying computer graphics. Logic is a tool used to reason about computer programs as well as the real world. Recursion is an important programming principle that comes with an associated proof rule, and other mathematical notions such as functions and relations are used routinely in computer science, for example when talking about database systems. Theoretical computer science can be considered an area of mathematics, and the unit also provides an introduction to the fundamental notions of this area.
Specifically the unit aims to
- introduce mathematical notions relevant to computer science and their applications;
- illustrate how abstraction allows the formulation and proof of properties for real-world and computational phenomena, and enable students to apply this technique;
- give an understanding and some practice in the fundamental notion of proof.
Students are required to undertake background reading, which is supported by lectures to explain various notions and to show the application of various techniques using examples. The coursework requires the students to solve exercises each week. Feedback for and help with this work is provided in the examples classes.
44 in total, 2 per week
22 in total, 1 per week
Attendance: 3 hours per week
Self-study and solving coursework: ca 4 hours per week
Revision and exams: ca 45 hours
Feedback methodsOne to one feedback will be provided during examples classes. Written feedback will be provided on the marked homework and exam papers. End of semester and end of year feedback on exam performance will also be provided.
- Assessment written exam (4 hours)
- Lectures (44 hours)
- Practical classes & workshops (22 hours)
- Analytical skills
- Problem solving
On successful completion of this unit, a student will be able to:
- perform the standard operations on complex numbers
- apply formal definitions and construct formal arguments based on these in the context of mathematics relevant to computer science.
- employ abstraction to move from concrete phenomena to ones which are amenable to the application of mathematical techniques.
- interpret the meaning of logical formulae as part of a natural deduction system, via the model based on truth values, or via a given intended model.
- construct logical formulae to describe aspects of a given system, and manipulate these formulae to derive properties of the system.
- apply concepts from the mathematical theory of probability to describe and analyse a variety of situations.
- use Bayesian reasoning to construct a simple algorithm for learning in a variety of situations.
- recognize recursively defined structures and define recursive operations satisfying some given specification, as well as construct inductive arguments to prove some given property for such operations.
- use vectors and matrices to describe suitable situations, such as systems of equations or operations in two- and three-dimensional space, and are able to carry out relevant calculations for these.
- choose suitable mathematical techniques to analyse questions from computer science and devise approaches to solving them.
|Linear alegbra: a modern introduction (4th edition)||Poole, David||9781285463247||Brooks/Cole||2014||✖|
|Discrete mathematics for new technology (2nd edition)||Garnier, Rowan and John Taylor||9780750306522||Taylor & Francis||2001||✖|
|Discrete mathematics for Computer Scientists (2nd edition)||Truss, J.K.||0201360616||Addison-Wesley||1999||✖|
|Interactive computer graphics: a top-down approach with WebGL (7th edition)||Angel, Edward and Dave Shreiner||9781292019345||Pearson||2015||✖|
|Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences (4th edition)||Jordan, D.W. and P. Smith||9780199282012||Oxford University Press||2008||✖|
|How to think like a mathematician: a companion to undergraduate mathematics||Houston, Kevin||9780521719780||Cambridge University Press||2011||✖|
|Discrete mathematics with applications (5th edition)||Epp, Susanna S.||9780357114087||Cengage Learning||2018||✖|
Course unit materials
Links to course unit teaching materials can be found on the School of Computer Science website for current students.