COMP11120 Mathematical Techniques for Computer Science syllabus 2015-2016
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
|Programme outcome||Unit learning outcomes||Assessment|
|A1||Have basic familiarity with complex numbers and the standard operations for these.|
|A1||Have an understanding of the standard propositional logic connectives and be able to convert logical expressions into conjunctive and disjunctive normal form.|
|A1 B1||Have an understanding of the standard logic connectives, including universal and existential quantification, and the role they play in making precise statements.|
|A1 B1||Understand the basics of using a formal logical system, equivalence of logical formulae, and conjunctive and disjunctive normal forms.|
|A1 B1||Understand the principle of recursion and the accompanying proof principle of induction, including carrying out standard indutive proofs.|
|A1 B1||Be familiar with the general concept of binary relation, equivalence and order relations and methods of combining relations; be familiar with the standard graphical representations of relations.|
|A1||Have a good appreciation of the basic laws of probability.|
|A1||Have the skills to tackle simple problems on discrete probability distributions, conditional probability and independence.|
|A1||Have an understanding of vectors and matrices and their associated operations.|
|A1||Be able to use vectors and matrices to solve simple geometrical problems.|
|A1 B1||Have an understanding of the role of vectors and matrices in graphics-based computation.|
|Applied statistics and probability for engineers (5th edition)||Montgomery, Douglas C. and George C. Runger||9780470505786||Wiley||2010||✖|
|Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences (4th edition)||Jordan, D.W. and P. Smith||9780199282012||Oxford University Press||2008||✖|
|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||✖|
|How to think like a mathematician: a companion to undergraduate mathematics||Houston, Kevin||9780521719780||Cambridge University Press||2011||✖|
|Discrete mathematics with applications (4th edition)||Epp, Susanna S.||9780495826163||Brooks/Cole||2011||✖|
Course unit materials
Links to course unit teaching materials can be found on the School of Computer Science website for current students.