MAT2003 - Continuous mathematics for computer science

On successful completion of this unit, students should be able to:

1. apply counting principles in combinatorics and derive key combinatorial identities;
2. describe the principles of elementary probability theory, evaluate conditional probabilities and use Bayes' Theorem;
3. recognise some standard probability density functions, calculate their mean, variance and standard deviation, demonstrate their properties and apply them to relevant problems;
4. implement the principles of experimental design based on those probability density functions, and apply confidence intervals to sample statistics;
5. demonstrate basic knowledge and skills of linear algebra, including to manipulate matrices, solve linear systems, and evaluate and apply determinants;
6. apply knowledge of linear algebra to relevant problems, such as network flow and Markov chains;
7. describe fundamental knowledge of calculus including to differentiate basic, composite, inverse and parametric functions;
8. calculate approximations of functions with tangent lines, evaluate power series and construct Taylor series;
9. perform key skills in the calculus of functions of several variables including to calculate partial derivatives, find tangent planes, identify stationary points and construct Taylor series.