Undergraduate - UnitMAT2003 - Continuous mathematics for computer science

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

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