Probability and combinatorics: elementary probability theory, random variables, probability distributions, expected value; counting arguments in combinatorics; statistics. Linear algebra: vectors and matrices, matrix algebra with applications to flow problems and Markov chains; matrix inversion methods. Calculus: differentiation and partial differentiation; constructing Taylor series expansions.
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.
Examination (3 hours): 70%; In-semester assessment: 30%
Minimum total expected workload equals 12 hours per week comprising:
(a.) Contact hours for on-campus students:
- Three hours of lectures
- One 1-hour laboratory
(b.) Additional requirements (all students):
- A minimum of 8 hours independent study per week for completing lab and project work, private study and revision.