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Mathematics for Statistics (3 days) (CANCELLED)

Cancellation Notice:
This course has been cancelled for Summer Programme 2012 due to insufficient enrolments. We will endeavour to run it again in a future NZSSN short course programme; if you are interested in such a course, please let us know in the meantime so that we can provide targetted followup when the time comes.
Dates: 
February 20, 2012 - February 22, 2012
Instructor: 
Dr Sepideh Stewart

This 3-day course is intended to improve mathematical understanding, which is essential in many statistical applications. The course will explore various mathematical techniques required for statistics. A mixture of theory and step-by-step examples from both mathematical and statistical applications will be presented. Participants will be given opportunities to work in class by way of doing examples, and will learn valuable skills throughout the sessions. Clear explanations of some vital mathematical ideas will equip the learner with skills to gain confidence in solving many real-life problems.
 

Prerequisites: 

Some background knowledge in maths; year 13 mathematics would be ideal.

Learning Objectives: 

Part I: Calculus
Logarithmic functions and their properties; Exponential functions; An introduction to limits; Differentiation rules (product, quotient, composite) for a variety of applications; Integration rules and techniques (substitution and by parts).
 
Part II: Linear Algebra
Solving Linear Systems of Equations; Matrix Algebra; Inverses; eigenvalues and eigenvectors; Least squares regression as an application of matrix theory (solution of the general least-squares problem, least squares error, column space) and Markov Chain processes (stochastic matrix, steady-state vector).
 

References: 

Anton, H., and Busby, R. C. (2003). Contemporary Linear Algebra, New York: Wiley.

Lay, D. (1996). Linear Algebra and its applications, Boston: Addison Wesley.

Stewart, J. (2006) Single variable calculus concepts and contexts, Thomson, Brooks/Cole.