 # MATH2099 Mathematics 2B

MATH2099 is a Level II course which is available only to students for whom it is specifically required as part of their program. See the course overview below.

Units of credit: 6

Prerequisites: MATH1231 or MATH1241 or MATH1251 or DPST1014

Exclusions: BEES2041, CVEN2002, MATH2501, MATH2601, MATH2801, MATH2901, MATH2859, MATH2089, ECON3209

Cycle of offering: Term 2

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This course outline (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH2099, you can log into UNSW Moodle for this course.

#### Course Aims

Statistics: The primary objective of the statistics stream is to enable students to apply and interpret statistical methods in an Engineering context, and to build foundations for future courses in their UG degree programs.

Linear Algebra: Linear algebra is a key tool in all of mathematics and its applications. For example, the output of many electrical circuits depends linearly on the input (over moderate ranges of input), and successfully correcting the trajectory of a space probe involves repeatedly solving systems of linear equations in hundreds of variables. Linear methods are vital in ecological population models, and in mathematics itself. You have begun to understand systems of linear equations and matrices, vector spaces and linear transformations in rst year mathematics courses. In MATH2099, you will learn about geometric transformations: projections (which can also be viewed as least squares approximations), rotations and re ections. You will see how to view many linear transformations as being made up of \stretches" in various directions, (the diagonalisation process), and the more general Jordan form. This will allow you to calculate functions of matrices (such as the exponential of a matrix) and hence to solve systems of linear differential equations.

#### Course Description

Probability and statistics: Sample spaces, probability, random variables and probability distributions, standard discrete and continuous distributions, multivariate distributions, Central Limit Theorem, statistical inference, confidence intervals and hypothesis testing, linear regression, inference in the linear model. Matlab will be used in this course.

Linear algebra: Vector spaces, linear transformations, change of basis, inner products, orthogonalization, least squares approximation, QR factorization, determinants, eigenvalues and eigenvectors, diagonalization, Jordan forms, matrix exponentials and applications to systems of differential equations, other applications of linear algebra.