## Level 2 Subjects

The following are our second year level subjects. The headings link to the full descriptions in the University Handbook.

MAST20004 Probability

Almost all real-life processes involve elements of randomness, so it is very important to be able to describe and model such situations. Probability theory is part of mathematics concerned with modeling and analyzing random phenomena. It provides foundation for statistics, which is essential to all human activities involving data analysis, and has numerous applications in sciences and industry, ranging from DNA analysis to telecommunications and stock trading. This subject offers grounding in probability theory and its applications**.**

MAST20005 Statistics

Statistics concerns the collection and analysis of data to make inferences about the parameters of a probability model. This subject introduces the mathematical theory underlying modern statistical inference. In particular, it demonstrates that many commonly used statistical procedures arise as applications of a common theory. Distribution free and Bayesian statistical methods are also introduced, along with the statistical computing software needed to implement statistical procedures.

MAST20006 Probability for Statistics

This subject develops the probability theory that is necessary to understand statistical inference. Properties of probability are reviewed, random variables are introduced, and probability models are systematically developed. Methods for studying the distributions of functions of random variables are also developed along with techniques to obtain the exact and approximate distributions of sums of random variables.

MAST20009 Vector Calculus

Vector calculus extends the ideas and tools of calculus to apply to scalar and vector fields, which represent quantities such as temperature, velocity fields or magnetic fields. It generalizes derivatives and integrals to vector differential operators, line, surface and volume integrals and relates them by various integral theorems. Curvilinear coordinates are introduced and used to evaluate integrals. Vector calculus is an important tool for many applications in physics and engineering such as electromagnetism, fluid mechanics and quantum mechanics**.**

MAST20018 Discrete Maths and Operations Research

This subject introduces operations research methods, which are used in business and industry to optimize processes and resource allocation, using mathematical techniques such as linear programming implemented using the simplex method. It also introduces the area of discrete mathematics as applied to social sciences, covering how mathematical reasoning can be used in scheduling, voting, fair division and bargaining.

MAST20022 Group Theory and Linear Algebra

This subject introduces the theory of groups, which is at the core of modern algebra, and which has applications in many parts of mathematics, chemistry, computer science and theoretical physics. It also develops the theory of linear algebra, building on material in earlier subjects and providing both a basis for later mathematics studies and an introduction to topics that have important applications in science and technology.

MAST20026 Real Analysis

Real analysis is a branch of mathematics that deals with real functions and sequences, including convergence and limits of sequences of real numbers, continuity, smoothness and related properties of real-valued functions, and differential and integral calculus. It is a critically important tool in mathematics and statistics. It is a starting point for areas such as complex analysis and functional analysis. This is a corner-stone subject for students whose studies involve mathematical sciences.

MAST20029 Engineering Mathematics

This subject introduces important mathematical methods required in engineering such as manipulating vector differential operators, computing multiple integrals and using integral theorems. A range of ordinary and partial differential equations are solved by a variety of methods and their solution behaviour is interpreted. The subject also introduces sequences and series including the concepts of convergence and divergence.

MAST20030 Differential Equations

Differential equations arise as common models in the physical, mathematical, biological and engineering sciences. This subject covers linear differential equations, both ordinary and partial, initial value problems and boundary value problems, eigenvalue problems arising from common classes of partial differential equations, Laplace transform methods, separation of variables method, Fourier series and Fourier transforms. The subject balances basic theory with concrete applications.

MAST20031 Analysis of Biological Data

A capacity to interpret data is fundamental to making informed decisions in everyday life. The design of experiments, analysis, and interpretation of biological data also lie at the very heart of the scientific enterprise. You cannot be a scientist without an understanding of data and design. This subject introduces you to fundamental concepts in data science for biology, with emphasis on modern statistical methods. Drawing on real biological problems and datasets, as well as drawing on data collected by the class, the lectures cover foundational concepts in experimental design and statistical modelling. The subject emphasises hands-on problem solving. As well as a solid grounding in statistical methodology, you will also develop practical skills, developing your capacity to design experiments, collect data, and analyse those data using the R statistical environment.