This unit is designed for science students who do not intend to undertake higher year mathematics and statistics. It establishes and reinforces the fundamentals of calculus, illustrated where possible with context and applications. Specifically, it demonstrates the use of (differential) calculus in solving optimisation problems and of (integral) calculus in measuring how a system accumulates over time. Topics studied include the fitting of data to various functions, the interpretation and manipulation of periodic functions and the evaluation of commonly occurring summations. Differential calculus is extended to functions of two variables and integration techniques include integration by substitution and the evaluation of integrals of infinite type.

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals.
Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates differential calculus and integral calculus of one variable and the diverse applications of this theory. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include complex numbers, functions of a single variable, limits and continuity, differentiation, optimisation, Taylor polynomials, Taylor's Theorem, Taylor series, Riemann sums, and Riemann integrals. Additional theoretical topics included in this advanced unit include the Intermediate Value Theorem, Rolle's Theorem, and the Mean Value Theorem. Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1921 Calculus of One Variable (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable.
Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

Calculus is a discipline of mathematics that finds profound applications in science, engineering, and economics. This unit investigates multivariable differential calculus and modelling. Emphasis is given both to the theoretical and foundational aspects of the subject, as well as developing the valuable skill of applying the mathematical theory to solve practical problems. Topics covered in this unit of study include mathematical modelling, first order differential equations, second order differential equations, systems of linear equations, visualisation in 2 and 3 dimensions, partial derivatives, directional derivatives, the gradient vector, and optimisation for functions of more than one variable. Additional topics covered in this advanced unit of study include the use of diagonalisation of matrices to study systems of linear equation and optimisation problems, limits of functions of two or more variables, and the derivative of a function of two or more variables. Students are strongly recommended to complete MATH1021 of MATH1921 before commencing MATH1023 or MATH1923.

The Mathematics Special Studies Program is for students with exceptional mathematical aptitude, and requires outstanding performance in past mathematical studies. Students will cover the material of MATH1923 Multivariable Calculus and Modelling (Adv), and attend a weekly seminar covering special topics on available elsewhere in the Mathematics and Statistics program.

MATH1002 is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering.
This unit of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. It parallels the normal unit MATH1002 but goes more deeply into the subject matter and requires more mathematical sophistication.

This unit is an introduction to Linear Algebra. Topics covered include vectors, systems of linear equations, matrices, eigenvalues and eigenvectors. Applications in life and technological sciences are emphasised.

In a data-rich world, global citizens need to problem solve with data and evidence based decision-making is essential in every field of research and work. This unit equips you with the foundational statistical thinking to become a critical consumer of data. You will learn to think analytically about data and to evaluate the validity and accuracy of any conclusions drawn. Focusing on statistical literacy, the unit covers foundational statistical concepts, including the design of experiments, exploratory data analysis, sampling and tests of significance.

This unit is designed to provide a thorough preparation for further study in mathematics and statistics. It is a core unit of study providing three of the twelve credit points required by the Faculty of Science as well as a Junior level requirement in the Faculty of Engineering. This Advanced level unit of study parallels the normal unit MATH1005 but goes more deeply into the subject matter and requires more mathematical sophistication.

DATA1001 is a foundational unit in the Data Science major. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology, DATA1001 develops critical thinking and skills to problem-solve with data. It is the prerequisite for DATA2002.

DATA1901 is an advanced level unit (matching DATA1001) that is foundational to the new major in Data Science. The unit focuses on developing critical and statistical thinking skills for all students. Does mobile phone usage increase the incidence of brain tumours? What is the public's attitude to shark baiting following a fatal attack? Statistics is the science of decision making, essential in every industry and undergirds all research which relies on data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem solving skills in a team setting. Taught interactively with embedded technology and masterclasses, DATA1901 develops critical thinking and skills to problem-solve with data at an advanced level. By completing this unit you will have an excellent foundation for pursuing data science, whether directly through the data science major, or indirectly in whatever field you major in. The advanced unit has the same overall concepts as the regular unit but material is discussed in a manner that offers a greater level of challenge and academic rigour.

Technological advances in science, business and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2002 is an intermediate unit in statistics and data sciences, focusing on learning data analytic skills for a wide range of problems and data In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with a statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skills to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

Technological advances in science, business, and engineering have given rise to a proliferation of data from all aspects of our life. Understanding the information presented in these data is critical as it enables informed decision making into many areas including market intelligence and science. DATA2902 is an intermediate unit in statistics and data sciences, focusing on learning advanced data analytic skills for a wide range of problems and data In this unit, you will learn how to ingest, combine and summarise data from a variety of data models which are typically encountered in data science projects as well as reinforcing your programming skills through experience with statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skills to analyse various types of data in order to answer a scientific question. From this unit, you will develop knowledge and skills that will enable you to embrace data analytic challenges stemming from everyday problems.

This unit provides an introduction to probability, the concept of random variables, special distributions including the Binomial, Hypergeometric, Poisson, Normal, Geometric and Gamma and to statistical estimation. This unit will investigate univariate techniques in data analysis and for the most common statistical distributions that are used to model patterns of variability. You will learn the method of moments and maximum likelihood techniques for fitting statistical distributions to data. The unit will have weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method. By doing this unit you will develop your statistical modeling skills and it will prepare you to learn more complicated statistical models.

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit has weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

Linear models are core to a wide range of real-world data analyses, for example in agriculture, health, sport and business. This unit provides an in-depth exploration of various linear models outlining when they can be applied, and how to assess if they are appropriate. The unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will consider linear models and robust regression methods with diagnostics for checking appropriateness of models and strategies for performing feature selection. You will learn to design and analyse experiments considering notions of replication, randomization and ideas of factorial designs. You will apply, construct and interpret multi-way ANOVA models and make inferences, including post-hoc tests and making corrections for multiple comparisons. Throughout the unit you will use the R statistical package to perform analyses and generate statistical graphics. By completing this unit you will learn how to generate, interpret, visualise and critique linear models.

This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such a thing as the best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the methods learnt to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will rigorously prove key results and apply these to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

This interdisciplinary unit provides students with the opportunity to address complex problems identified by industry, community, and government organisations, and gain valuable experience in working across disciplinary boundaries. In collaboration with a major industry partner and an academic lead, students integrate their academic skills and knowledge by working in teams with students from a range of disciplinary backgrounds. This experience allows students to research, analyse and present solutions to a real¿world problem, and to build on their interpersonal and transferable skills by engaging with and learning from industry experts and presenting their ideas and solutions to the industry partner.

Data Science is an emerging and inherently interdisciplinary field. A key set of skills in this area fall under the umbrella of Statistical Machine Learning methods. This unit presents the opportunity to bring together the concepts and skills you have learnt from a Statistics or Data Science major, and apply them to a joint project with NUTM3888 where Statistics and Data Science students will form teams with Nutrition students to solve a real world problem using Statistical Machine Learning methods. The unit will cover a wide breadth of cutting edge supervised and unsupervised learning methods will be covered including principal component analysis, multivariate tests, discrimination analysis, Gaussian graphical models, log-linear models, classification trees, k-nearest neighbors, k-means clustering, hierarchical clustering, and logistic regression. In this unit, you will continue to understand and explore disciplinary knowledge, while also meeting and collaborating through project-based learning; identifying and solving problems, analysing data and communicating your findings to a diverse audience. All such skills are highly valued by employers. This unit will foster the ability to work in an interdisciplinary team, and this is essential for both professional and research pathways in the future.

A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops important properties and limit theorems of discrete-time Markov chain and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, such as the memoryless property, super positioning, thinning, Kolmogorov's equations and limiting probabilities. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modeling and analyzing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics.

This unit will study basic concepts and methods of time series analysis applicable in many real world problems applicable in numerous fields, including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. This unit will investigate the basic methods of modelling and analyzing of time series data (ie. Data containing serially dependence structure). This can be achieved through learning standard time series procedures on identification of components, autocorrelations, partial autocorrelations and their sampling properties. After setting up these basics, students will learn the theory of stationary univariate time series models including ARMA, ARIMA and SARIMA and their properties. Then the identification, estimation, diagnostic model checking, decision making and forecasting methods based on these models will be developed with applications. The spectral theory of time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows will be studied in detail. Further, the methods of analyzing long memory and time series and heteroscedastic time series models including ARCH, GARCH, ACD, SCD and SV models from financial econometrics and the analysis of vector ARIMA models will be developed with applications. By completing this unit, students will develop the essential basis for further studies, such as financial econometrics and financial time series. The skills gain through this unit of study will form a strong foundation to work in a financial industry or in a related research organization.

In our ever-changing world, we are facing a new data-driven era where the capability to efficiently combine and analyse large data collections is essential for informed decision making in business and government, and for scientific research. Statistics and data analytics consulting provide an important framework for many individuals to seek assistant with statistics and data-driven problems. This unit of study will provide students with an opportunity to gain real-life experience in statistical consulting or work with collaborative (interdisciplinary) research. In this unit, you will have an opportunity to have practical experience in a consultation setting with real clients. You will also apply your statistical knowledge in a diverse collection of consulting projects while learning project and time management skills. In this unit you will need to identify and place the client's problem into an analytical framework, provide a solution within a given time frame and communicate your findings back to the client. All such skills are highly valued by employers. This unit will foster the expertise needed to work in a statistical consulting firm or data analytical team which will be essential for data-driven professional and research pathways in the future.

A stochastic process is a mathematical model of time-dependent random phenomena and is employed in numerous fields of application, including economics, finance, insurance, physics, biology, chemistry and computer science. After setting up basic elements of stochastic processes, such as time, state, increments, stationarity and Markovian property, this unit develops important properties and limit theorems of discrete-time Markov chain and branching processes. You will then establish key results for the Poisson process and continuous-time Markov chains, such as the memoryless property, super positioning, thinning, Kolmogorov's equations and limiting probabilities. Various illustrative examples are provided throughout the unit to demonstrate how stochastic processes can be applied in modeling and analyzing problems of practical interest. By completing this unit, you will develop the essential basis for further studies, such as stochastic calculus, stochastic differential equations, stochastic control and financial mathematics.

Linear models are core to a wide range of real-world data analyses, for example in agriculture, health, sport and business. This unit provides an in-depth exploration of various linear models outlining when they can be applied, and how to assess if they are appropriate. The unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will consider linear models and robust regression methods with diagnostics for checking appropriateness of models and strategies for performing feature selection. You will learn to design and analyse experiments considering notions of replication, randomization and ideas of factorial designs. You will apply, construct and interpret multi-way ANOVA models and make inferences, including post-hoc tests and making corrections for multiple comparisons. Throughout the unit you will use the R statistical package to perform analyses and generate statistical graphics. By completing this unit you will learn how to generate, interpret, visualise and critique linear models.

This unit will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. You will first consider linear models and regression methods with diagnostics for checking appropriateness of models, looking briefly at robust regression methods. Then you will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course you will use the R statistical package to give analyses and graphical displays. This unit is essentially an Advanced version of STAT3012, with additional emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods.

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such a thing as the best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will apply the methods learnt to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will rigorously prove key results and apply these to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

Data Science is an emerging and inherently interdisciplinary field. A key set of skills in this area fall under the umbrella of Statistical Machine Learning methods. This unit presents the opportunity to bring together the concepts and skills you have learnt from a Statistics or Data Science major, and apply them to a joint project with NUTM3888 where Statistics and Data Science students will form teams with Nutrition students to solve a real world problem using Statistical Machine Learning methods. The unit will cover a wide breadth of cutting edge supervised and unsupervised learning methods will be covered including principal component analysis, multivariate tests, discrimination analysis, Gaussian graphical models, log-linear models, classification trees, k-nearest neighbors, k-means clustering, hierarchical clustering, and logistic regression. In this unit, you will continue to understand and explore disciplinary knowledge, while also meeting and collaborating through project-based learning; identifying and solving problems, analysing data and communicating your findings to a diverse audience. All such skills are highly valued by employers. This unit will foster the ability to work in an interdisciplinary team, and this is essential for both professional and research pathways in the future.

This unit will study basic concepts and methods of time series analysis applicable in many real world problems applicable in numerous fields, including economics, finance, insurance, physics, ecology, chemistry, computer science and engineering. This unit will investigate the basic methods of modelling and analyzing of time series data (ie. Data containing serially dependence structure). This can be achieved through learning standard time series procedures on identification of components, autocorrelations, partial autocorrelations and their sampling properties. After setting up these basics, students will learn the theory of stationary univariate time series models including ARMA, ARIMA and SARIMA and their properties. Then the identification, estimation, diagnostic model checking, decision making and forecasting methods based on these models will be developed with applications. The spectral theory of time series, estimation of spectra using periodogram and consistent estimation of spectra using lag-windows will be studied in detail. Further, the methods of analyzing long memory and time series and heteroscedastic time series models including ARCH, GARCH, ACD, SCD and SV models from financial econometrics and the analysis of vector ARIMA models will be developed with applications. By completing this unit, students will develop the essential basis for further studies, such as financial econometrics and financial time series. The skills gain through this unit of study will form a strong foundation to work in a financial industry or in a related research organization.

In our ever-changing world, we are facing a new data-driven era where the capability to efficiently combine and analyse large data collections is essential for informed decision making in business and government, and for scientific research. Statistics and data analytics consulting provide an important framework for many individuals to seek assistant with statistics and data-driven problems. This unit of study will provide students with an opportunity to gain real-life experience in statistical consulting or work with collaborative (interdisciplinary) research. In this unit, you will have an opportunity to have practical experience in a consultation setting with real clients. You will also apply your statistical knowledge in a diverse collection of consulting projects while learning project and time management skills. In this unit you will need to identify and place the client's problem into an analytical framework, provide a solution within a given time frame and communicate your findings back to the client. All such skills are highly valued by employers. This unit will foster the expertise needed to work in a statistical consulting firm or data analytical team which will be essential for data-driven professional and research pathways in the future.