# Statistics

##### Errata

item | Errata | Date |
---|---|---|

1. | MATH1021 Calculus Of One Variable: Semester 2 session has been added. |
1/2/2018 |

## STATISTICS

Advanced coursework and projects will be available in 2020 for students who complete this major.

## Statistics major

A major in Statistics requires 48 credit points from this table including:

(i) 12 credit points of 1000-level units according to the following rules:

(a) 6 credit points of calculus and 3 credit points of linear algebra and 3 credit points of statistics; or

(b) 3 credit points of calculus and 3 credit points of linear algebra and 6 credit points of data science

(ii) 12 credit points of 2000-level core units

(iii) 12 credit points of 3000-level core units

(iv) 12 credit points of 3000-level selective units

## Statistics minor

A minor in Statistics requires 36 credit points from this table including:

(i) 12 credit points of 1000-level units according to the following rules:

(a) 6 credit points of calculus and 3 credit points of linear algebra and 3 credit points of statistics; or

(b) 3 credit points of calculus and 3 credit points of linear algebra and 6 credit points of data science

(ii) 12 credit points of 2000-level core units

(iii) 12 credit points of 3000-level selective units

### Units of study

The units of study are listed below.

#### 1000-level units of study

###### Calculus units

**MATH1021 Calculus Of One Variable**

Credit points: 3 Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr tutorial per week Prohibitions: MATH1011 or MATH1901 or MATH1906 or MATH1111 or ENVX1001 or MATH1001 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: exam, quizzes, assignments Mode of delivery: Normal (lecture/lab/tutorial) day

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.

Textbooks

As set out in the Junior Mathematics Handbook.

**MATH1921 Calculus Of One Variable (Advanced)**

Credit points: 3 Session: Semester 1 Classes: 2x1-hr lectures; and 1x1-hr tutorial per week Prohibitions: MATH1001 or MATH1011 or MATH1906 or MATH1111 or ENVX1001 or MATH1901 or MATH1021 or MATH1931 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: exam, quizzes, assignments Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1931 Calculus Of One Variable (SSP)**

Credit points: 3 Session: Semester 1 Classes: 2x1-hr lectures; 1x1-hr seminar; and 1x1-hr tutorial per week Prohibitions: MATH1001 or MATH1011 or MATH1901 or MATH1111 or ENVX1001 or MATH1906 or MATH1021 or MATH1921 Assumed knowledge: Band E4 in HSC Mathematics Extension 2 or equivalent. Assessment: exam, quizzes, assignments, seminar participation Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only.

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.

**MATH1011 Applications of Calculus**

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1001 or MATH1901 or MATH1906 or MATH1111 or BIOM1003 or ENVX1001 or MATH1021 or MATH1921 or MATH1931 Assumed knowledge: HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics. Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1023 Multivariable Calculus and Modelling**

Credit points: 3 Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr tutorial per week Prohibitions: MATH1013 or MATH1903 or MATH1907 or MATH1003 or MATH1923 or MATH1933 Assumed knowledge: HSC Mathematics Extension 1. Students who have not completed HSC Extension 1 Mathematics (or equivalent) are strongly advised to take the Extension 1 Mathematics Bridging Course (offered in February). Assessment: exam, quizzes, assignments Mode of delivery: Normal (lecture/lab/tutorial) day

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1923 Multivariable Calculus and Modelling (Adv)**

Credit points: 3 Session: Semester 2 Classes: 2x1-hr lectures; and 1x1-hr tutorial per week Prohibitions: MATH1003 or MATH1013 or MATH1907 or MATH1903 or MATH1023 or MATH1933 Assumed knowledge: (HSC Mathematics Extension 2) OR (Band E4 in HSC Mathematics Extension 1) or equivalent. Assessment: exam, quizzes, assignments Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1933 Multivariable Calculus and Modelling (SSP)**

Credit points: 3 Session: Semester 2 Classes: 2x1-hr lectures; 1x1-hr seminar; and 1x1-hr tutorial per week Prohibitions: MATH1003 or MATH1903 or MATH1013 or MATH1907 or MATH1023 or MATH1923 Assumed knowledge: Band E4 in HSC Mathematics Extension 2 or equivalent. Assessment: exam, quizzes, assignments, seminar participation Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

Note: Enrolment is by invitation only.

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.

###### Statistics units

**MATH1005 Statistical Thinking with Data**

Credit points: 3 Session: Semester 2,Summer Main,Winter Main Classes: Lectures 2 hrs/week; Practical 1 hr/week Prohibitions: MATH1015 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 Assumed knowledge: HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

In a data-rich world, global citizens need to problem solve with data, and evidence based decision-making is essential is 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 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.

Textbooks

Freedman, Pisani and Purves, Statistics, Norton, 2007

**MATH1905 Statistical Thinking with Data (Advanced)**

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1005 or MATH1015 or STAT1021 or STAT1022 or ECMT1010 or ENVX1001 or ENVX1002 or BUSS1020 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1015 Biostatistics**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1005 or MATH1905 or STAT1021 or STAT1022 or ECMT1010 or BIOM1003 or ENVX1001 or ENVX1002 or BUSS1020 Assumed knowledge: HSC Mathematics. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

MATH1015 is designed to provide a thorough preparation in statistics for students in the Biological and Medical Sciences. It offers a comprehensive introduction to data analysis, probability and sampling, inference including t-tests, confidence intervals and chi-squared goodness of fit tests.

Textbooks

As set out in the Junior Mathematics Handbook

###### Linear algebra units

**MATH1002 Linear Algebra**

Credit points: 3 Session: Semester 1,Summer Main Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1012 or MATH1014 or MATH1902 Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 of study introduces vectors and vector algebra, linear algebra including solutions of linear systems, matrices, determinants, eigenvalues and eigenvectors.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1902 Linear Algebra (Advanced)**

Credit points: 3 Session: Semester 1 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1002 or MATH1012 or MATH1014 Assumed knowledge: (HSC Mathematics Extension 2) OR (90 or above in HSC Mathematics Extension 1) or equivalent Assessment: One 1.5 hour examination, assignments and quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

Note: Department permission required for enrolment

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.

Textbooks

As set out in the Junior Mathematics Handbook

**MATH1014 Introduction to Linear Algebra**

Credit points: 3 Session: Semester 2 Classes: Two 1 hour lectures and one 1 hour tutorial per week. Prohibitions: MATH1012 or MATH1002 or MATH1902 Assumed knowledge: HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Please note: this unit does not normally lead to a major in Mathematics or Statistics or Financial Mathematics and Statistics. Assessment: One 1.5 hour exam, assignments, quizzes (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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.

Textbooks

As set out in the Junior Mathematics Handbook.

###### Data science units

**DATA1001 Foundations of Data Science**

Credit points: 6 Teacher/Coordinator: Dr Di Warren Session: Semester 1,Semester 2 Classes: lecture 3 hrs/week; computer tutorial 2 hr/week Prohibitions: MATH1005 or MATH1905 or MATH1015 or MATH1115 or ENVX1001 or ENVX1002 or ECMT1010 or BUSS1020 or STAT1021 Assessment: assignments, quizzes, presentation, exam Mode of delivery: Normal (lecture/lab/tutorial) day

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.

Textbooks

Statistics, Fourth Edition, Freedman Pisani Purves

#### 2000-level units of study

###### Core

**DATA2002 Data Analytics: Learning from Data**

Credit points: 6 Teacher/Coordinator: Jean Yang Session: Semester 2 Classes: lecture 3 hrs/week; computer tutorial 2 hr/week Prerequisites: [DATA1001 or ENVX1001 or ENVX1002] or [MATH10X5 and MATH1115] or [MATH10X5 and STAT2011] or [MATH1905 and MATH1XXX (except MATH1XX5)] or [BUSS1020 or ECMT1010 or STAT1021] Prohibitions: STAT2012 or STAT2912 Assumed knowledge: (Basic Linear Algebra and some coding) or QBUS1040 Assessment: written assignment, presentation, exams Mode of delivery: Normal (lecture/lab/tutorial) day

Technological advances in science, business, engineering has 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 course in statistics and data sciences, focusing on learning data analytic skills for a wide range of problems and data. How should the Australian government measure and report employment and unemployment? Can we tell the difference between decaffeinated and regular coffee ? In this course, 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 their programming skills through experience with statistical programming language. You will also be exposed to the concept of statistical machine learning and develop the skill to analyze 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.

**STAT2912 Statistical Tests (Advanced)**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 Prohibitions: STAT2012 or STAT2004 or DATA2002 Assumed knowledge: STAT2911 Assessment: One 2-hour exam, assignments and/or quizzes, computer practical reports and one computer practical exam (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2012 with an emphasis on both methods and the mathematical derivation of these methods: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric methods, non-parametric smoothing, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

**STAT2011 Probability and Estimation Theory**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory week. Prerequisites: (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and (MATH1XX5 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2901 or STAT2001 or STAT2911 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random models like the binomial, Poisson and geometric, continuous models including the normal and exponential will be studied along with elementary regression models. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2911 Probability and Statistical Models (Adv)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: [MATH19X3 or MATH1907 or (a mark of 65 in MATH1023 or MATH1003)] and [MATH1905 or MATH1904 or (a mark of 65 in MATH1005 or ECMT1010 or BUSS1020)] Prohibitions: STAT2001 or STAT2901 or STAT2011 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

#### 3000-level units of study

###### Major core

STAT3X22 and STAT3X23 to be developed for offering in 2019.

###### Major selective

STAT3021 and STAT3024 to be developed for offering in 2019.

###### Minor selective

STAT3021, STAT3X22, STAT3X23 and STAT3024 to be developed for offering in 2019.