Program Overview

Overview

This unit provides an introduction to multivariable differential calculus and modelling as well as mathematical statistics. 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. The statistics part provides an introduction to mathematical statistics including descriptive statistics, the normal model and hypothesis testing. Concepts will be illustrated using statistical software.

Unit Details and Rules

• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 6
• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1905 or MATH1903 or MATH1923 or MATH1907 or MATH1933 or MATH1062 or MATH1972 or MATH1003 or MATH1023 or MATH1005 or MATH1015
• Assumed knowledge: (HSC Mathematics Extension 2) or equivalent
• Available to study abroad and exchange students: Yes

Teaching Staff

• Coordinator: Milena Radnovic
• Lecturer(s): Milena Radnovic, Wei Zhang

Assessment

The census date for this unit availability is 1 September 2025

• Type: Written exam
  • Description: Final exam Multiple choice and written calculations or mathematical arguments
  • Weight: 60%
  • Due: Formal exam period
  • Length: 2 hours
  • Use of AI: AI prohibited
• Type: Out-of-class quiz
  • Description: Weekly online quizzes 3-10
  • Weight: 8%
  • Due: Multiple weeks
  • Length: 2 hours per week
  • Use of AI: AI allowed
• Type: Out-of-class quiz
  • Description: Weekly online quizzes 1-2 #earlyfeedbacktask
  • Weight: 2%
  • Due: Week 03
  • Length: 2 hours per quiz
  • Use of AI: AI allowed
• Type: Written work
  • Description: Assignment 1
  • Weight: 5%
  • Due: Week 04
  • Length: 3-4 pages
  • Use of AI: AI allowed
• Type: In-person written or creative task
  • Description: Quiz
  • Weight: 13%
  • Due: Week 07
  • Length: 40 minutes
  • Use of AI: AI prohibited
• Type: Written work
  • Description: Assignment 2
  • Weight: 10%
  • Due: Week 10
  • Length: 6-8 pages
  • Use of AI: AI allowed
• Type: Contribution
  • Description: Tutorials
  • Weight: 2%
  • Due: Weekly
  • Length: 2x50 minutes per week
  • Use of AI: AI allowed

Learning Support

• Simple extensions: If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.
• Special consideration: If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Weekly Schedule

Learning Outcomes

At the completion of this unit, you should be able to:

• LO1. apply mathematical logic and statistical thinking to solve problems
• LO2. express mathematical and statistical ideas and arguments coherently in written and oral form
• LO3. identify and analyse appropriate methods to describe, summarise and visualise a given data set
• LO4. identify and apply appropriate methods of inference for a variety of data types
• LO5. apply statistical software such as R to analyse example sets of data
• LO6. express surfaces and curves in two or three dimensions in implicit or explicit form
• LO7. calculate partial derivatives of functions of several variables and use these to find directional derivatives and gradient vectors and to interpret the physical and geometric significance of these quantities
• LO8. set up differential equations models and use a variety of techniques to solve these differential equations and interpret their solutions in terms of the original problem
• LO9. apply concepts of mathematical statistics and calculus to a variety of contexts and applications

Graduate Qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course.

• GQ1: Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
• GQ2: Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
• GQ3: Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
• GQ4: Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
• GQ5: Inventiveness Generating novel ideas and solutions.
• GQ6: Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures.
• GQ7: Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
• GQ8: Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
• GQ9: Influence Engaging others in a process, idea or vision.

Additional Information

• Lectures: Lectures are face-to-face and streamed live with online access from Canvas.
• Tutorials: Tutorials are small classes in which you are expected to work through questions from the tutorial sheet in small groups on the white board.
• Tutorial and exercise sheets: The question sheets for a given week will be available on the MATH1962 Canvas page.
• Ed Discussion forum:
• Science student portal
• Mathematics and Statistics student portal
• Work, health and safety:
• Disclaimer: The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.