Mathematician

Highly relevant tasks include:

• formulating mathematical models to simulate processes.
• applying models to experimental observations, and adjusting and recasting the models.
• using numerical analysis methods to develop algorithms and perform computations.

Additional tasks may include:

• developing mathematical theory underlying processes in the physical, biological and social sciences.
• may develop theoretical mathematical constructs and hypotheses.
• applying mathematical principles and techniques to solve problems in research, development, production, distribution and other functional areas.
• liaising with management and clients to determine the subject area to be examined.

An applicant should be undertaking the majority of these tasks as their core duties in an employment role. Although it is not mandatory that they perform all tasks listed, an applicant is required to demonstrate that their daily tasks and skillset matches the nominated occupation.

In Australia, there are currently no legal requirements for licensing or registration for the occupation of Mathematician. 

Mathematicians typically do the following:  

• Expand knowledge in mathematical areas, such as algebra or geometry, by developing new rules, theories, and concepts  
• Use mathematical formulas and models to prove or disprove hypotheses and conjectures  
• Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, or other fields

Applied Mathematicians 

use theories and techniques, such as mathematical modelling, to solve practical problems. These mathematicians typically work with individuals in other occupations to solve these problems. For example, they may work with Chemists and Materials Scientists and Chemical Engineers to analyse the effectiveness of new drugs. Other Applied Mathematicians may work with Industrial Designers to study the aerodynamic characteristics of new automobiles.

Theoretical Mathematicians 

do research to identify unexplained issues in mathematics and resolve them. They are primarily concerned with exploring new areas and relationships of mathematical theories to increase knowledge and understanding about the field. Although some may not consider the practical use of their findings, the knowledge they develop can be an important part of many scientific and engineering achievements. Despite the differences, these areas of mathematics frequently overlap. Many Mathematicians will use both applied and theoretical knowledge in their job duties.

Operations Research Analyst (ANZSCO specialisation) 

An Operations Research Analyst applies scientific method to problems concerning the management of systems of people, machines, materials and money in industry, business government and defence. 

Highly relevant tasks include, but may not be limited to:  

• Identifying and solving real-world problems in areas such as business, logistics, healthcare, or other fields.  
• Collecting and organising information from a variety of sources, such as computer databases, sales histories, and customer feedback.
• Examining information to figure out what is relevant to a problem and what methods might be used to analyse it .
• Using optimisation, data mining, statistical analysis, simulations, predictive modelling, or other methods to analyse information and develop practical solutions to business problems.  
• Advising managers and other decision makers on the impacts of various courses of action to take in order to address a problem.

Computational Scientist (specialisation)

A Computational Scientist seeks to gain understanding of scientific and engineering problems principally through the implementation, use and analysis of mathematical models on high performance computers. 

Highly relevant tasks include, but may not be limited to:  

• Undertaking numerical simulation of complex systems and natural phenomena that would be too expensive or dangerous to study by direct experimentation.  
• Working with specialist Scientists and Engineers to deliver computer-based mathematical models in areas such as climate modelling, oceanography, mining, nuclear engineering and medical imaging.

Mathematical Modeller / Quantitative Analyst (specialisation)

Mathematical Modellers are Applied Mathematicians who construct mathematical representations of real-world situations or hypothetical scenarios in order to predict outcomes and consequences or to create visualisations. Applications can range from manufacturing, environmental modelling through to computer/video games and computer-generated imagery (CGI). 

Highly relevant tasks include, but may not be limited to:  

• Quantifying real world problems and scenarios using appropriate mathematical tools and in consultation with domain specialists.
• Working with software engineers and computational scientists to implement mathematical models as computer algorithms with suitable user interfaces and visualisation tools.
• In scientific and commercial environments, advising researchers, managers and other decision makers of likely outcomes and impacts of various hypothetical scenarios.

Cryptographer (specialisation)

Cryptographers/cryptanalysts use the mathematical theories of cryptology and computer coding to create and decipher digital codes. They are employed by companies, institutions, government agencies, police and the armed forces to maintain security and privacy of sensitive commercial and government transactions and communications. 

Highly relevant tasks include, but may not be limited to: 

• Creating, setting up, and evaluating algorithms designed to solve number theory problems.
• In government and military sectors, protecting sensitive communication and data systems from foreign governments and hackers. 
• Also providing decryption expertise for intelligence and counter-intelligence services.
• In the financial sector, ensuring that credit card, inter-bank, automatic teller machine, and other online transactions are secure. 
• In the communications sector, developing technology to protect mobile phone and internet networks.