MATHEMATICS

Mathematics is one of the most enduring fields of study, and is essential in an expanding number of disciplines and professions. Many mathematicians continue to develop new mathematics for its own sake. Today, however, mathematicians also combine their knowledge of mathematics and statistics with modelling and computational skills and use the latest computer technology to solve problems in the physical and biological sciences, engineering, information technology, economics, and business.

This major is administered by the School of Mathematics and Physics.
 
For further information please contact the Science Faculty.

What will I study?

UQ offers a wide range of courses in mathematics and its applications. In their first year, students study essential topics in calculus, linear algebra and differential equations. In later years students select from more specialised courses. These emphasise new ideas in mathematics, and include recent applications in coding and cryptology, mathematical physics, mathematical biology, bioinformatics, and finance.

Pure Mathematics (Algebra & Discrete Mathematics)

Algebra studies abstract mathematical structures beginning with vector spaces, groups, and rings. It leads on to the study of number theory and to applications in mathematical physics, coding, and cryptology. Discrete mathematics studies the ways objects can be rearranged and linked together, and includes combinatorics and graph theory. These subjects are basic to many of the large problems arising in information technology and bioinformatics. The department has a particularly strong research program in combinatorics, covering a wide variety of subdisciplines including algebraic combinatorics, bioinformatics, combinatorial group theory, design theory, and graph theory.

Pure Mathematics (Analysis)

Mathematical analysis is the area of mathematics that most appeals to people who like calculus. It provides a rigorous foundation for differentiation and integration, and its ideas are basic in the understanding of many fields of contemporary mathematics, including differential equations, probability theory, stochastic processes, and control theory. Current research in this area includes nonlinear differential equations arising from physical and biological models, dynamical systems, control theory and economics, stochastic processes, and applications to financial mathematics and biology.  

Applied Mathematics

Applied mathematicians use mathematics to understand the world around us. The applied mathematics courses develop the mathematical methods that have proved particularly useful, and apply these methods to physical and biological systems. The department has significant research strengths in material science and mathematical ecology.

Financial Mathematics

Today, advanced mathematical models are used routinely in finance. Mathematics is used to monitor and direct the investments of superannuation funds and investment managers. Partial differential equations are used to price options. The new Basel 2 accord on international bank regulation requires sophisticated modeling of a bank’s overall risk. The core courses in financial mathematics provide a background in finance and an introduction to the basic techniques of stochastic processes, statistics, and computational methods. These can be combined with further courses in finance, statistics, or computational mathematics. The mathematics department hosts an interdisciplinary group of statisticians, mathematical analysts, and computational mathematicians interested in financial mathematics and its application in the energy markets. 

Mathematical Physics

Many breakthroughs in the development of physical theories, particularly in the realm of quantum physics, have been underpinned by the application of novel mathematical techniques. Research in mathematical physics at UQ covers a broad spectrum from areas of pure mathematics (Lie and quantum algebras, supersymmetry, low dimensional topology) through to applications in areas such as Bose-Einstein condensates, superconductivity, and condensed matter systems.

 

Study Plans

Mathematics is available as a Single Major or an Extended Major. For the Single Major you are required to complete #14 (#6 at Level 2 and #8 at Level 3) and for the Extended Major you are required to complete #22 (#10 at Level 2 and #12 at Level 3) from the Mathematics course list. The following are suggested study plans for this major and should be used as a guide to planning your program.

Please refer to the course list below to ensure you complete the major requirements.

How do I use the Study Plans?

  1. Choose a study plan.
  2. Take all Compulsory Courses in each semester.
  3. Select required number of units in Key Coursesfor each year level. 
  4. Ensure you take at least #12 of level 3 (or 4) courses from the BSc list.
  5. Fill any gaps in each semester with Keyor Recommended Courses or electives from BSc or other programs.
    (Standard full-time semester load #8.)
  6. Ensure you meet the BSc requirements and rules.

What do the different columns mean?

  • Compulsory courses – compulsory for the major.
  • Key courses – electives from the major's course list.
  • Recommended courses – complement the major. 

Mathematics (Single Major) - Pure (Algebra and Discrete Mathematics)

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
Sem 1
 MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
MATH2301 Linear & Abstract Algebra
 
Sem 2  –
MATH2302 Discrete Mathematics II
MATH2100 Applied Mathematical Analysis
STAT2004 Statistical Model. & Analysis
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1  MATH3401 Complex Analysis
MATH3302 Coding & Cryptography
MATH3303 Abstr Algebra & Number Th
MATH3202 Operations Research
MATH3402 Functional Analysis
STAT3003 Experimental Design
Sem 2
 
MATH3306 Set Theory & Logic (Not offered 2011)
MATH3301 Graph Theory & Geometry
MATH3404 Optimisation Theory

 

Mathematics (Single Major) - Pure (Analysis)

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1 MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
 
 
MATH2301 Linear & Abstract Algebra
STAT2003 Probability & Statistics
Sem 2  –
MATH2100 Applied Mathematical Analysis
COSC2500 Num Meth in Computational Sci
MATH2302 Discrete Mathematics II
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1
 MATH3401 Complex Analysis
 
MATH3402 Functional Analysis
MATH3101 Bifurcation and Chaos
MATH3303 Abstr Algebra & Number Th
Sem 2   MATH3403 Partial Differential Equations
MATH3404 Optimisation Theory
MATH3102 Applied Mathematics
STAT3004 Prob Models & Stochastic Proc

 

Mathematics (Single Major) - Applied Mathematics

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
#6 for:
Recommended Courses
 
Sem 1  
MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
 
 
BIOL2010 Ecology
SCIE2100 Intro to Bioinfomatics
STAT2003 Probability & Statistics
Sem 2
–  
COSC2500 Num Meth in Computational Sci
MATH2100 Applied Mathematical Analysis
PHYS2100 Dynamics, Chaos & Special Rela
STAT2004 Statistical Model. & Analysis
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1  
MATH3401 Complex Analysis
MATH3101 Bifurcation and Chaos
MATH3104 Mathematical Biology
MATH3090 Financial Mathematics
MATH3202 Operations Research
 
Sem 2
 
MATH3102 Applied Mathematics
BIOL3014 Advanced Bioinformatics
MATH3403 Partial Differential Equations
STAT3004 Prob Models & Stochastic Proc

 

Mathematics (Single Major) - Mathematical Physics

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1  MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
 
MATH2301 Linear & Abstract Algebra
 
Sem 2  –
MATH2100 Applied Mathematical Analysis
PHYS2100 Dynamics, Chaos & Special Rela
COSC2500 Num Meth in Computational Sci
PHYS2041 Quantum Physics
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1  
MATH3401 Complex Analysis
MATH3101 Bifurcation and Chaos
 
PHYS3040 Quantum Physics
Sem 2
 
MATH3102 Applied Mathematics
MATH3403 Partial Differential Equations

 

Mathematics (Single Major) - Financial Mathematics

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1 MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
 
STAT2003 Probability & Statistics
 
Sem 2  –
STAT2004 Statistical Model. & Analysis
COSC2500 Num Meth in Computational Science
MATH2100 Applied Mathematical Analysis
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #6 from:
Recommended Courses
 
Sem 1  
MATH3401 Complex Analysis
MATH3090 Financial Mathematics
MATH3202 Operations Research
MATH4091 Financial Calculus
FINM3402 Investments & Portfolio Manag1
Sem 2
 
STAT3004 Prob Models & Stochastic Processes
MATH4090 Financial Math Computation
MATH3404 Optimisation Theory

1. These courses are not listed in Part B of the BSc list. It cannot count towards the #12 of Late Year courses required for Part B.

Mathematics (Extended Major)

You can find details about the first year of the program here.

Year 2 Compulsory Courses
Complete all courses
Key Courses
Choose at least #4 from:
Key Courses
Choose at least #2 from:
Sem 1
MATH2001 Advanced Calculus and Linear Algebra
MATH2400 Mathematical Analysis
MATH2301 Linear & Abstract Algebra
STAT2003 Probability & Statistics
MATH2301 Linear & Abstract Algebra
STAT2003 Probability & Statistics
SCIE2100 Intro to Bioinfomatics
Sem 2
MATH2100 Applied Mathematical Analysis
MATH2302 Discrete Mathematics II
COSC2500 Num Meth in Computational Science
STAT2004 Statistical Model. & Analysis
MATH2070 Natural Resource Mathematics
MATH2100 Applied Mathematical Analysis
MATH2302 Discrete Mathematics II
PHYS2100 Dynamics, Chaos & Special Rela
 
Year 3 Compulsory Courses
Complete all courses
Key Courses
Choose at least #10 from:
Recommended Courses
 
Sem 1 MATH3401 Complex Analysis
MATH3090 Financial Mathematics
MATH3104 Mathematical Biology
MATH3302 Coding & Cryptography
MATH3303 Abstr Algebra & Number Theory
MATH3101 Bifurcation and Chaos
MATH3201 Scientific Computing: Advanced techniques and applications
MATH3202 Operations Research
MATH3402 Functional Analysis

 
 
Sem 2
 
MATH3102 Applied Mathematics
MATH3103 Algebraic Methods of Mathematical Physics
MATH3306 Set Theory & Logic (Not offered 2011)
MATH3301 Graph Theory & Geometry
MATH3403 Partial Differential Equations
MATH3404 Optimisation Theory
MATH3405 Differential Geometry
STAT3004 Prob Models & Stochastic Processes
 

Major Convenor

Dr Tony Roberts

What I do

I apply mathematical methods to predict or optimize the properties of complex materials using models  of their microstructure.  I have studied numerous materials  including foams, ceramics and gas-barrier films, which involve the development of suitable statistical structural models.  Recently I have used mathematical techniques to design optimal bone implants, and predict the diffusive and electrical properties of fractal networks. The two areas of mathematics that I use most frequently are partial differential equations and probability theory.

 What I teach

I teach a number of courses which develop mathematical and computational techniques to solve physical, engineering and biological problems. This includes second year courses on calculus and linear algebra as well as specialized advanced courses on partial differential equations and asymptotic analysis.  Partial differential equations are the one of the most important concepts in applied mathematics, describing, for example, heat and mass transfer, motions of electrons, deformation of solids, flow in liquids, and prices of options on the stock-market.
 

 

Careers

Mathematics graduates are respected for their excellent quantitative skills and problem solving abilities. They win a wide range of rewarding positions in the public and private sectors. The latest figures from the Graduate Careers Australia (www.graduatecareers.com.au) show 87 per cent of young (<25) mathematics graduates had found jobs by the April following their graduation or were undertaking further study. These figures compare well with those for the related professional degrees of engineering (91 per cent), accounting (86 per cent), and computer science (78 per cent). People who are enthusiastic about doing mathematics can confidently look forward to a rewarding career.

Students with a strong interest and ability in mathematics should consider doing an honours degree. This is an extra year of advanced courses and work on an individual research project. This gives students experience in reading the mathematics research literature and applying recent results and methods to solve problems. An honours degree is the usual path for students who wish to continue doing research and go on to a do a PhD

Mathematics graduates use their quantitative problem solving skills to successfully compete with graduates in other disciplines for a range of jobs in the private and public sector.  The areas of mathematics that are most often used in industry in Australia are operations research, statistics, and financial mathematics. Mathematicians are also employed in research organisations such as the CSIRO, DSTO and the Bureau of Meteorology, universities and in industry.

Mathematicians at The University of Queensland have established a careers web site for the Australian Mathematical society (www.austms.org.au/Careers). This now gives listings of current job advertisements for mathematics graduates throughout Australia, and gives examples of the diverse career paths of many past mathematics graduates.