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Unit of study_

MATH4076: Computational Mathematics

Sophisticated mathematics and numerical programming underlie many computer applications, including weather forecasting, computer security, video games, and computer aided design. This unit of study provides a strong foundational introduction to modern interactive programming, computational algorithms, and numerical analysis. Topics covered include: (I) basics ingredients of programming languages such as syntax, data structures, control structures, memory management and visualisation; (II) basic algorithmic concepts including binary and decimal representations, iteration, linear operations, sources of error, divide-and-concur, algorithmic complexity; and (III) basic numerical schemes for rootfinding, integration/differentiation, differential equations, fast Fourier transforms, Monte Carlo methods, data fitting, discrete and continuous optimisation. You will also learn about the philosophical underpinning of computational mathematics including the emergence of complex behaviour from simple rules, undecidability, modelling the physical world, and the joys of experimental mathematics. When you complete this unit you will have a clear and comprehensive understanding of the building blocks of modern computational methods and the ability to start combining them together in different ways. Mathematics and computing are like cooking. Fundamentally, all you have is sugar, fat, salt, heat, stirring, chopping. But becoming a good chef requires knowing just how to put things together in creative ways that work. In a previous study, you should have learned to cook. Now you're going to learn how to make something someone else might want to pay for more than one time.

Code MATH4076
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
[A mark of 65 or above in (12cp of MATH2XXX) or (6cp of MATH2XXX and 6cp of STAT2XXX or DATA2X02)] or (12cp of MATH3XXX)
MATH3076 or MATH3976
Assumed knowledge:
(MATH2X21 and MATH2X22) or (MATH2X61 and MATH2X65)

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

  • LO1. apply the basic ingredients of any programming language including syntax, definition of variables, control structures and memory management
  • LO2. investigate and resolve sources of error in numerical computation
  • LO3. explain how binary and floating-point decimal numbers are represented on a computer
  • LO4. critique the uses and dangers of iteration and recursion
  • LO5. leverage and compute linear operations on data
  • LO6. create numerical routines using fundamental numerical methods to solve computational problems in science, engineering and mathematics
  • LO7. create reports that combine a description of a practical problem, its numerical framing and the results of computation to solve this problem.