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Learning activities
Learning outcomes
Formulate and use recursive definitions in various contexts and applications.
Write MATLAB programs to solve various mathematical and applied problems.
Perform base conversions and explain aspects of computer arithmetic.
Use counting techniques and understand the basics of discrete probability.
Use matrix algebra and derive linear transformations of the plane.
Apply propositional logic to analyse the validity of arguments, express statements in predicate logic and use proof by mathematical induction.
Solve basic problems in Boolean algebra and represent a Boolean function as a logic network.
Appreciate the important role that computing has in mathematics and the essential importance of discrete mathematics for the foundations of computer science.
Present coherent written solutions to various problems related to the material in the Unit.
Assessments
Additional information
This unit covers a variety of mathematical topics that are particularly important for computing and computer science. The prominent mathematical computing package MATLAB is used throughout the unit to perform basic procedures and to illustrate different concepts in discrete mathematics. MATLAB provides a convenient and powerful programming environment for solving a wide variety of mathematical problems. The unit starts with recursively defined sequences and their applications (a fundamental concept for computing) with MATLAB programs being developed to generate such sequences. Other MATLAB features are then explored, including plotting in two and three dimensions, the graphical and iterative solution of equations and finding minima and maxima of functions. Next follows a discussion of base conversion, computer arithmetic and the effect of roundoff error in computations. We will also take an introductory look at counting and discrete probability theory. This will include some basic set theory that is fundamental to many areas of mathematics. Another major topic is matrix theory and its implementation in MATLAB. It is applied to linear transformations of the plane, the central mathematical tool in computer graphics, including the generation of interesting images. The final third of the unit deals with logic and Boolean algebra. These topics are closely related and have a special significance in computer science. In particular, the design of logic networks is fundamental to the construction of modern digital computers. Logic is also important for its own sake in order to gain a clear understanding of the reasoning process itself and to provide a basis for proving things in mathematics and computer science. Included here is the important method of proof called mathematical induction.