This course teaches the learner the basics of computer related mathematics. The course is a prerequisite for learners that intend to enter the IT industry in a technical capacity. The following topics are covered:
- Set Theory
In this section a brief overview of set theory is given in order to (i) define the notation which will be used in subsequent sections of this and related course notes; (ii) examine the basic set operations and (iii) introduce the fundamental number sets.
- Number Systems
This topic is designed to refresh the learner’s understanding of the basic arithmetical operations and to elaborate on number systems as they relate to the implementation of certain data types in any computer architecture. Included are the representation and conversions of binary, octal and hexadecimal numbers and the encoding of IEEE floating point numbers.
- Boolean Algebra
In this section an overview is given of the basics of Boolean Algebra and the relationship to (i) programming concepts and (ii) digital circuits.
- Graph Theory
This topic gives a brief introduction to graph theory. It illustrates the application of graphs in the implementation of tree structures, directed graphs and the relationship to finite state machines and regular grammars.
- Basic Statistics
In this topic basic statistical methods and distributions are covered
- Data Structures
A description and the use of the major abstract data structures that are used to implement both hardware and software related systems.
The course is practical in nature in that a series of online tutorials guide the learner through the practical application of the theoretical aspects taught in the course.
At the completion of the course the learner will be able to:
- Recognize computer numbers and determine their context. In addition the learner will be able to convert number from one radix to another and perform basic arithmetic operations using numbers encoded in different radices.
- Construct truth tables to determine prepositions. Perform various Boolean calculations.
- Analyse statistical distributions and calculate the mean and standard deviation of such distributions. Calculate a simple arithmetic regression line and forecast future trends.
- Analyse the paths in a graph and construct finite state machines (FSM’s) and associated matrices to solve certain classes of problems. The learner will also be able to describe regular sets and their relationship to FSM’s.
- Select a given abstract data structure to implement a solution to storing data in a manner as dictated by the problem class.
The computer platform used is Linux. The academy uses the SuSE distribution.
The following material is supplied:
- A full set of notes covering the course outline.
- A CD with solutions to all the assignments plus all the examples covered in the notes.
- Grade 12 with mathematics.