Mode of Delivery
- Blended mode online and face to face
The importance of linear programming derives in part from its many applications and in part from the existence of good general-purpose techniques for finding optimal solutions. Linear programming is useful for guiding quantitative-related decision making in business, industrial engineering enterprises, and to a lesser extent activities within the social and life sciences. The linear programming skills will help teachers in some aspects of their own personal life management activities and in their professional practice.
This module acts as a smooth and non-intimidating entry into the mathematical worlds of dynamic linear programming, networks, and operations research for the learner who will develop some interest in majoring those fields. Also it:
(a) is important in and of itself as a degree level mathematics course because it introduces to the mathematics student new mathematical content with a distinctive style of mathematical thinking;
(b) beautifully integrates theoretical concepts with their practical applications – both of a mathematical and everyday – life in nature;
(c) is necessary for the prospective teacher of science and mathematics because modern day youth and school students are now pre-disposed to a range of career interests, many of which would be facilitated by a preparation that involves dealing with linear programming and optimisation that are covered in this module.
2. Prerequisite or knowledge
The Prerequisite courses are Basic Mathematics and Linear Algebra, which are offered in this degree program. Knowledge of linear independence, basis, matrix operation, inverses, inequalities, vector spaces, convex sets, and graph plotting is essential. These concepts and skills are generally covered in the pre-requisite course (or equivalents) mentioned above and constitute important background knowledge required to undertake this module. A basic understanding of these and related concepts, and reasonable competence in related manipulative skills (such as matrix and graphical representations and associated algebraic manipulations), are essential background knowledge for this module. Familiarity with these basic concepts and skills, which are assumed in this module, must be secured first before proceeding with the module.
3. General objectives
Upon completion of this module students should:
a) have a general appreciation of the types of problems which are amenable to analysis using linear programming
b) be able to formulate linear programming problems and solve them using geometrical and linear algebraic techniques.
c) be able to use mathematical software packages to solve linear programming problems
d) be able to discuss some theoretical notions of linear algebra and geometry with concrete/practical contexts.
e) have developed some familiarity with the language of operations research
f) have developed a sense of algorithmic thinking
The recommended total time for this module is at least 120 study hours, with Unit 1 taking 40 hours [20 hours for each of the 2 Activities], and Unit 2 taking 80 hours [20 hours for the first Activity, 34 hours for the second Activity, and 20 hours for the third Activity], and the remaining 6 hours to be allocated for the pre-assessment (2hours) and summative (4 hours) evaluation activities.
Students should have access to the core readings specified later. Also, they will need a computer to gain full access to the core readings. Additionally, students should be able to install the computer software wxMaxima and Graph and use them to practice algebraic concepts. These should be regarded as learning materials to facilitate easier accessing and processing of the core concepts and skills that constitute the course. The following are materials necessary to engage with the module meaningfully and, hopefully, complete it successfully: The student’s edition of the module (print form); a computer with effective internet connectivity and Microsoft Office 2003 and above; a scientific or programmable calculator; graph plotting materials; CDs with materials downloaded from sites recommended in the module; CDs with mathematical software such as MathType or WinShell, Graph, wxMaxima, and at least one linear programming software that is free-downloadable, recommended readings from texts identified in the module. [The recommended readings can also be in print form].