# Basic Mathematics

By
Khalagai, J. M. (Jairus M.)
(2010)

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This module consists of three units which are as follows: Unit 1: (i) Sets and Functions (ii) Composite Functions This unit starts with the concept of a set. It then intoroduces logic which gives the learner techniques for distinguishing between correct and incorrect arguments using propositions and their connectives. A grasp of sets of real numbers on which we define elementary functions is essential. The need to have pictorial representations of a function necessitates the study of its graph. Note that the concept of a function can also be viewed as an instruction to be carried out on a set of objects. This necessitates the study of arrangements of objects in a certain order, called permutations and combinations. Unit 2: Binary Operations In this unit we look at the concept of binary operations. This leads to the study of elementary properties of integers such as congruence. The introduction to algebraic structures is simply what we require to pave the way for unit 3. Unit 3: Groups, Subgroups and Homomorphism This unit is devoted to the study of groups and rings. These are essentially sets of numbers or objects which satisfy some given axioms. The concepts of subgroup and subring are also important to study here. For the sake of looking at cases of fewer axiomatic demands we will also study the concepts of homomorphisms and isomorphisms. Here we will be reflecting on the concept of a mapping or a function from either one group to the other or from one ring to the other in order to find out what properties such a function has.