MAT1103: Foundations of Mathematics

This course is a foundation course that introduces learners to the basic mathematical concepts. It covers the following topics: Set theory; Number systems; The Complex plane; Permutation to logic and Mathematical proofs; and Boolean Algebra.

Course Objectives  
On successful completion of this course unit, the learners should be able to: 

• Define a sets: Work with sets including relations between sets, operations on sets, algebra of sets and other important proof of laws of algebra of sets; Ordered pairs and Cartesian products. 
• Explain the concepts of Real number system, R and extend to Natural Numbers N, integers Z, Rational Numbers Q, Irrational Numbers I, and the Complex Plane C.  
• Define a relation: Give types of relations; work with relations to define a function and types of functions; do further work on functions. 
• Define a Logical Proposition: Work with logical connectivity in Truth tables; Algebra of propositions; Mathematical statements 
• Explain Axioms, Theorems, corollaries, propositions, lemmas and conjectures 
• Investigate various methods of proof including mathematical induction; direct proof: 
• existence, by exhaustion, deduction, construction; Indirect proof: by contradiction, counterexample; Common mistakes in proofs 
• Define circuits in Boolean algebra: Lattices, distributive and Boolean lattices, 
• Boolean functions, logic networks
• Define permutations and combinations and work with them in various problems 

Expected Learning Outcome 
This course unit is meant: 

• To discuss the basic competence in the concepts, principles, and procedures in elementary mathematics application to mathematical symbolism and computation. 
• To encourage orderliness, speed and accuracy in the presentation of mathematical expressions. 
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly. 
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills. 
• To build a strong foundation in mathematical presentation as preparation for subsequent courses in pure mathematics and other sciences.