Course: MAT 111 2.0 Fundamentals of Logic and Set Theory (Compulsory)
Course content:
Logic: Propositional logic, Logical operators, Analyze compound Propositions, Tautologies and Contradictions, Logically equivalent, The Algebra of Propositions, Predicate logic and quantifiers, Predicate, Quantifiers, The Universal quantifier, The existential quantifier “, Quantifiers and ‘not’, Introduction to proofs, Argument, Proofs in mathematics, Direct proofs, Proof by Contradiction, Indirect proofs, Proof by case, Principle of Mathematical Induction; The real number system : Axioms of Real Numbers, The order axioms and axiom of bounds, Supremum and Infimum of subsets of , Concept of infinity and Intervals of ; Sets and Relations: Introduction to Sets, Subset, Equality of sets, singleton set, the empty set, Universal set , Set Operations, Set Identities, Venn Diagrams, Products of sets, Relations, Representations of a relation, Graph of a relation ,Composition of two relations, Types of relations; Functions: Definition and graph of function, Basic functions and their graphs, Graph of functions by transform, Algebraic operations on functions, Properties of functions (Odd functions, Even functions and Monotonic functions), Inverse functions and their graphs; Limits and Continuity: One sided limits, limit of a function, The precise definition of a limit, Continuous and Discontinuous functions
Recommended Readings: