Elements of logic:
Mathematical statements, Logical connectives, Conditional and bi-conditional statements. Truth tables and tautologies, Quantifiers, Logical implication and equivalence, Deductive reasoning. Methods of proof (direct, indirect and Method of Induction.)
Set Theory:
Sets and subsets, Set
operations, Cartesian product of two sets, De Morgan’s laws.
Relations and functions:
Relation and Functions, Order
relation, Equivalence relations. Functions. Images and inverse images of sets
Injective, surjective and bijective functions. Inverse functions.
The Real Number System:
Field and order properties,
Natural numbers, integers and rational numbers, Absolute value and their
properties. Basic inequalities.(Including inequalities of means, powers;
inequalities of Cauchy, Chebyshev, Weierstrass).
The Complex Number System:
Field of Complex numbers, De
Moivre’s theorem and its applications.
Theory of equations:
Number of roots of polynomial
equation.Relations between roots and coefficients, Symmetric functions of
roots, Sum of the powers of roots, Synthetic division, Des Cartes rule of
signs, Multiplicity of roots, Transformation of equations.
Elementary number theory:
Divisibility, Fundamental
theorem of arithmetic, Congruences (basic properties only)
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