Logic axiomatic systems and the need for proof; implication and negation.

Concept of proof; proof by contradiction, contraposition and induction.

Revision of integers, rational and real numbers.

Sets: definition of a set; order; subsets; union and intersection;

injections, surjections and bijections between finite sets;

cartesian products.

Introduction to number theory: divisibility, LCM and HCF; primes;

Euclid
's proof of infinite number of primes.

Fundamental Theorem of Arithmetic; modular arithmetic; Fermat's theorem;

Wilson
's theorem; solution of x^2+y^2=z^2 in integers. Continued fractions.

Some basic notions of elementary Euclidean geometry (time permitting):

Pythagoras’ theorem, Cauchy-Schwarz inequality, triangle inequality.

Introduction to plane geometry.