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;
Introduction to number theory: divisibility, LCM and HCF; primes;
's proof of infinite number of primes.
Fundamental Theorem of Arithmetic; modular arithmetic; Fermat's theorem;
'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.