What are good textbooks to cover these topics?
Sets: sets and their elements, finite and infinite sets,operations on sets (unions, intersections and complements),relations between sets(inclusion, equivalence), non equivalentinfinite sets, cardinal numbers.
Binary Operations: basic definitions, associativitycommutativity, neutral elements, inverse elements, groups.
Functions: introduction, Cartesian products, functions assubsets of Cartesian products, graphs, composition of functions,injective, bijective and surjective functions, invertiblefunctions, arithmetic operations on real functions, groups offunctions.
Plane isometries: definition, reflections, translations androtations, compositions of reflections, congruent triangles andisometry, classification of the plane isometries, the group ofplane isometries, applications in Euclidean geometry.
Axiom systems: undefined terms, axioms and theorems of axiomaticmathematical theories, models, consistency, independence,completeness and categoricity of axiom systems, finite affinegeometries.
Euclidean geometry: historical notes, a modern representation ofEuclidean plane geometry as an axiomatic theory. The naturalnumbers: an introduction to peano's axioms,arithmetic operations,order relations, first steps in number theory, mathematicalinduction.
