Introduction to Set Theory. Sets, naïve definition, description, subsets, power set. Algebra of sets.  Infinite unions and intersections, examples (examples of subsets of the real line). Cartesian product. Binary relations, functions, composition of functions, one-to-one functions, reversible functions, line and inverse image of subset, lines and inverse images of unions and intersections. Equivalence relations, Equivalence classes, set-quotient, partitions, order relations. Countability, countability of NxN, uncountability of real numbers, algebraic and transcendent numbers.
Introduction to Number Theory.The set of natural numbers. Standard and strong induction, well-ordering principle. The Euclidean division, the greatest common divisor, the least common multiple, prime numbers, the fundamental theorem of arithmetic, equivalence relation mod n, equivalence classes and their algebra.
Introduction to the field of Complex Numbers. Complex plane, algebra and modulus of complex numbers, polar form and roots of unity.
Polynomials: Division, factorization, roots of polynomials.

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