Recursive problems: Hanoi Tower, plane partition, Flavious Josephus problem. Fundamental combinatorial analysis: basic principles, combinatorics formations. Calculus of Finite sums: properties, multiple sums. Discrete calculus: association of calculus and discrete calculus, negative factorial power, differential tables – sums. Binomial coefficients – special numbers: binomial coefficients, sums of multiplications, Stirling numbers, harmonic numbers, Fibonacci, Catalan numbers. Basic principles of number theory: Euclidean division, divisibility, greatest common divisor, linear Diophantine equation, least common multiple, prime numbers, sum of divisors. Integer functions – generating functions: integer part of real numbers, Euler function, Legendre function. Generating functions: exponential generating function, Catalan Numbers generating function, Fibonacci numbers generating function, Stirling Numbers generating function, calculus with generating functions.
