Discrete Mathematics

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.

1. Discrete Mathematics: Mathematics of Computer Science, L. Kyrousis, Ch. Bouras and P. Spyrakis, Gutenberg, 1992
2. Discrete Mathematics: Problems and Solutions, C. Voutsadakis, L. Kyrousis, Ch. Bouras and P. Spyrakis, Gutenberg, 1994.
3. Introduction to Combinatorial Mathematics, CL Liu, Mc Graw Hill Ch. Charalambides, Combinatorics (1st issue) Symmetry
4. Elements of Discrete Mathematics, CL Liu, McGraw-Hill, Second Edition.
5. Discrete Mathematics, Seymour Lipschutz Marglipson, McGraw-Hill, Second Edition.
6. Discrete Mathematics A Unified Approach, Stephen A. Wiitala, McGraw-Hill.
7. Discrete Mathematics and Its Applications, Kenneth H. Rosen, McGraw-Hill, Fourth Edition