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.
| Code | Hours | Type | eClass | Semester |
|---|---|---|---|---|
| ΜΘ120 | 4 | Compulsory | e-Class | 2 |
Bibliography:
- “Discrete Mathematics: Mathematics of Computer Science, L. Kyrousis, Ch. Bouras and P. Spyrakis, Gutenberg, 1992”
- “Discrete Mathematics: Problems and Solutions, C. Voutsadakis, L. Kyrousis, Ch. Bouras and P. Spyrakis, Gutenberg, 1994.”
- “Introduction to Combinatorial Mathematics, CL Liu, Mc Graw Hill Ch. Charalambides, Combinatorics (1st issue) Symmetry”
- “Elements of Discrete Mathematics, CL Liu, McGraw-Hill, Second Edition.”
- “Discrete Mathematics, Seymour Lipschutz Marglipson, McGraw-Hill, Second Edition”
- “Discrete Mathematics A Unified Approach, Stephen A. Wiitala, McGraw-Hill.”
- “Discrete Mathematics and Its Applications, Kenneth H. Rosen, McGraw-Hill, Fourth Edition”