Applied Combinatorics

Livro digital

Título:
Applied Combinatorics

Autor:
Mitchel T. Keller, William T. Trotter

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Combinatorics is where simple questions about arrangements, choices, and connections become powerful methods for solving hard problems. Mitchel T. Keller and William T. Trotter build that toolkit from strings, sets, binomial coefficients, and induction, then expand it through graph theory, partially ordered sets, inclusion-exclusion, generating functions, and recurrence equations. The second half turns those foundations into deeper applications. Probability is brought into combinatorial reasoning; graph algorithms lead naturally to network flows and their uses; Pólya’s enumeration theorem handles symmetry; and a final survey reveals the many forms the subject can take. Exercises, background material, notation, and integrated SageMath cells support both careful study and computational experimentation. The text rewards readers who want more than a catalogue of formulas. Its examples show how to recognize structure, translate a problem into the right discrete model, and select a proof or counting technique that exposes the answer. Suitable for students of mathematics and theoretical computer science, it develops the habits behind algorithmic reasoning while keeping advanced ideas connected to concrete questions about graphs, schedules, distributions, probability, and networks.