Discrete Mathematics: An Open Introduction

Livro digital

Título:
Discrete Mathematics: An Open Introduction

Autor:
Oscar Levin

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Almost every discrete mathematics textbook opens with logic as a preliminary. This one deliberately refuses to. Chapter 0 covers just enough ground to talk — mathematical statements, implications, predicates and quantifiers, sets, Venn diagrams — and then the book jumps straight into counting. Logic and proofs only arrive after you have spent weeks on problems actually worth proving something about. Oscar Levin explains the inversion without ceremony: two weeks of proof technique up front overwhelmed his students, and by the time combinatorics began, most of that progress had already evaporated. The four main areas are combinatorics, sequences, logic and proofs, and graph theory, in that order, with induction placed at the end of the sequences chapter rather than treated as its own event. A closing chapter carries the material that did not fit the main sequence — generating functions and a first pass at number theory. The third edition adds a section on trees to the graph theory chapter and rewrites the exposition on functions. Scattered throughout are "Investigate!" activities: open problems placed before the explanation rather than after it, with no solutions provided anywhere. The frustration is intentional, and the author says so. What you get is a text built for an inquiry-based classroom that still works alone at a kitchen table. There are 473 exercises, and the choice of which ones carry hints or full solutions was reworked specifically so instructors could assign homework straight from the book without handing over the answer key. Clicking an exercise number in the PDF jumps to its solution and back. Released under Creative Commons Attribution-ShareAlike, with the source available to anyone who wants to cut it apart and rebuild it.