A Gentle Introduction to the Art of Mathematics

Livro digital

Título:
A Gentle Introduction to the Art of Mathematics

Autor:
Joseph E. Fields

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
If mathematical notation feels like a language everyone else learned in secret, this book begins by making that language readable: basic sets, number systems, logical connectives, quantifiers, and even algorithms and flowcharts become the starting point for learning how mathematicians think. Joseph E. Fields builds the path from familiar objects toward precise definitions and valid arguments, with a direct style that treats proof as a skill to be practiced rather than a ritual to be memorized. The progression moves through implication, logical equivalence, two-column proofs, contradiction, contraposition, counterexamples, cases, and existential statements before returning to sets, relations, and functions with greater depth. From there, induction, combinatorial arguments, the pigeonhole principle, cardinality, Cantor's theorem, and ordering relations broaden the reader's toolkit. Exercises, diagrams, puzzles, and examples such as graph pebbling and the bridges of Konigsberg keep abstract ideas tied to concrete reasoning. What distinguishes this introduction is its willingness to show the craft behind formal mathematics, including the false starts, conventions, and creative leaps that polished proofs often hide. It is especially valuable for students preparing for discrete mathematics, computer science, or higher-level proof courses, and for self-learners who want more than formulas: a disciplined but approachable way to ask better questions, construct arguments, and recognize why a proof works.