An Infinite Descent into Pure Mathematics

Livro digital

Título:
An Infinite Descent into Pure Mathematics

Autor:
Clive Newstead

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
A reader who wants to move beyond routine calculation needs a guide to proof, structure, and abstraction, and the opening sequence here makes that transition explicit: Chapter 0, “Getting started,” is followed by core chapters on logical structure, sets, functions, and mathematical induction. That progression signals a book built to teach how pure mathematics is actually assembled. The contents keep widening from relations and finite versus infinite sets into number theory, enumerative combinatorics, real numbers, infinity, and discrete probability theory, with additional topics on orders, lattices, and inductively defined sets. The appendices then return to proof-writing, foundations, number-set constructions, limits, and even LaTeX typesetting, which makes the book both technical and unusually practical for learners working through formal mathematics. This is a proof-centered foundation text for readers ready to think like mathematicians rather than simply apply formulas. Its range, from propositions and quantifiers to cardinality and convergence, gives the reader a structured path into rigorous reasoning, while the exercises and appendices reinforce independent problem solving and mathematical writing.