Yet Another Introductory Number Theory Textbook

Livro digital

Título:
Yet Another Introductory Number Theory Textbook

Autor:
Jonathan A. Poritz

Categoria:
Matemática & Lógica > Álgebra e Teoria dos Números

Pessoa doadora:
Raffaello D. N.

Sinopse:
This textbook starts with the arithmetic backbone of number theory, moving from well-ordering and induction into divisibility, the Euclidean algorithm, and representations in different bases. That opening sequence signals a book built for students who need proof-based tools, not just worked examples, and it keeps the reader anchored in the logic of the integers from the first chapter onward. The table of contents then advances through congruences, linear congruences, the Chinese Remainder Theorem, and Euler’s phi function before turning to primes, Wilson’s theorem, multiplicative order, and the Fermat and Euler theorems. The authorial voice is singular, but the preface shows a classroom-tested text shaped by student feedback and adapted from Wissam Raji’s earlier work. The cryptology emphasis arrives naturally in a dedicated chapter on the Caesar cipher, frequency analysis, RSA, digital signatures, and man-in-the-middle attacks, then continues into discrete logarithms, primitive roots, Diffie-Hellman, and ElGamal. What emerges is a compact, introductory undergraduate path through classical number theory with a practical cryptographic payoff. Readers get a proof-oriented foundation, a clear progression from basic integer properties to public-key cryptosystems, and a distinctive blend of pure and applied mathematics that makes the subject feel immediate rather than abstract.