Fundamentals of Number Theory (Dover Books on Mathematics) by William J. LeVeque (PDF)

Description

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun’s theorem on twin primes, and the transcendence of e, to mention a few.Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is probably a great book if you have enough math education. It’s not quite what I thought I was buying.

⭐wish the proofs were more concise and there was some background context for the motivation of the proofs

⭐Fantastic book that has changed the way I look at numbers and symbols. It has left me with an impression that impresses others.

⭐It was not what I expected.

⭐For a class, but after I buy it, I drop the class.

⭐nice

⭐This book covers all the basics in number theory. The greatest common divisor, the Euclidean algorithm, congruences, primitive roots, quadratic reciprocity and more. If one has taken abstract algebra, then this is a great introductory number theory book, if one hasn’t taken abstract algebra, then a few chapters would be difficult to understand (such as chapters 3, 4 and 8), but the rest don’t need abstract algebra.I like the topics that are covered, in particular, I think Leveque does a very good job of explaining important concepts in elementary number theory in chapter 6. I really like Brun’s theorem on twin primes and the order of magnitude of several famous number theory functions.The last chapter has some interesting sections including the proof of the trascendence of e.Another thing I like about the book, is that it has mini biographies of important number theorists throughout the history of mathematics. I’ve always enjoyed reading about great mathematicians.

⭐This book is very well written and organized; the author clearly loves the subjectand writes with genuine feeling for it.The books covers linear diophantine equations, and classical topics such asquadratic reciprocity, Fermat’s theorem, Lagrange’s theorem and other nice stuff.The book even has proofs of the transcendence of e and pi that are easy to follow.I found the proofs easy to follow; there are plenty of exercises.A nice feature is the historical asides on past number theorists.It is well suited for self-study, and is pitched at the undergraduate level.The reader has to have a good knowledge of algebra; knowledge calculus helps.- and the price can’t be beat.

⭐Good but not easy to read.

⭐This is the 2nd Edition of an ealier book “Topics in Number Theory, Vol .1” by the author that covers the classics topics in Number Theory. A very useful and unique feature of the book are the links made between Number Theory and Abstract Algebra at an elementary level. These links serve as very good illustrative examples of ring and module theory of Abstract Algebra again at an elementary level.

⭐Il libro è interessante, ma la lettura delle formule e delle tabelle non è molto agevole su kindle in quanto sono immagini.

⭐

⭐Amazon price, for this product is to high

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