- Hardcover: 356 pages
- Publisher: Springer; 1st ed. 1976. Corr. 5th printing 1998 edition (28 May 1998)
- Language: English
- ISBN-10: 0387901639
- ISBN-13: 978-0387901633
- Product Dimensions: 16.5 x 2.2 x 23.9 cm
- Average Customer Review: 4.7 out of 5 stars See all reviews (11 customer reviews)
- Amazon Bestsellers Rank: 81,299 in Books (See Top 100 in Books)
- See Complete Table of Contents
Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics) Hardcover – 28 May 1998
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From the reviews:
Introduction to Analytic Number Theory
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read."
“After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. … I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains its own set of … exercises. … this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory.” (Álvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)
Inside This Book(Learn More)
The theory of numbers is that branch of mathematics which deals with properties of the whole numbers, 1, 2, 3, 4, 5, . . . also called the counting numbers, or positive integers. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Top Customer Reviews
The first few chapters deal with "elementary" ideas, such as arithmetic functions and congruences. There is also a look at group theory and Dirichlet characters, which are relevant to L series. The book ends with a look at the partition function and infinite products, which is a really interesting and beautiful topic!
There are exercises at the end of every chapter, but unfortunately there are no answers in the back, which is a shame, because the reader cannot check if his/her work is correct.
This book has been in print for about 30 years and has deservedly attained a reputation as something of a classic, in mathematical circles.
By the way, it took me a while to figure out what the diagram on the front cover is supposed to be. It's a diagram of the GCD function (greatest common divisor).
I found that by combining this book with Burton `Elementary Number Theory' or Hardy and Wrights `Introduction to the theory of Numbers' this textbook provides an excellent introduction for anyone with an interest in Analytic Number Theory.
A highly recommended textbook.
While the author claims that this is book suitable for undergraduates, much of the content requires a high degree of Pure Mathematical rigour and so would be suitable for a final year undergrad or preferably a Masters level course in the subject.
The "core" of the book is dedicated to Analytic Number Theory but it also dedicates much space and attention to other important topics. Starting with a revision of basic concepts like divisibility and the fundamental theorem of Arithmetic, the book quickly flows into the definition, inter-relationships between and application of the Arithmetic functions. The distribution of prime number is introduced early. Thereafter, following the introduction of tools like congruences, Abelian Groups and their Characters, Periodic Arithmetical Functions and Gauss Sums, the book moves into in depth exposition of Dirichlet's theorem, Dirichet Series, the Reimann Zeta function and the Analyic proof of the Prime Number Theorem. The chapter on the Prime Number Theorem also includes a useful discussion of the Riemann hypothesis. These latter chapters assume knowledge of Complex Variable Theory.
Another merit of the book are the chapters on topics like the Quadratic Reciprocity Law, Primitive Roots and Partitions. Though the book lacks worked examples, as is the case with Apostol's other books, it more than makes up for this by the numerous problems at the end of each chapter. It is a pity that hints and/or solutions are not included.
Most Recent Customer Reviews
Does all the proofs you could ever want. Takes some ploughing through, but useful exercises.Published 14 months ago by C. Wells
My standard review, if applicable, would be, I am most pleased with this purchase. With these words, I now conclude.Published 23 months ago by James A. Andrews
one of the books on my reading list for uni, includes what expected and a little bit more help, easy to read!Published on 1 Feb. 2014 by me
I like very much number theory even if i have never studied it in any school. A friend, who share my same passion, suggested me this book and i'm glad to have listened his... Read morePublished on 7 Nov. 2013 by Ivan