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Joseph H. Silverman
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A Friendly Introduction to Number Theory (4th Edition) 4th Edition

by Joseph H. Silverman (Author)
4.3 4.3 out of 5 stars 125 ratings
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There is a newer edition of this item:

Friendly Introduction to Number Theory, A (Classic Version) (Pearson Modern Classics for Advanced Mathematics Series)
Friendly Introduction to Number Theory, A (Classic Version) (Pearson Modern Classics for Advanced Mathematics Series)
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A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

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  1. ISBN-10
    0321816196
  2. ISBN-13
    978-0321816191
  3. Edition
    4th
  4. Publisher
    Pearson
  5. Publication date
    January 28, 2012
  6. Language
    English
  7. Dimensions
    6 x 1.1 x 9.1 inches
  8. Print length
    432 pages
  9. See all details
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Editorial Reviews

About the Author

Joseph H. Silverman is a Professor of Mathematics at Brown University. He received his Sc.B. at Brown and his Ph.D. at Harvard, after which he held positions at MIT and Boston University before joining the Brown faculty in 1988. He has published more than 100 peer-reviewed research articles and seven books in the fields of number theory, elliptic curves, arithmetic geometry, arithmetic dynamical systems, and cryptography. He is a highly regarded teacher, having won teaching awards from Brown University and the Mathematical Association of America, as well as a Steele Prize for Mathematical Exposition from the American Mathematical Society. He has supervised the theses of more than 25 Ph.D. students, is a co-founder of NTRU Cryptosystems, Inc., and has served as an elected member of the American Mathematical Society Council and Executive Committee.

Product details

  • Publisher ‏ : ‎ Pearson; 4th edition (January 28, 2012)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 432 pages
  • ISBN-10 ‏ : ‎ 0321816196
  • ISBN-13 ‏ : ‎ 978-0321816191
  • Item Weight ‏ : ‎ 1.57 pounds
  • Dimensions ‏ : ‎ 6 x 1.1 x 9.1 inches
  • Customer Reviews:
    4.3 4.3 out of 5 stars 125 ratings

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Joseph H. Silverman

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Customer reviews

4.3 out of 5 stars
4.3 out of 5
125 global ratings

Top reviews from the United States

T. Janowski
5.0 out of 5 stars Great content! Poor quality of the book.
Reviewed in the United States on November 15, 2021
Verified Purchase
I knew the content of first 100 pages before purchase, as I had access to this book from different sources before. It is a very readable text on a rather abstract mathematical subject at the beginner's level.

But I am gravely disappointed by the fact that the paperback version (Pearson; 4th edition) is printed on a newspaper quality paper, probably the lowest grade possible. Quite a disappointment for a book at this price. I never had a textbook printed on paper that poor (I had some investigative journalism books or budged classic novels printed like that, but they were for for 10 bucks each).
4 people found this helpful
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ChicagoK8
5.0 out of 5 stars fun side of number theory
Reviewed in the United States on May 28, 2013
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I would expect that anyone curious enough about number theory to look up this book would likely have enough background in math to follow this text. It doesn't require much knowledge beyond algebra, but it does require algebra. I took a college course in number theory and this was the text. I have found it to be an easy read, only requiring a few visits to Wolfram Alpha to clarify some background knowledge. The style and organization of the book reflects an appreciation for the creativity involved in math and number theory.
13 people found this helpful
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Gus
4.0 out of 5 stars THE CHAPTERS SWITCH ORDER TOWARDS THE END OF THE BOOK
Reviewed in the United States on August 18, 2021
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This book is the exact same as the US version, with the exception that some of the end-of-chapter problems might vary, and the order of the chapters switch towards the end of the book compared to the US version. If you're buying this for a class, just make sure to pay attention to that detail, and always compare the questions in your book to a classmate with the US version before submitting any homework etc... Otherwise, it's an amazing book for the price.
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Debbie Maxwell
5.0 out of 5 stars Gift for my son
Reviewed in the United States on February 1, 2023
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My son asked for this book for Christmas. It was recommended to him by one of his math professors. He is enjoying it! Thank you!
One person found this helpful
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Jonathan Hills
5.0 out of 5 stars Great introduction
Reviewed in the United States on January 11, 2013
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I had to buy this for an undergraduate number theory course. It's well-named: a friendly introduction to a pretty interesting field of mathematics. Well-written and accessible, this book also moves fairly quickly and includes challenging exercises.
6 people found this helpful
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Amazon Customer
3.0 out of 5 stars Arrived on time but the book is falling apart
Reviewed in the United States on August 27, 2019
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The book is falling apart after I opened the book for the firs time. Hoping that it stays in tact for a few months of use..
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Thomas Kurian
5.0 out of 5 stars Best math book I've ever read!
Reviewed in the United States on October 21, 2014
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I just bought this book yesterday and I'm already addicted to it! Unlike usual math textbooks, which just give definitions and proofs, this book has a friendly conversational style. I think it's a great introduction to number theory.
4 people found this helpful
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Gustav8191
1.0 out of 5 stars a hack job compared to the US edition
Reviewed in the United States on April 13, 2022
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Do not purchase this "Pearson New International" edition. It's missing critical sections compared to the US edition, such as the proofs of when -1 and 2 are quadratic residues. Even worse, it's sort of duplicitous about the omissions: In the US edition, these results are proven in one chapter, and the next chapter begins by saying, "in the previous chapter we proved [this result]...." In this edition, is SKIPS the chapter containing the proofs, and the next chapter mysteriously starts with, "we find that we can prove [this result]...."

This is a hack job. Just compare the indexes to this and the US edition; this one feels like it was put together by school children. Absolutely avoid.

(By the way, Silverman's book, when presented in its proper form, is excellent!)
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Top reviews from other countries

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Jay Jina
5.0 out of 5 stars A good text covering undergraduate material.
Reviewed in India on April 5, 2024
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As the title suggests, this is a friendly introduction to Number Theory. Suitable for undergraduates, the author takes a gentle approach to what many find to be a challenging subject.

One finds all of the topics in "Elementary" Number Theory in the book - here it is to be noted that "elementary" does not in any way signify simple or easy, but rather that the foundational, and yet sophisticated nature of the subject.

Rather than teaching the student various techniques and tricks and use them to mechanistically solve problems, the author's focus is on raising curiosity and encouraging mathematical thinking. As the author says, Natural Numbers are an ideal means for this purpose.

Divided into 50 shortish chapters, the text covers everything from Pythagorean triples, Divisibility, Linear equations with greatest common divisor, the Fundamental theorem of Arithmetic, Congruences, Various types of Primes, Quadratic Reciprocity, the so-called Pell's Equation, Modulo Arithmetic, and Continued Fractions.

A delightful book with plenty of worked examples and exercises for both the beginning and more capable students.
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catenary
1.0 out of 5 stars You may better not buy an Indian Edition. インドバージョンに手を出すな。2つの章が欠落！！
Reviewed in Japan on December 29, 2018
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Wonderful contents!　But the Indian edition doesn't have the 21st and the 40th chapters that exist in the original 4th versin copy. It is not ”an accidental missing."
内容は素晴らしい。★5つです。読み終わったらにコメントを書きます。ただ、安いからと言って、”Indian Edition textbook with identical content as the US version”　という説明を信頼して買うと驚く。原著第４版の21章がない。抜けている。いわゆる製本時の「落丁」ではない。その証拠に、ページ表示はきちんとつながっている。意図的だと思う。各章の表題に章番号が書かれていない。そしてその章の最初のページの脚注に、From Chapter ＊＊ of A friendly Introduction to Number Theory ,Fourth Edition と書かれている。 その脚注に”From Chapter21”と書かれた章が存在しない。21章が抜けていることは、次の章を読み始めた時、つじつまが合わないので気づいた。これは困った。積み重ねてこそ理解できる数学の本でありながら、重要な定理とその証明が抜けていては後が理解できない。そこで、インターネットサイトでその抜けている第21章を探した。あった！！　第21章本文がインターネットで読めることが分かった。ダウンロードして印刷したので、何とかなった。A Friendly Introduction to Number Theory でInternet search(検索)すると、ブラウン大学のサイトbrown.eduが検索できる。そこにあった。

もしあなたがIndian edition を買うなら、そのつもりで買ってください。それが嫌なら、多少、ではなくかなり高くてもIndean edition（古本）は決して買わないように。なお、買ってから気づいたのだが、Indian edition には「インド・パキスタン、・・・以外の「circulation of this edition is UNORTHORIZED」と書かれている。日本は含まれていない。なぜ日本で買えたのだろう。
ついでに付け加えるが、この本のIndexはきわめてお粗末。ある言葉の定義を再確認しようと思ってもまずインデクスには書かれていない。全く役に立たない。その点、第3版の翻訳書「初めての数論原著第3版」（翻訳鈴木治郎）はしっかりしたものとなっているのは、翻訳者は自らきちんと作り直したのだろう。

2019/1/20追記
原著第4版の第26章が欠落している。ブラウン大学のサイトで検索すると、第4版には第3版にはなかった章が追加されているとある。There is a new chapter on mathematical induction (Chapter 26).この第26章がない。内容は数学的帰納法についてらしい。この際最後まで省の続きを見ていくと、もう1章、第41章がないことに気づいた。安物買いの銭失いになった。
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Jovack22
5.0 out of 5 stars Definitely a great starting point for a gifted high schooler
Reviewed in Canada on September 15, 2015
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Definitely a great starting point for a gifted high schooler, or undergrad starting with number theory. Material is explained well, with contextual anecdotes and examples included. It is not so "wishy-washy" that it keeps some more difficult concepts from you, but also won't throw you into the deep end. That being said, a more advanced text is recommended after you read this one -- but as the title says "A friendly intro...", and it delivers on that promise.
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Abe
5.0 out of 5 stars Great quality
Reviewed in India on July 8, 2023
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Great quality pages.

Read some of the chapter, it's a great introduction to number theory. I myself am not very good at math, but I found the book easy to digest and learn.
Proofs are also provided, not too formal with a lot of notations, but rigorous. They are well presented and really capture the essence and the idea.
Has good exercises too, to improve your understanding.
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Abe
5.0 out of 5 stars Great quality
Reviewed in India on July 8, 2023
Great quality pages.

Read some of the chapter, it's a great introduction to number theory. I myself am not very good at math, but I found the book easy to digest and learn.
Proofs are also provided, not too formal with a lot of notations, but rigorous. They are well presented and really capture the essence and the idea.
Has good exercises too, to improve your understanding.
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2 people found this helpful
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David W.
4.0 out of 5 stars Friendly as number theory can get
Reviewed in Canada on April 24, 2014
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Organized logically from the standpoint of the non math person. Leads you gently into the world of natural numbers. The text is easy to read and straight forward. It could benefit with a few more examples but generally is good for an introductory text for those requiring a basic grounding in number theory, such as in an elementary teacher training program.
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