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  • Elementary Number Theory (Springer Undergraduate Mathematics Series)

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Elementary Number Theory (Springer Undergraduate Mathematics Series)

by Gareth A. Jones (Author), Josephine M. Jones (Author) Format: Paperback
4.5 out of 5 stars (94)
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Our intention in writing this book is to give an elementary introduction to number theory which does not demand a great deal of mathematical back­ ground or maturity from the reader, and which can be read and understood with no extra assistance. Our first three chapters are based almost entirely on A-level mathematics, while the next five require little else beyond some el­ ementary group theory. It is only in the last three chapters, where we treat more advanced topics, including recent developments, that we require greater mathematical background; here we use some basic ideas which students would expect to meet in the first year or so of a typical undergraduate course in math­ ematics. Throughout the book, we have attempted to explain our arguments as fully and as clearly as possible, with plenty of worked examples and with outline solutions for all the exercises. There are several good reasons for choosing number theory as a subject. It has a long and interesting history, ranging from the earliest recorded times to the present day (see Chapter 11, for instance, on Fermat's Last Theorem), and its problems have attracted many of the greatest mathematicians; consequently the study of number theory is an excellent introduction to the development and achievements of mathematics (and, indeed, some of its failures). In particular, the explicit nature of many of its problems, concerning basic properties of inte­ gers, makes number theory a particularly suitable subject in which to present modern mathematics in elementary terms.
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  1. ISBN-10
    3540761977
  2. ISBN-13
    978-3540761976
  3. Edition
    Corrected
  4. Publication date
    January 14, 1998
  5. Part of series
    Springer Undergraduate Mathematics
  6. Language
    English
  7. Dimensions
    7.01 x 0.72 x 9.25 inches
  8. Print length
    200 pages
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Editorial Reviews

Review

From the reviews:

BULLETIN OF MATHEMATICS BOOKS

"?as a nice concluding chapter on Fermat? Last Theorem, with a brief discussion on the coup de grace."

G.A. Jones and J.M. Jones

Elementary Number Theory

"A welcome addition . . . a carefully and well-written book."―THE MATHEMATICAL GAZETTE

"This book would make an excellent text for an undergraduate course on number theory."

―MATHEMATICAL REVIEWS

Product details

  • Publisher ‏ : ‎ Springer
  • Publication date ‏ : ‎ January 14, 1998
  • Edition ‏ : ‎ Corrected
  • Language ‏ : ‎ English
  • Print length ‏ : ‎ 200 pages
  • ISBN-10 ‏ : ‎ 3540761977
  • ISBN-13 ‏ : ‎ 978-3540761976
  • Item Weight ‏ : ‎ 1.2 pounds
  • Dimensions ‏ : ‎ 7.01 x 0.72 x 9.25 inches
  • Part of series ‏ : ‎ Springer Undergraduate Mathematics
  • Best Sellers Rank: #174,151 in Books (See Top 100 in Books)
  • Customer Reviews:
    4.5 out of 5 stars (94)

About the author

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Gareth A. Jones

Gareth A. Jones

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Customer reviews

4.5 out of 5 stars
94 global ratings
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Customers say

Customers find the book perfect for elementary number theory education, packed full of great results, and appreciate its unique presentation of math history. The difficulty level receives mixed feedback - while some find it well-written, others say it's not straightforward, and several mention it can be difficult to understand sometimes. The problem content also gets mixed reviews, with one customer noting the lack of "in between" problems.
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17 customers mention content, 14 positive, 3 negative
Customers appreciate the book's content, which is packed with great number theory results and offers a unique presentation of math history. One customer notes that students with limited background in abstract mathematics will find it accessible, while another mentions that every topic is explained with more than enough detail.
...If you're interested in number theory, this is a great place to get started.Read more
...One positive is that all the examples have done out solutions in the back, but unfortunately since decimal points may or may not actually represent...Read more
...It does use an elementary approach, and assumes little knowledge of advanced mathematics from the reader, but if you are a neophyte in mathematics...Read more
...well written of books on the subject - it helped me tremendously with Rudin and Brown and Churchill. I still hate number theory.Read more
9 customers mention difficulty level, 6 positive, 3 negative
Customers have mixed opinions about the difficulty level of the book, with some finding it not straightforward and not suitable for beginners, while another customer notes that the theorems have easy-to-follow proofs.
...Highly recommended, particularly for beginners.Read more
...It makes the reading of the book painful - certainly not easy when you are trying to figure out number theory for the first time....Read more
...They questions aren't very difficult (full worked solutions for every problem if needed), but they are just hard enough to make you have to...Read more
...do proofs, working through this book can give a good and relatively painless introduction to some of the proofs that will be useful in algebra other...Read more
9 customers mention writing style, 6 positive, 3 negative
Customers have mixed opinions about the writing style of the book.
...However, this is a great book, possibly the clearest and well written of books on the subject - it helped me tremendously with Rudin and Brown and...Read more
...But even as it stands, it's a tour-de-force of pedagogy and expository mathematical writing. One last quibble....Read more
The writing is clear. It is a unique way of looking at math history....Read more
...For the small size it has there is a lot inside it, and the writing style is pleasant, although, sometimes, important details are, in an undesirable...Read more
7 customers mention readability, 4 positive, 3 negative
Customers have mixed opinions about the book's readability, with some finding it difficult to understand at times.
...However, this is a great book, possibly the clearest and well written of books on the subject - it helped me tremendously with Rudin and Brown and...Read more
...roots and Section 7.1 (Quadratic congruences), not a word of which was comprehensible, where I stopped in frustration and disgust....Read more
This book presumes so little of the reader that anyone can start learning number theory using this book....Read more
...Also, it is not very clear in its approaches, since it assumes the reader has learned many mathematical notations...Read more
6 customers mention problem content, 3 positive, 3 negative
Customers have mixed opinions about the problem content of the book, with some finding it well-structured while others note that it lacks intermediate problems and solutions.
...number theory is a challenge to master, but with all the solutions to problems provided, I find it quite palatable to work toward an understanding...Read more
Good number theory book. Needs work on the solutions in the back of the book, can be difficult to understand sometimes.Read more
...There are plenty of exercises and all of them have solutions....Read more
...This book only gives me 1 or 2 of those problems, and then moves on....Read more
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