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An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

• Sales Rank: #215217 in Books
• Brand: Brand: Springer
• Published on: 1998-07-31
• Original language: English
• Number of items: 1
• Dimensions: 9.25" h x .72" w x 7.01" l, .95 pounds
• Binding: Paperback
• 200 pages

Features

• Used Book in Good Condition

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

Most helpful customer reviews

2 of 2 people found the following review helpful.
Phenomenal book for Self-study
By Madhusa Karunanayake
The pacing in this book is phenomenal. Every topic is explained with more than enough detail and without tangents.

The one thing this book does better than any other Number Theory book are the in-chapter questions. The questions are done so well that WANT to do them. You feel as if you are missing vital information by not doing them. This is one of the few books I can study for hours on end because you are constantly being engaged as you are working through the chapter, instead of mindlessly reading and hoping you remember everything you've just read. 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 think.

That is also it's only downside. You cannot jump between sections sometimes. The book assumes you follow it from the beginning of a section to the end as it sometimes teaches you vital information via the in-chapter questions.

If you are looking to self-study then you will not find a better book. I've tried every Number Theory book with decent ratings on Amazon, and this is by far the best.

7 of 7 people found the following review helpful.
An almost perfect square
By Itai
That the book's almost square is easily gathered from the photo. That it's almost perfect must be verified by reading it. And what an enjoyable verification indeed awaits those who take on the challenge! Not that reading it is a challenge - on the contrary, the Joneses take every effort to ensure your learning experience be as painless as possible. Every proof is complete, all exercises are solved. The proofs are always selected for their instructional merit, rather than for their mathematical "elegance" (read: brevity and algebraic gimmickry). As one Amazonian reviewer put it: you could read it through, lying in a bubble bath.

Another Amazonian reviewer commented that "Number theory is like the cement on your driveway. Real and Complex analysis are the Porsche and Ferrari you drive home every night." I disagree. In any case, in my opinion the book's weak spots are those sections where the discussion forays into the realm of real and complex analysis, namely 9.4-6 ("Random Integers", "Evaluating Zeta(2)", "Evaluating Zeta(2k)"), 9.9 ("Complex variables"), 10.2 ("The Gaussian Integers"), a part of 10.6 ("Minkowsky's Theorem") and 11.9 ("Lame and Kummer"). "Sums of two squares" (Section 10.1) could also use improvement, but this is compensated by the excellent, independent treatment this topic receives in the "Minkowsky's Theorem" chapter.

On several occasions, from the very beginning, the book assumes familiarity with single-variable polynomials (particularly the division algorithm and the x^n-y^n expansion). Be prepared.

If it weren't for the forays mentioned above, the book would have been a straight fiver. But even as it stands, it's a tour-de-force of pedagogy and expository mathematical writing.

One last quibble. The book doesn't have a homepage, nor is there any indication of a way to contact the authors. Textbook publishers should learn from their colleagues in the applied computer science publishing industry (such as O'Reilly, Wrox, Apress, etc.) and always make a homepage available for every book, with, at the minimum, a link to an errata page, and a forum where readers of the book can discuss it, (preferably with the involvement of the author(s)).

4 of 5 people found the following review helpful.
A Satisfactory Text for Elementary Number Theory
By Joseph A. Schrock
I've recently received my copy of Elementary Number Theory by Jones and Jones, and I'm (thus far) satisfied with the textbook. Although I'm not a professional mathematician, I have worked toward a degree in math and still love to study it. For me, the current textbook for 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 of number theory, using this text.
In view of my current experiences with this textbook, I would recommend it to a mathematical hobbyist like myself, or to a professional student of mathematics -- or anyone wishing to tackle number theory.

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[Q430.Ebook] Download Ebook Remaking the World: Adventures in Engineering, by Henry Petroski

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This collection of informative and pleasurable essays by Henry Petroski elucidates the role of engineers in shaping our environment in countless ways, big and small.

In Remaking the World Petroski gravitates this time, perhaps, toward the big: the English Channel tunnel, the Panama Canal, Hoover Dam, the QE2, and the Petronas Twin Towers in Malaysia, now the tallest buildings in the world. He profiles Charles Steinmetz, the genius of the General Electric Company; Henry Martyn Robert, a military engineer who created Robert's Rules of Order; and James Nasmyth, the Scotsman whose machine tools helped shape nineteenth-century ocean and rail transportation. Petroski sifts through the fossils of technology for cautionary tales and remarkable twists of fortune, and reminds us that failure is often a necessary step on the path to new discoveries. He explains soil mechanics by way of a game of  "rock, scissors, paper," and clarifies fundamental principles of engineering through the spokes of a Ferris wheel.

Most of all, Henry Petroski continues to celebrate the men and women whose scrawls on the backs of envelopes have immeasurably improved our world.


From the Hardcover edition.

• Sales Rank: #615427 in eBooks
• Published on: 2011-01-05
• Released on: 2011-01-05
• Format: Kindle eBook

Amazon.com Review
Engineers, Henry Petroski observes, are sometimes their own worst enemies, at least so far as communicating their work to the general public is concerned. Some engineers, of course, have been exceptions. One of the unlikely heroes of Petroski's Remaking the World, an entertaining foray into some of engineering's finest (and, on occasion, less exalted) moments, is Karl August Rudolf Steinmetz, who combined a great talent for design and engineering with a keenly practiced flair for self-promotion. Another is Washington Gale Ferris, the inventor of the Ferris wheel, who concocted several dangerous eyesores before arriving at the design familiar to amusement-park patrons.

Successful at explaining themselves or not, engineers are largely responsible for the world as we know it, and Petroski examines their work to discuss how good design and technology combine to produce the desired results. That combination involves much trial and error, and, as Petroski writes, "artifacts from paper clips to steamships evolve by removing some real or perceived failure of their ancestors to achieve unqualified success." Drawing on examples from past and present, Petroski offers an up-close view of how engineers do their work, and his history is full of surprises and pleasures. --Gregory McNamee

From Library Journal
Petroski, perhaps best known for The Pencil (LJ 3/1/90) and The Evolution of Useful Things (LJ 12/92), here collects columns written originally as essays for American Scientist, an engineering society publication. As such, the 18 selections, aimed at raising the reader's consciousness about how important and far-reaching engineering is to civilization and society, are accessible to a lay readers with an interest in technology and society. Several pieces are about particular engineers (e.g., Henry Robert, who wrote the Rules of Order, was first a military engineer) or engineering projects (the Channel Tunnel, the Ferris Wheel); others are provocative (the flaws of engineering software, the creep of technology). Always well written, though seldom off the "engineering is crucial!" soapbox, this is an excellent choice for general collections with a literate readership interested in technology?and a good gift for the engineers on your Christmas list.?Mark L. Shelton, Univ. of Massachusetts Medical Ctr., Worcester
Copyright 1997 Reed Business Information, Inc.

From Kirkus Reviews
A disappointingly flat collection of musings on engineering history. Petroski's concern, as in previous works such as The Pencil (1990), is the interdependence of engineering and society--the role of engineers in shaping the world we live in, but also the fact that engineering's achievements are driven not purely by technology but by economics, politics, and culture. But in demonstrating these truths through chronicles of great engineered projects and portraits of interesting engineers like Isambard Kingdom Brunel, he largely leaves out the ingredient that would really enlighten the reader--the engineering itself. ``The tapering at the top of the building demanded some especially tricky structural engineering,'' Petroski hints, with regard to Malaysia's Petronas Twin Towers, the world's tallest. But he leaves it at that, satisfied to provide a sketchy account of the building's materials and facilities, and a slight chronology of the project. Similarly, ``improvements in tunneling, such as the chore of getting rid of the soil,'' would seem to be a main topic in the history of the Channel Tunnel, but that phrase appears merely as a transition in Petroski's lifeless parade of 19th-century tunnel plans. Without using his tantalizing examples--pioneering soil mechanicist Karl Terzaghi and the rise and decline of the transatlantic steamship--to explain any engineering principles, they remain little more than aimless encyclopedia entries. Perhaps this is because they were written for a scientifically oriented audience (most appeared in American Scientist), with the intention of highlighting the historical and social context. Still, only occasionally, as in a chapter using the various uses of wireless communication to illustrate the unpredictable evolution of technology, do they seem to ascend above the assembled facts to a salient idea. Petroski is a little petulant about the respect engineering gets (as from the executors of Alfred Nobel's bequest), but he's squandered an opportunity to propagate a real sense of the science and labor of builders and inventors. (22 illustrations, not seen) -- Copyright ©1997, Kirkus Associates, LP. All rights reserved.

Most helpful customer reviews

26 of 28 people found the following review helpful.
For Petroski Fans Only
By Steve Harrison
This is a collection of articles written for Petrowski's monthly column in American Scientist magazine. Many are brief biographies of 19th-century engineers; a (very) few look (very) briefly at particular pieces of historical engineering (an article on the Ferris wheel is probably the best); others are ruminations on such hazards of the engineering practice as the stress that keeps them up at night and their failure to be awarded Nobel prizes. These seem quite satisfactory articles for a magazine column but they are slender stuff for a book. And Petroski's tendency to return to the same subjects, pardonable in a monthly column, becomes repetitive when the columns are collected. All but die-hard Petroski fans can skip this one

11 of 12 people found the following review helpful.
Excellent Read
By Jim T
This is a fine tome about engineering for those of us who scraped thru algebra! Should be required reading for *every* high school student. It gives a lot of basic information in understandable writing. Such as how did radio get to where it is today. Because of yacht racing... Now if that doesn't tease the brain, I don't know what else will...

6 of 6 people found the following review helpful.
Spendid short essays - (a must for any Petroski fan)
By from the US
I'm like those awful teachers who rarely give "10s" (although Petroski's The Pencil would get a 10!) Despite his protestation that these are slightly altered essays for the "American Engineer", as I recall, - he'd be hurt to realize that it's not common reading for most of us. For me it was all new territory - not covered in prior Petroski books and full of the interesting mix of social history and engineering history that he does so well. The order is arbitrary - except for the first chapter which is a bit autobiographical and perhaps should be read first - but I mostly skipped to topics I felt like reading and did them in my own order. My only criticisms are that a) the essays have some but could have used a bit more visuals - diagrams or photographs and b) many chapters - maybe not all but many - could easily have supported treatment at greater length. But I am a very tough grader. Also maybe at hardcover prices the publisher could be chided for not including more of the colums, this is a selection from thirty or so - and I doubt that Petroski was the parsimonious one! (but you can grab it while Amazon.com has it at 30% off) Its definitely nice to have this collection of columns from a journal I don't ever see, wrapped up in one volume.

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• Published on: 2013-09-12
• Original language: English
• Dimensions: 9.00" h x .29" w x 6.00" l,
• Binding: Paperback
• 128 pages

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During her work with Woman Made Gallery in Chicago, Janet Bloch decided to write this workbook to reach as many artists as possible because there is a serious lack of information for artists regarding strategies for embarking on a successful career. There is a great deal of mystery about the art world and its workings. As a result, artists often feel like outsiders. Combining this common perception with the competitive and secretive world of art can fuel the artist's sense of isolation and insecurity. Fortunately, as an artist, she shares a mindset with many of the artist's she's met. She also understands the 'other side' of the art world - the business side. In this book, she explains: what makes a great submission packet, what belongs in an artist s statement, what steps should be taken to build an impressive resume`. Strategic Marketing Tools for Visual Artists takes the mystery out of the professional expectations that exist in the art world. Artists who want to exhibit their work will be guided through a step by step process of creating superior materials to send to venues. This friendly manual is perfectly suited for artists' support groups, classrooms, or for individual use.

• Sales Rank: #1809827 in Books
• Published on: 2011-03-01
• Original language: English
• Number of items: 1
• Dimensions: 8.90" h x .40" w x 6.90" l, .60 pounds
• Binding: Paperback
• 121 pages

Review
Janet has spoken at our conference for many years. Now, all of this vital information is gathered together into one workbook that any artist can utilize to help them reach their desired success. This is a 'must' for any emerging artist who wants to make a career in the arts. --Amy Rogers, Director, Self-Employment in the Arts Conference

Janet's guidance and advice was invaluable to my ability to execute the artist's marketing process. She knows what to do, how to do it and when to do it. Her broad experience and knowledgeable guidance offers a comprehensive and clear direction that I could find nowhere else. --Susie Smith Trees, sculptor

Janet Bloch's advice was invaluable to me in taking my career to a new level. I now have the knowledge and resources I need to confidently approach new exhibiting prospects in a professional manner. New doors are opening for me all over the place. --Shari Pettis, painter

About the Author
Janet Bloch earned a Master of Fine Arts from the School of the Art Institute of Chicago in 1980. After her graduation she had no idea how to approach galleries or write grants. Then, as the director of Chicago's Woman Made Gallery she experienced the art world from the 'gallery side.' Her perceptions led to practices that advanced her own art career, such as solo shows and earned her such awards as an Illinois Arts Council Fellowship, a National Endowment of the Arts Regional/Midwest Fellowship and two Individual Artist's Grants from the Indiana Arts Commission. She currently serves as Education Director and the Lubeznik Center for the Arts in Michigan City, Indiana.

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• Sales Rank: #12153377 in Books
• Published on: 1999
• Binding: Paperback

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• Sales Rank: #4378036 in Books
• Published on: 2013-09-16
• Original language: English
• Number of items: 1
• Dimensions: 11.02" h x .39" w x 8.27" l, .94 pounds
• Binding: Paperback
• 184 pages

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• Sales Rank: #23531 in Audible
• Published on: 2015-08-03
• Format: Unabridged
• Original language: English
• Running time: 381 minutes

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2 of 2 people found the following review helpful.
On the "must-read list" for anyone in a relationship!
By Love Paris
Excellent book with information helpful for any relationship. Straight forward, easy to understand concepts that can be applied immediately to improve conflict -ridden communication. The author gives interesting examples which help to illustrate the concepts. Ideal, both for couples who have been together for years, as well as newly-weds, this well-written book offers rich wisdom for improving our most significant relationships. The author's easy to read style is embedded with humorous touches. This unique perspective offers hope and optimism for couples locked in dysfunctional communication and conflict. It also offers solid principles for those with good marriages who want to make them even better. Definitely a must-read for anyone wanting to improve their significant relationships.

0 of 0 people found the following review helpful.
I never review anything
By Virginia
I purchase beauty products, household goods and audio books from Amazon nearly daily. I think I've written one review in my life; nothing is great enough to warrant the time it takes to provide feedback.
Thia book, however, is worth sharing and telling people to read/listen. From a relationship/self development/communication standpoint, it's unique for a number of key reasons: 1. Practical application and a process. Although not first nature to do much of what he teaches, he tells you what to do, how to do it and why. 2. It doesn't have a gender bias. Too often these books are authored and told from one perspective. Worst yet, the basis of their insight is on sweeping generalizations of one of both genders. "Women today are bossy and controlling." "Men and are lazy, inconsiderate and useless." Emil's ideas go beyond that. He doesn't need to generalize how one partner is in order to get your buy in on his ideas.
3. Lastly, it's benefit goes beyond marriage and relationships. It's about communicating with respect, understanding and thoughtfulness to avoid conflict in all relationships.
Really, really great read!
I love that he's the audible voice too! It adds an authenticity, a live seminar feel to the reading.

1 of 1 people found the following review helpful.
This was a great book. Easy to read
By Susan Seper
This was a great book. Easy to read. You can start using the principles he teaches today, and in any relationship you have not just in marriage.

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