Elementary Number Theory: Second Edition (Dover Books on Mathematics) by Underwood Dudley (PDF)

Description

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems—some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat’s and Wilson’s theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and answers to selected exercises and problems.

User’s Reviews

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

⭐Elementary Number Theory: Second Edition is a relatively short mathematics book that deals a lot with prime number theory. The topics covered in this book are senior college level topics, making the name “Elementary” in the title somewhat deceptive. While topics they talk about in an intro to proofs class focus on the basics, this book focuses on the applied basics. The book is short and has many examples for the student to work out, but it is limited in that there are few examples that the author worked out. Because of the level of this book, many steps are also removed, however, even for a math student, some of the steps skipped left me stumped, and many topics are still out of grasp through independent study. There is a nice section of the book that has some induction problems, which is geared towards those who have already done proofs and now are working on number theory. This book is solid for the $10 it cost, but there is a reason other math texts run from $100-200, and that’s because of the extensive amount of problems worked out in those texts. (You get what you pay for)

⭐I picked up this book after taking a course in set theory/math logic. It was my first experience with proof based math and I found it very challenging and rewarding. I decided over the summer I would teach myself number theory as well. So far I am about 3 or 4 weeks into the summer and I’ve chopped down sections 1-6. Keep in mind I am also doing undergrad physics research and a directed study astrophysics course as well, you could easily progress further. I really have enjoyed this book thus far. I often get so caught up in it that I am up until morning toying with problems. The author did a fantastic job of finding the fine line between too difficult and elementary. It seems just short of a graduate text but a little above a common undergraduate text. Thanks to this text I am becoming much more confident in my ability to set up and execute proofs. I don’t want to spoil the methods- but it seems MOSTLY up until this point all proofs are found in the same manner. I have not been able to execute a variety of proof methods (e.g. deduction, mathematical induction, contrapositive, and contradiction.) I would have liked to be able to switch it up some. However, I am no expert and this may be my own doing.If that is the best “CON” I can come up with for this book, that says a lot. I HIGHLY recommend ANY student who enjoys thinking to pick up this book and complete it in it’s entirety. I feel deprived that I wasn’t given this opportunity sooner.I am a 3rd year math+physics major. This book changed me from physics and chemistry to math and physics student and possibly from a physics grad student to a math grad.

⭐Explicit examples. Difficult principles made understandable. I would recommend this book to anyone who has enough background math to understand these principles. Good read.

⭐Simply excellent. For someone such as myself who is mathematically-inclined but never had exposure to a number theory course, this book offers a perfect balance of accessibility and depth. The organization of the material has clearly been carefully thought-out so as to inflict minimal pain on newcomers like me. The practice problems are numerous, varied, interesting, and span a fairly broad range of difficulty, meaning you can push yourself to *really* absorb the material if you like.Perhaps, above all else, what this book offers — or at least what I have found myself experiencing as each chapter unfolds — is a glimpse at the beauty of number theory. The book has turned something that I once thought to be an abstract, toy-problem-ish area of mathematics into a genuine joy as I come to understand more and more this strange, oft-baffling, occasionally outright-magical branch of math. It is, dare I say, quite a fun read 🙂

⭐This is not the first instance of a technical book which has been greatly maimed by a poor choice of visual display. Because no one was paid to take the time and trouble to edit it carefully, the formulas, an essential part of any mathematical text, are displayed in totally inadequate type, font and format. It is a pity that no one in the editing department cares enough about the reader to insist on correcting such failings – of course it is cheaper just to digitalize and throw it on the market without putting in the extra effort.In the old days book publishers were book lovers and cared about qualitynow it is just the accounting office who rules all.

⭐I’m using this to teach advanced highschool students. I find the topic choice and length of each section perfect to keep students interested. The exercises at the end of each section are rather simple, but the additional problems at the end of the book offer a wealth of much more challenging problems.

⭐Super clear examples, easy to read

⭐If you have a math background this book is to elementary to get you started. It also has too many display and typo problems to be followed in detail unless you like finding typos. Dover is very uneven in the quality of their digital math books. Some are fine some are not.I got the book because it was recommend as a starting point on number theory in another review but found too elementary. As a calibration, I spent 20 years doing statistical pattern recognition and still know that math.

⭐Teoria dos Números não é bem minha área. Vi bem por cima na época da faculdade e nem aprendi direito. Esse livro cobriu esta minha falha.Que livro bom!Empfehlenswertes Buch… ich habe es auch Interesse und zum Selbststudium gekauft… Themen werden gut erläutert…C’est une façon très douce d’aborder la théorie des nombres qui est très formatrice d’un esprit de mathématicien. C’est une autre manière de voir les nombres, on n’étudie pas 3 kilos de pommes mais on recherche les propriétés du nombre 3; c’est du lourd.

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