A Friendly Introduction to Number Theory

by Joseph H. Silverman

Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Provides a new chapter that introduces the theory of continued fractions. Includes a new chapter on ";Continued Fractions, Square Roots and Pell’s Equation."; Contains additional historical material, including material on Pell’s equation and the Chinese Remainder Theorem. A useful reference for mathematics teachers.

Genres: Mathematics, Nonfiction, Textbooks, Number Theory, Science

448 pages, Hardcover

First published November 1, 2013

Reviews

[Mark Moon · Rating 5 out of 5]

A very nice introduction! It's as friendly as the name implies, and does get into some relatively advanced material towards the end, too.

[Hannah Thomas · Rating 4 out of 5]

This is really more of a computational textbook for a college class, but there are some areas that you have to use "proofs." To understand Number Theory, you really do need to some basic Abstract Algebra background. There are times in here that you do get that "background" knowledge of the abstract part, but it's very vague because only the "uniqueness" part is provided. It's the "existence" you need to understand and prove (that's where your background knowledge comes in handy!). The author really does want to work your mind around proofs and computation and that's the fun part :) If you really want to pursue further into mathematics, in the Abstract Algebra branch, this is a book for you!

[Chris · Rating 4 out of 5]

It lives up to the title. If you think mathematics is work and not play, you might find yourself surprised with this slim volume.

In addition to being an instrument of a peculiar kind of pleasure, it's free of data pseudoscience.



Programmers who want to learn more about the elliptic curves in cryptography could do worse than giving Joe Silverman 1/4th the price of a typical language/database doorstop.

[Shaun Zhang · Rating 4 out of 5]

It is a readable book. As the title shows, it is friendly. And all basic important theorems are well presented by examples and rigorous proofs. Recommend it for whoever first touches number theory.

[Xiangnong · Rating 4 out of 5]

As a high school student and a math competition participant, I found this book to be a very good enlightenment of my Number Theory knowledge. It is not extremely hard to understand. Some of them are even easy. Everything is introduced as a level which is just enough to be understood and applied.
Things I found interesting and helpful are those exercising examples provided. It will always provide a complete example to show an algorithm or explain how to prove a theorem. As an OIer once, I learned several algorithms including EGCD and Fast Powering several years ago, but I have neither tried to work it out by hand, nor tried to test and prove the validity of those algorithms.
One thing I learned from this book is that you need to test out and play around with numbers in order to discover some new patterns and modes. And I believe I will read this book again because this time I didn't really tried to work on those exercises. It's required, just like people need to go underwater in order to learn swimming.
Then I realized that, the key of this book is not to learn how to prove fancy theorems and how to become a master in Number Theory, but how to start working on studying numbers.
Because of that, this book purposefully serves as an introduction, not a guidance, it can only provide basic knowledges of Number Theory and some fundamental proofs. The solutions provided for practice problems is really brief and not very helpful. I personally found it more helpful to re-read the examples than reading the solutions.
I think this book is very helpful to students who know nothing about Number Theory and want to know about it and are not college students yet. College number theory definitely requires more skills and deeper understanding beyond this book, and college students can find more helpful books such as Elementary Number Theory and Its Applications.
But for students like me or even younger, it is a good way to let them know about what is Number Theory and what do mathematicians do with it.

[Poonam · Rating 5 out of 5]

nice introductory text. kinda weak on elliptic curves

[Robert Allen · Rating 1 out of 5]

As the expositions are minimal, as most of the problems are out of left field, they cannot be worked, much less understood without the answers which I was able to purchase on line for $30.00--and even the answers are difficult to understand!!!!! In short, this book is everything but friendly and Silverman and those on this thread who gave it a top rating are no more than frauds, cheats and liars.

[Hülya · Rating 5 out of 5]

bu kitabı da burda gördüm ya daha ne olsun :D silverman amcayada teşekkürler süper eğlenceli bir kitap yazmış. number theoryi hiç böyle bilmezdim ben :P

[Samantha · Rating 3 out of 5]

I read this book for Number Theory this past semester. It makes the concepts very accessible and was very enjoyable.

[Dev]

good

[Joe Cole · Rating 5 out of 5]

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.