Number Theory: A Lively Introduction with Proofs, Applications, and Stories

This book is amazing! It is rigorous and is full of theorems/proofs but most of the ones that are not simple are prefaced with an expository section that builds intuition for the proof. By the time you get to the proof, it is easy to follow the logic.Each chapter begins with a fictional story, but most of them involve a practical scenario that gives you a sense of why the chapter's content is important. They are also quite humorous - my favorite involves Gauss being drugged by aliens. They are full of clever puns about the history of mathematics but they never feel childish. I will forever think about potatoes when solving a linear Diophantine equation...I am required to use another number theory text for my class (Rosen) but this one explains things so much better and the proofs are much easier to follow. In my number theory class, we do proofs in groups and other students are always commenting on the high quality of my proofs and how good I am at finding errors in their proofs. I think much of that has to do with this book. It really focuses on connections between concepts and the "why" behind the math, which makes it easier for me to write my own proofs and give feedback to others.There are some minor print errors as described by another reviewer, but no more than any other math text I have read. When you do encounter one, the mistake is obvious and does not detract from the experience. I would LOVE to see what the authors could do with another topic such as abstract algebra, a subject in desperate need of a similar treatment.

This book is a fantastic intro to Number Theory. It's fun and engaging. It's accessible. It leads you through proofs in plain English, but with still rigorous mathematics. It doesn't give impenetrable proofs that leave out intermediate steps or require a leap of intuition that an arrogant mathematician assumes you should know. It gives real-world applications. It contains short, interesting bios on the giants in the field. It provides excellent exercises that lead you step-by-step into deeper thinking. This book is the best intro, bar none. If you have a child in the middle school or high school who likes math, this is a book they will love. The earlier a child can master these concepts, the more likely he or she will be to internalize the abstract thinking processes involved, giving a real advantage in tackling a host of problems in physics, computer science, networking, engineering, genetics and on and on. This is not to say that a 6th grader is going to pick the book up and read it cover to cover like it was Harry Potter. Some parental assistance and encouragement will be required. But, if a child has mastered this book by some point in high school, the sky is the limit. The only knock is that it does not provide answers to the exercises - the text says they can be found on the web (on the Wiley web site), but when I click on the links I have been unable to get to the answers. This should be fixed. Nevertheless, the book is truly a 5-star work. Kudos to the three authors - well done!

I am a professor of electrical engineering. I recently started working on a research project involving encryption. I assigned the task to one of my students who needed a lot of deep-math help which threw us into the ocean of group theory, finite fields, cyclotomic polynomials, oh man! You name it. I must have checked out 20 books from the library and tried to scrape one topic from this book, one from that. Wikipedia this, google that. I also desperately needed to learn deep reasons of the simplest concepts, the way gauss and legendre visualized it. Every, I mean, EVERY book, written by big shots at big schools were hopeless !!! You could learn barely two, three subjects from the best ones, since you were familiar with the subject anyway ! Due to the desperate previous attempts to learn it from other pathetic books !!!,... Then came this book. I could not put this book down. Although the authors sometimes overdo the explanations, I am forgiving all of it. One thing is superior with this book: the authors' analogies in explaining difficult topics. Every single analogy is well thought of and nails the concept into your brain permanently. These three authors are the Euler, Gauss, and Sophie Germain of math education . They can teach my cat what a quadratic residue is. These authors should write another 50 books explaining all other difficult topics in math. We will advance 10x in this century.

There seems to be an unwritten rule that mathematics texts must be written in a turgid theorem/proof formatwhere the presentation is cold and mechanical. In my opinion, many mathematics texts are snobby and elitist; written by authors who dare not stray from the mainstream by showing a sense of humor and making their subjects fun and interesting.Morris Kline wrote a very interesting book "Why the Professor Can't Teach" that goes into detail into why thisapproach to teaching and textbook writing has become the standard approach. I am happy to say that this textbookbreaks the standard mold and makes this subject interesting and relevant. The book is also rigorous in thesense that it is still a college level mathematics textbook and not bedtime reading. The book also uses humor and cartoons effectively to teach and explain.Of course, someone with a deep interest in mathematics will have to go much further than this book and will require a more rigorous treatment. However, this book does no harm and no one will have to unlearn anything presented here. It would be a great complement to other more standard texts on this material and is a great stepping stonefor those who want a easier path to success in advanced number theory.In summary a great first book on number theory. Highly recommended !

The best book on the subject but no answers in book.Answers are referred to WEB but do not give the site address to obtain them.

Un libro maravilloso para introducirse en el fascinante mundo de la teoria de numeros. Con gran cantidad de ejemplos y anecdotas. Muy recomendable.

Satistified with quality of the book and delivery time.