Elementary Number Theory

Rating:
Summary: Good starting point!
Review: A few weeks ago I ordered three books about Number Theory, and this is the one I like most. I am not a beginner in maths, but I am a beginner in Number Theory. This book start with the basics, and it has exercises with answers! I think this is a good book for self-study, it is easier to read than the books from Leveque.

Rating:
Summary: Great buy for aspiring cryptographers
Review: I bought this book while studying cryptography, a field that relies heavily on Number Theory for inspiration and from which it draws many, if not most, of its constructions. Most books on Cryptography summarily relegate the relevant number-theoretic aspects to short appendices that fail to build any intuition about what is going on. This book delivers precisely what is missing: a very readable, easily accessible introduction to the main topics of number theory that leaves the reader with a much better idea of how everything fits together. The book is very well suited for self-study, and includes answers to all exercises.

It should be noted, though, that the book does not address any of the computational aspects of Number Theory that are so dear to Cryptography (e.g it's easy to take square roots mod p if p is prime, hard to take square roots mod pq unless you know p,q). This, however, does not reduce its usefulness, since such results become very easy to absorb once one has a decent understanding of number theory and its workings. To fill the computational gaps, I would suggest Dana Angluin's "Lecture Notes on the Complexity of Some Problems in Number Theory" which are freely available on the web (the 2001 LaTeX'ed version)

Rating:
Summary: Pure Joy
Review: I picked this up when I hit a small snag as I reviewed my undergraduate mathematics in order to return to graduate school for my master's in mathematics.

What started off as a small aside while reviewing another text (to recall some fundamentals, but in a rigorous way), turned into pure joy as I began a delightful excursion into "Elementary Number Theory," for its own sake, under the guidance of Jones & Jones.

Although many find Gallian and a host of others, Rudin included, to be the way to go, Jones & Jones [parallel to these authors] have a way of setting out proofs that appealed to me - for whatever that's worth.

ALL exercises have answers at the back, practically a sine qua non for all people who self-study and have to "grade" their own homework. The authors tie the relevance of the theories together without the sometimes heavy handed pop references to the Beatles, or to arcane things such as "yellow pigs." This is not to say the authors did not pay attention to the history and dates which they sprinkle in as they spin the development of the theories. Yet, they are always mindful of the mathematics which they teach and never get too cute.

It is the beauty of the number theory that is center stage, here, and like Zen, is achieved on the basis of its own elegant simplicity. But simplicity does not mean simple minded nor so brief that the authors lose the student. I felt in lock step with the authors page after page, proof after proof.

Perhaps I never understood Abstract Algebra quite well enough because I did not have as strong as grasp in elementary number theory as I should have had, but Jones & Jones certainly present the subject matter in a way that a somewhat rusty college grad could quickly sink her teeth into and enjoy. In short, this helped me close ground, but fast, while at the same time it opened my eyes to other proofs in other courses that I had committed to memory yet never full appreciated.

In any case this book was money VERY well spent and worth its modest price of admission.

Rating:
Summary: Pure Joy
Review: I picked this up when I hit a small snag as I reviewed my undergraduate mathematics in order to return to graduate school for my master's in mathematics.

What started off as a small aside while reviewing another text (to recall some fundamentals, but in a rigorous way), turned into pure joy as I began a delightful excursion into "Elementary Number Theory," for its own sake, under the guidance of Jones & Jones.

Although many find Gallian and a host of others, Rudin included, to be the way to go, Jones & Jones [parallel to these authors] have a way of setting out proofs that appealed to me - for whatever that's worth.

ALL exercises have answers at the back, practically a sine qua non for all people who self-study and have to "grade" their own homework. The authors tie the relevance of the theories together without the sometimes heavy handed pop references to the Beatles, or to arcane things such as "yellow pigs." This is not to say the authors did not pay attention to the history and dates which they sprinkle in as they spin the development of the theories. Yet, they are always mindful of the mathematics which they teach and never get too cute.

It is the beauty of the number theory that is center stage, here, and like Zen, is achieved on the basis of its own elegant simplicity. But simplicity does not mean simple minded nor so brief that the authors lose the student. I felt in lock step with the authors page after page, proof after proof.

Perhaps I never understood Abstract Algebra quite well enough because I did not have as strong as grasp in elementary number theory as I should have had, but Jones & Jones certainly present the subject matter in a way that a somewhat rusty college grad could quickly sink her teeth into and enjoy. In short, this helped me close ground, but fast, while at the same time it opened my eyes to other proofs in other courses that I had committed to memory yet never full appreciated.

In any case this book was money VERY well spent and worth its modest price of admission.

Rating:
Summary: Great buy for aspiring cryptographers
Review: I used this book as a reference book to review the basic number theory that I tend to foreget while I was in graduate school. I hope I had that book while I was undergraduate, because the all the proofs are clearly written. The exercises are all meaningful, but it will be nice to include some challenging problems. I highly recommend this book to any undergraduate or even bright high school students who want a quick introduction to number theory.

Rating:
Summary: Perfect for elementary number theory education
Review: This book delivers exactly what the title states. If you're interested in number theory, this is a great place to get started.

Rating:
Summary: Perfect for elementary number theory education
Review: This book delivers exactly what the title states. If you're interested in number theory, this is a great place to get started.