Fundamentals of Number Theory

Rating:
Summary: If you actually like number theory...
Review: ...stay away from this book. This book was required for an upper-division number theory course I took, and the teacher used it for one of our eight assignments. I assume he did this because there are few worthwhile problems in the book. The author spends too much time explaining the history behind the theorems and too little time discussing applications. He proves the theorems but the proofs make no sense to someone learning just from the book. The teacher for my course explained all of the theorems in ways that actually made sense and were easily reproducable. When studying I never looked at this book and instead used Nathanson's GTM for number theory. If you only care about the history of number theory, this book has some redeeming quality. Otherwise, stay away. Dover math books tend to be inferior to texts like UTMs and GTMs, as evidenced by the latter costing literally ten times as much sometimes.

Rating:
Summary: If you actually like number theory...
Review: ...stay away from this book. This book was required for an upper-division number theory course I took, and the teacher used it for one of our eight assignments. I assume he did this because there are few worthwhile problems in the book. The author spends too much time explaining the history behind the theorems and too little time discussing applications. He proves the theorems but the proofs make no sense to someone learning just from the book. The teacher for my course explained all of the theorems in ways that actually made sense and were easily reproducable. When studying I never looked at this book and instead used Nathanson's GTM for number theory. If you only care about the history of number theory, this book has some redeeming quality. Otherwise, stay away. Dover math books tend to be inferior to texts like UTMs and GTMs, as evidenced by the latter costing literally ten times as much sometimes.

Rating:
Summary: Good for self teaching
Review: I am currently working through this book, and I really like the format, which is usually a small, digestible chapter followed by a set of exercises (usually 10 or so). Quite a wide variety of topics are covered including congruences, primitive roots, analysis of the number theoretic functions (e.g., the number of primes below x), and a little on diophantine approximations and continued fractions. Nothing post-calculus is used in the book except for some algebraic structures such as fields and rings, however, they are fully explained at the beginning of the book. (And some previous acquaintance with these would probably be good.) The exercises are especially good, being not too easy and not too hard. In response to the review below, to actually understand math like this you must be willing to do some work yourself. If you are looking to sit back in your easy chair and be entertained, then you should buy a book on the history of number theory, not a textbook.

Rating:
Summary: Deceptive Title
Review: No concept is beyond the reach of an intelligent mind, so long as that concept is brilliantly explained. If there were a race for explanatory brilliance, this book would fall somewhere short of the starting line. For example, an appendix lists 58 mathematical symbols, (most of which you won't encounter in high school). These symbols are blithely used throughout the text, yet none is adequately explained. If you don't have calculus, statistics, trigonometry and a few other disciplines already firmly under your belt, forget this text. Of interest to all readers may be the occasional insets giving concise biographies of important mathematicians.