Number Theory An Introduction to Mathematics - Coppel, W.A.; SpringerLink (Online service) (New York, NY : Springer New York, 2009)
"Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study. From the reviews: "This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics." -Canadian Mathematical Society "As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work." -Mathematical Association of America
The Expanding Universe of Numbers -- Divisibility -- More on Divisibility -- Continued Fractions and Their Uses -- Hadamard's Determinant Problem -- Hensel's -adic Numbers -- The Arithmetic of Quadratic Forms -- The Geometry of Numbers -- The Number of Prime Numbers -- A Character Study -- Uniform Distribution and Ergodic Theory -- Elliptic Functions -- Connections with Number Theory.
Keywords: MATHEMATICS; NUMBER THEORY; MATHEMATICS; NUMBER THEORY; MATHEMATICS, GENERAL