Elementary Methods in Number Theory (Broché)

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion of the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods.
Part Il is about multiplicative number theory, and includes two of the most famous results in mathematics : the Erdós-Selberg elementary proof of the prime number theorem, and Dirichlet's theorem on primes in arithmetic progressions. Part Ill is an introduction to three classical topics in additive number theory : Waring's problem for polynomials, Uouville's method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions.
Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of two other graduate texts : Additive Number Theory : The Classical Bases and Additive Number Theory : Inverse Problems and the Geometry of Sumsets.