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Number Theory - An Introduction via the Density of Primes (Paperback, Softcover reprint of the original 2nd ed. 2016)
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Number Theory - An Introduction via the Density of Primes (Paperback, Softcover reprint of the original 2nd ed. 2016)
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Now in its second edition, this textbook provides an introduction
and overview of number theory based on the density and properties
of the prime numbers. This unique approach offers both a firm
background in the standard material of number theory, as well as an
overview of the entire discipline. All of the essential topics are
covered, such as the fundamental theorem of arithmetic, theory of
congruences, quadratic reciprocity, arithmetic functions, and the
distribution of primes. New in this edition are coverage of p-adic
numbers, Hensel's lemma, multiple zeta-values, and elliptic curve
methods in primality testing. Key topics and features include: A
solid introduction to analytic number theory, including full proofs
of Dirichlet's Theorem and the Prime Number Theorem Concise
treatment of algebraic number theory, including a complete
presentation of primes, prime factorizations in algebraic number
fields, and unique factorization of ideals Discussion of the AKS
algorithm, which shows that primality testing is one of polynomial
time, a topic not usually included in such texts Many interesting
ancillary topics, such as primality testing and cryptography,
Fermat and Mersenne numbers, and Carmichael numbers The
user-friendly style, historical context, and wide range of
exercises that range from simple to quite difficult (with solutions
and hints provided for select exercises) make Number Theory: An
Introduction via the Density of Primes ideal for both self-study
and classroom use. Intended for upper level undergraduates and
beginning graduates, the only prerequisites are a basic knowledge
of calculus, multivariable calculus, and some linear algebra. All
necessary concepts from abstract algebra and complex analysis are
introduced where needed.
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