For courses in Number Theory. Classical theory meets modern applications and outstanding exercise sets Elementary Number Theory is known for its rich exercise sets, careful and rigorous proofs, examples and applications. A full range of exercises helps students explore key concepts and push their understanding to new heights. Computational exercises and computer projects are available for Maple, Mathematica, Sage Math, and the book''s many online resources. The 7th Edition is revised throughout for a presentation that is easier to teach and to learn from, while incorporating advancements and recent discoveries in number theory. Several hundred new exercises enhance the exercise sets even further. Hallmark features of this title Proven approach Careful proofs explain and support a number of the key results of number theory. Applications are well integrated, illustrating the usefulness of the theory.
Computer exercises and projects in each section cover specific concepts or algorithms, guiding students on combining the math with their computing skills. Extensive exercise sets Diverse exercise levels include basic skills, intermediate (put concepts together and develop new results), challenging, and exercises using technology tools. Answers are provided to all odd-numbered exercises within the text, and solutions to all odd-numbered exercises are in the Student Solutions Manual. New and updated features of this title Up-to-date, engaging coverage of essential topics Expanded coverage of cryptography including Elliptic curve photography; coverage of knapsack ciphers has been removed. Also, the important notion of homomorphic encryption is introduced in this edition. Coverage of recent numerical discoveries, including four new Mersenne primes; the largest known twin primes; the evidence supporting many important conjectures, and more. Coverage of new theoretical discoveries, such as the proof of weak Goldbach conjecture and the result that there is an algorithm to multiply two n-bit integers using O (nlog2n) bit operations. A proven approach Enhanced exercise sets have been examined and improved sets even further, plus several hundred new exercises, from routine to challenging.
New computational and exploratory exercises are included. Connections with abstract algebra:The book does not assume prior knowledge of abstract algebra, but introduces some basic algebraic structures such as groups, rings, and fields. Available resources for the 7th Edition are posted on the Pearson media servers here. Features of Pearson eText for the 7th Edition Now available as a Pearson eText. This new interactive version of the book provides many interactive applets that can be used by students for some common computations in number theory and to help understand concepts and explore conjectures. A collection of cryptographic applets is provided along with algorithms for computations in number theory, These include applets for encryption, decryption, cryptanalysis, and cryptographic protocols, addressing both classical ciphers and the RSA cryptosystem. Cryptographic applets can be used for individual, group, and classroom activities. Learn more about Pearson eText.