Elementary Number Theory and Its Applications (English Edition, 5th Edition)

Author: (USA) Rosen (Rosen, K.H.)
Publisher:
Publish Date: 2005-03-01
Features: This book is a classic textbook for number theory courses and has been highly praised by readers since its publication. It has been adopted by hundreds of top universities in the United States, such as the University of California, Berkeley, the University of Illinois, and the University of Texas. The combination of classic theory and modern applications is a major feature of this book. This edition enhances examples and exercises, bringing the applications of number theory to a higher level while updating and expanding the discussion on cryptography, a hot topic. Keeping pace with the times is another feature of this book. To elegantly integrate the latest research findings and recent theories, the author has devoted significant effort. The book is also renowned for its unique exercise arrangements. The challenging exercises included are designed to help readers explore key concepts in number theory. At the same time, it provides two types of exercises: computational problems and computer programming exercises, which enable readers to connect mathematical theory with programming skills. The core of this book is to present classic elementary number theory in a way that is both helpful for understanding and engaging. The historical context and significance of key results are recorded, and after carefully laying out the basic material for each topic, the book discusses more complex results in the same field. The main strength of this book lies in its inclusion of various applications of number theory. Once the necessary theory is established, applications are incorporated into the text in a flexible manner. These applications are designed to promote the extension of theory and illustrate the uses of elementary number theory in different aspects. Number theory is widely applied in cryptography, including classical cryptography, block ciphers, stream ciphers, public-key cryptography systems, and cryptographic protocols. Other applications in computer science include fast integer multiplication, pseudorandom numbers, and checksums. Applications in many other fields, such as scheduling, telephones, entomology, and zoology, can also be found in the textbook. This textbook includes a wide range of diverse exercises. Many routine exercises are included to train basic skills, with both odd-numbered and even-numbered problems included in this category. A large number of medium-difficulty problems help students combine several concepts to derive new results. Many other exercises or sets of exercises are designed to develop new concepts. Sufficiently challenging exercises are also included, marked with a single asterisk for difficult problems and a double asterisk for very difficult ones. Some problems include results that will be used in later chapters, marked with a finger symbol, and these exercises should be assigned by teachers when appropriate. This book includes the latest discoveries in number theory, describing the status of many unsolved problems, such as new theoretical achievements. The new discoveries about prime numbers and factorization announced in September 2004 have been included in this edition's second printing. These findings will help readers understand number theory as an extremely active research field, where they can even participate in the discovery of new primes.