Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the tex
This book grew. out of lectures given at the University of Maryland in 1979/1980. The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians of varying backgrounds. The reader is assumed to have had at least one semester of algebraic number theory (though one of my students took such a course concurrently). In particular, the following terms should be familiar: Dedekind domain, class number, discriminant, units, ramification, local field. Occasionally one needs the fact that ramification can be computed locally. However, one who has a good background in algebra should be able to survive by talking to the local algebraic number theorist. I have not assumed class field theory; the basic facts are summarized in an appendix. For most of the book, one only needs the fact that the Galois group of the maximal unramified abelian extension is isomorphic to the ideal class group, and variants of this statement. The chapters are intended to be read consecutively, but it should be possible to vary the order considerably. The first four chapters are basic. After that, the reader willing to believe occasional facts could probably read the remaining chapters randomly. For example, the reader might skip directly to Chapter 13 to learn about Zp-extensions. The last chapter, on the Kronecker-Weber theorem, can be read after Chapter 2.
Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number
Thanks to the pioneering tours of the Creole Band, jazz began to be heard nationwide on the vaudeville stages of America from 1914 to 1918. This seven-piece band toured the country, exporting for the first time the authentic jazz strains that had developed in New Orleans at the start of the 20th century. The band's vaudeville routines were deeply rooted in the minstrel shows and plantation cliches of American show business in the late 19th century, but its instrumental music was central to its performance and distinctive and entrancing to audiences and reviewers. Pioneers of Jazz reveals at long last the link between New Orleans music and the jazz phenomenon that swept America in the 1920s. While they were the first important band from New Orleans to attain national exposure, The Creole Band has not heretofore been recognized for its unique importance. But in his monumental, careful research, jazz scholar Lawrence Gushee firmly establishes the group's central role in jazz history. Gushee traces the troupe's activities and quotes the reaction of critics and audiences to their first encounters with this new musical phenomenon. While audiences often expected (and got) a kind of minstrel show, the group transcended expectations, taking pride in their music and facing down the theatrical establishment with courage. Although they played the West Coast and Canada, most of their touring centered in the heartland. Most towns of any size in Iowa, Illinois, and Indiana heard them, often repeatedly, and virtually all of their appearances were received with wild enthusiasm. After four years of nearly incessant traveling, members of the band founded or joined groups in Chicago's South Side cabaret scene, igniting the craze for hot New Orleans music for which the Windy City was renowned in the early 1920s. The best-known musicians in the group--cornetist Freddie Keppard, clarinetist Jimmy Noone and string bassist Bill Johnson--would play a significant role in jazz, becoming famous for recordings in the 1920s. Gushee effectively brings to life each member of the band and discusses their individual contributions, while analyzing the music with precision, skillful and exacting documentation. Including many never before published photos and interviews, the book also provides an invaluable and colorful look at show business, especially vaudeville, in the 1910s. While some of the first jazz historians were aware of the band's importance, attempts to locate and interview surviving members (three died before 1935) were sporadic and did little or nothing to correct the mostly erroneous accounts of the band's career. The jazz world has long known about Gushee's original work on this previously neglected subject, and the book represents an important event in jazz scholarship. Pioneers of Jazz brilliantly places this group's unique importance into a broad cultural and historical context, and provides the crucial link between jazz's origins in New Orleans and the beginning of its dissemination across the country.
For twenty years, Lawrence Dingman’s well-written, comprehensive Physical Hydrology has set standards for balancing theoretical depth and breadth of applications. Rich in substance and written to meet the needs of future researchers and experts in the field, Dingman treats hydrology as a distinct geoscience that is continually expanding to deal with large-scale changes in land use and climate. The third edition provides a solid conceptual basis of the subject and introduces the quantitative relations involved in answering scientific and management questions about water resources. The text is organized around three principal themes: the basic concepts underlying the science of hydrology; the exchange of water and energy between the atmosphere and the earth’s surface; and the land phase of the hydrologic cycle. Dingman supplies the basic physical principles necessary for developing a sound, instructive sense of the way in which water moves on and through the land; in addition, he describes the assumptions behind each analytical approach and identifies the limitations of each.
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