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Modern Computer Algebra
Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Rethinking Bach
This book a offers a multitude of provocative new perspectives on one of the most iconic composers in the Western classical tradition. Its collective rethinking of some of our most cherished narratives and deeply held beliefs about Johann Sebastian Bach will allow readers to see the man in a new light and to hear his music with new ears.
Analyzing Bach Cantatas
Bach's cantatas are among the highest achievements of Western musical art, yet studies of the individual cantatas that are both illuminating and detailed are few. In this book, noted Bach expert Eric Chafe combines theological, historical, analytical, and interpretive approaches to the cantatas to offer readers and listeners alike the richest possible experience of these works. A respected theorist of seventeenth-century music, Chafe is sensitive to the composer's intentions and to the enduring and universal qualities of the music itself. Concentrating on a small number of representative cantatas, mostly from the Leipzig cycles of 1723-24 and 1724-25, and in particular on Cantata 77, Chafe s...
Number Theory
This book contains proceedings presented at the fourth Canadian Number Theory Association conference held at Dalhousie University in July 1994. The invited speakers focused on analytic, algebraic, and computational number theory. The contributed talks represented a wide variety of areas in number theory.
Analytic Methods in the Analysis and Design of Number-theoretic Algorithms
This book makes a substantial contribution to the understanding of a murky area of number theory that is important to computer science, an area relevant to the design and analysis of number-theoretic algorithms and to the construction of cryptographic protocols.Contents: Introduction; 1: Explicit Bounds for Primality Testing; Ankeny's Theorem and its Algorithmic Consequences; Background from Analytic Number Theory; Roots; Asymptotic Theorems; Zeta-function Estimates; Numerical Theorems; Computing Bounds for Specific Moduli; Comparisons with Empirical Results; 2: The Generation of Random Factorizations; Introduction; A Method That Almost Works; Doctoring the Odds; A Factor Generation Procedure; The Complete Algorithm; 2.5 Bounds for the Number of Prime Tests; A Single-precision Time Bound; The Use of Probabilistic Primality Tests.Eric Bach received his doctorate from the University of California at Berkeley. He is currently an Assistant Professor of Computer Science at the University of Wisconsin at Madison. Analytic Methods in the Analysis and Design of Number Theoretic Algorithms is a 1984 ACM Distinguished Dissertation.
Tears into Wine
In 1714, the 29 year-old Johann Sebastian Bach was promoted to the position of concertmaster at the ducal court of Weimar. This post required him for the first time in his already established career to produce a regular stream of church cantatas-one cantata every four weeks. Among the most significant works of this period is Ich hatte viel Bekümmernis in meinem Herzen (Cantata 21). Generally known in English as "I had much affliction," Cantata 21 draws from several psalms and the Book of Revelations and offers a depiction of the spiritual ascent of the soul from intense tribulation to joy and exaltation. Although widely performed and loved by musicians, Cantata 21 has endured much criticism...
J. S. Bach's Johannine Theology
Bach's Johannine Theology: The St. John Passion and the Cantatas for Spring 1725 is a fertile examination of this group of fourteen surviving liturgical works. Renowned Bach scholar Eric Chafe begins his investigation into Bach's theology with the composer's St. John Passion, concentrating on its first and last versions. Beyond providing a uniquely detailed assessment of the passion, Bach's Johannine Theology is the first work to take the work beyond the scope of an isolated study, considering its meaning from a variety of musical and historical standpoints. Chafe thereby uncovers a range of theological implications underlying Bach's creative approach itself. Building considerably on his pre...
Handbook to Bach's Sacred Cantata Texts
The German church cantata of the eighteenth century was the culmination of a long tradition of Lutheran "sermon music" that used the proclamation, amplification, and interpretation of scripture to teach and persuade the listener. Bach's cantatas also served this didactic purpose and typically incorporate numerous allusions to scriptural passages or themes in their librettos. Unfortunately, many of these passages remain obscure to the twentieth-century musician because they demand a much closer familiarity with the Bible than is common today. The Handbook to Bach's Sacred Cantata Texts identifies scriptural references for the wording, imagery, and themes that Bach's listeners would have known. In addition, the religious or literary theme of each text is summarized within the specific context of the cantata as a whole. With interlinear translations and a full complement of indexes.
Bachanalia
An exuberant and offbeat guide to Johann Sebastian Bach's keyboard masterwork, the Well-Tempered Clavier, presents a series of forty-eight essays--one for each of the piece's fugues--that incisively illuminate one of the world's most famous musical works.
