This is the first-ever book on computational group theory. It provides extensive and up-to-date coverage of the fundamental algorithms for permutation groups with reference to aspects of combinatorial group theory, soluble groups, and p-groups where appropriate. The book begins with a constructive introduction to group theory and algorithms for computing with small groups, followed by a gradual discussion of the basic ideas of Sims for computing with very large permutation groups, and concludes with algorithms that use group homomorphisms, as in the computation of Sylowsubgroups. No background in group theory is assumed. The emphasis is on the details of the data structures and implementation which makes the algorithms effective when applied to realistic problems. The algorithms are developed hand-in-hand with the theoretical and practical justification.All algorithms are clearly described, examples are given, exercises reinforce understanding, and detailed bibliographical remarks explain the history and context of the work. Much of the later material on homomorphisms, Sylow subgroups, and soluble permutation groups is new.

Compositional Choices and Meaning in the Vocal Music of J. S. Bach collects seventeen essays by leading Bach scholars. The authors each address in some way such questions of meaning in J. S. Bach's vocal compositions-including his Passions, Masses, Magnificat, and cantatas-with particular attention to how such meaning arises out of the intentionality of Bach's own compositional choices or (in Part IV in particular) how meaning is discovered, and created, through the reception of Bach's vocal works. And the authors do not consider such compositional choices in a vacuum, but rather discuss Bach's artistic intentions within the framework of broader cultural trends-social, historical, theological, musical, etc. Such questions of compositional choice and meaning frame the four primary approaches to Bach's vocal music taken by the authors in this volume, as seen across the book's four parts: Part I: How might the study of historical theology inform our understanding of Bach's compositional choices in his music for the church (cantatas, Passions, masses)? Part II: How can we apply traditional analytical tools to understand better how Bach's compositions were created and how they might have been heard by his contemporaries? Part III: What we can understand anew through the study of Bach's self-borrowing (i.e., parody), which always changed the earlier meaning of a composition through changes in textual content, compositional characteristics, the work's context within a larger composition, and often the performance context (from court to church, for example)? Part IV: What can the study of reception teach us about a work's meaning(s) in Bach's time, during the time of his immediate successors, and at various points since then (including our present)? The chapters in this volume thus reflect the breadth of current Bach research in its attention not only to source study and analysis, but also to meanings and contexts for understanding Bach's compositions.

The official publication of the American Bach Society, Bach Perspectives pioneers new areas of research into the life, times, and music of the master composer. In Volume 10 of the series, Matthew Dirst edits a collection of groundbreaking essays exploring various aspects of Bach's organ-related activities. Lynn Edwards Butler reconsiders Bach's report on Johann Scheibe's organ at St. Paul's Church in Leipzig. Robin Leaver clarifies the likely provenance and purpose of a collection of chorale harmonizations copied in Dresden. George Stauffer investigates the ways various independent trio movements served Bach as an artist and teacher. In separate contributions, Christoph Wolff and Gregory Butler seek the origins of concerted Bach cantata movements spotlighting the organ and propose family trees of both parent works and offspring. Finally, Matthew Cron provides a broad cultural frame for such pieces and notes how their components engage in a larger discourse about the German Baroque organ's intimation of heaven.

Compositional Choices and Meaning in the Vocal Music of J. S. Bach collects seventeen essays by leading Bach scholars. The authors each address in some way such questions of meaning in J. S. Bach's vocal compositions-including his Passions, Masses, Magnificat, and cantatas-with particular attention to how such meaning arises out of the intentionality of Bach's own compositional choices or (in Part IV in particular) how meaning is discovered, and created, through the reception of Bach's vocal works. And the authors do not consider such compositional choices in a vacuum, but rather discuss Bach's artistic intentions within the framework of broader cultural trends-social, historical, theological, musical, etc. Such questions of compositional choice and meaning frame the four primary approaches to Bach's vocal music taken by the authors in this volume, as seen across the book's four parts: Part I: How might the study of historical theology inform our understanding of Bach's compositional choices in his music for the church (cantatas, Passions, masses)? Part II: How can we apply traditional analytical tools to understand better how Bach's compositions were created and how they might have been heard by his contemporaries? Part III: What we can understand anew through the study of Bach's self-borrowing (i.e., parody), which always changed the earlier meaning of a composition through changes in textual content, compositional characteristics, the work's context within a larger composition, and often the performance context (from court to church, for example)? Part IV: What can the study of reception teach us about a work's meaning(s) in Bach's time, during the time of his immediate successors, and at various points since then (including our present)? The chapters in this volume thus reflect the breadth of current Bach research in its attention not only to source study and analysis, but also to meanings and contexts for understanding Bach's compositions.

As the official publication of the American Bach Society, Bach Perspectives has pioneered new areas of research in the life, times, and music of Bach since its first appearance in 1995. In a series long known for its major essays by leading Bach scholars and performers, Bach Perspectives, Volume 6 is no exception. This volume opens with Joshua Rifkin's seminal study of the early source history of the B-minor orchestral suite. It not only elaborates on Rifkin's discovery that the work in its present form for solo flute goes back to an earlier version in A minor, ostensibly for solo violin, but also takes this discovery as the point of departure for a wide-ranging discussion of the origins and extent of Bach's output in the area of concerted ensemble music. Jeanne Swack presents an enlightening comparison of Georg Phillip Telemann's and Bach's approach to the French overture as concerted movements in their church cantatas, and Steven Zohn views the B-minor orchestral suite from the standpoint of the "concert en ouverture," responding to Rifkin by suggesting that the early version of the B-minor orchestral suite may also have been scored for flute.