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Rational Homotopical Models and Uniqueness (Memoirs of the American Mathematical Society)
Martin Majewski
Manufacturer: American Mathematical Society
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ASIN: 0821819208 |
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Covers and Envelopes in the Category of Complexes of Modules (Research Notes in Mathematics Series)
J.R. Garcia Rozas
Manufacturer: Chapman & Hall/CRC
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ASIN: 158488004X |
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Over the last few years, the study of complexes has become increasingly important. To date, however, most of the research is scattered throughout the literature or available only as lecture notes. Covers and Envelopes in the Category of Complexes of Modules collects these scattered notes and results into a single, concise volume that provides an account of recent developments in the theory and presents several new and important ideas. The author introduces the theory of complexes of modules using only elementary tools-making the field more accessible to non-specialists. He focuses the study on envelopes and covers in this category with respect to some well established and important classes of complexes. He places particular emphasis on DG-injective and DG-projective complexes and flat and DG-flat covers. Other topics covered include Zorn's Lemma for categories, preserving and reflecting covers by functors, orthogonality in the category of complexes, Gorenstein injective and projective complexes, and pure sequences of complexes. Along with its value as a collection of recent work in the field, Covers and Envelopes in the Category of Complexes of Modules presents powerful new ideas that will undoubtedly advance homological methods. Mathematicians-especially researchers in module theory and homological algebra-will welcome this volume as a reference guide and for its new and important results.
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Geometric Models for Noncommutative Algebra (Berkeley Mathematics Lecture Notes, V. 10)
Ana Cannas da Silva , and
Alan Weinstein
Manufacturer: American Mathematical Society
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ASIN: 0821809520 |
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The volume is based on a course, "Geometric Models for Noncommutative Algebras" taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras.
Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids.
Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics)
Giovanni Landi
Manufacturer: Springer
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Binding: Unknown Binding
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ASIN: 354014949X |
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These notes arose from a series of introductory seminars on noncommutative geometry the author gave at the University of Trieste. They are mainly an introduction to Connes' noncommutative geometry and could serve as a "first aid kit" before one ventures into the beautiful but bewildering landscape of Connes' theory. The main difference with other available introductions to Connes' work is the emphasis on noncommutative spaces seen as concrete spaces. Important examples of noncommutative spaces are provided by noncommutative lattices. The latter the are subject of intensive work the author is doing in collaboration with others. These notes are also meant to be an introduction to this research.
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Logic and Algebra (Contemporary Mathematics)
Manufacturer: American Mathematical Society
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ASIN: 082182984X |
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Model Theory and Linear Extreme Points in the Numerical Radius Unit Ball (Memoirs of the American Mathematical Society)
Michael A. Dritschel , and
Hugo J. Woerdeman
Manufacturer: American Mathematical Society
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ASIN: 0821806513 |
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This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented:
A complete description of the linear extreme points of the $n\times n$ matrix (numerical radius) unit ball
Several equivalent characterizations of matricial extremals in the unit ball; that is, those members which do not allow a nontrivial extension remaining in the unit ball
Applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks
In addition, an explicit construction for unitary 2-dilations of unit ball members is given, Ando's characterization of the unit ball is further developed, and a study of operators satisfying $|A| - \textnormal{Re} (e^{i\theta}A)\geq 0$ for all $\theta$ is initiated.
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Model Theory of Fields (Lecture Notes in Logic, 5)
Dave Marker ,
M. Messmer , and
Anand Pillay
Manufacturer: Springer
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ASIN: 3540607412 |
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The model theory of fields is a fascinating subject stretching from Tarski's work on the decidability of the theories of the real and complex fields to Hrushovksi's recent proof of the Mordell-Lang conjecture for function fields. This volume provides an insightful introduction to this active area, concentrating on connections to stability theory.
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- A fantastic, accessible survey
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Model Theory, Algebra and Geometry
Manufacturer: Cambridge University Press
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ASIN: 0521780683 |
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Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. It provides a unifying framework for the understanding of old results and more recently has led to significant new results, such as a proof of the Mordell-Lang conjecture for function fields in positive characteristic. Perhaps surprisingly, it is sometimes the most abstract aspects of model theory that are relevant to those applications. This book gives the necessary background for understanding both the model theory and the mathematics behind the applications. Aimed at graduate students and researchers, it contains introductory surveys by leading experts covering the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations), and introducing and discussing the diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) to which the model theory is applied. The book begins with an introduction to model theory by David Marker. It then broadens into three components: pure model theory (Bradd Hart, Dugald Macpherson), geometry(Barry Mazur, Ed Bierstone and Pierre Milman, Jan Denef), and the model theory of fields (Marker, Lou van den Dries, Zoe Chatzidakis).
Customer Reviews:
A fantastic, accessible survey.......2007-09-03
If you know a few of the ideas of model theory and want to know what the subject does today this fast-paced survey is the book for you. If you want just the most exciting current results look at van den Dries TAME TOPOLOGY AND O-MINIMAL STRUCTURES. Either way you will have to know some algebra and analysis.
In principle this book introduces model theory. I don't know how well it would work as an absolutely first look at the subject. Years ago I read a few hundred pages of Chang and Keisler MODEL THEORY. I.e. half of it. That classic, great, and now dated book is still indispensable to mastery of the subject. And it gives a fuller account of the very first steps than this one so beginners should probably look at both. The books written in between by Hodges, Poizat, and Marker seem to have virtues largely in between these two -- so you might as well read these two first: the classic Chang and Keisler, and the brisk up to date Haskell et al.
This one surveys the latest most exciting work in model theory, and it is exciting indeed. At the hands of Macintyre, van den Dries, Hrushovski and others model theory has focussed less on models of powerful foundational theories (notably arithmetic, and set theory) where Goedel incompleteness puts strong limits on how simple and thorough the results can ever be. It now focusses more on exploring the extremely nice and useful properties of structures *definable* in elegant weaker models (paradigmatically: algebraically closed fields like the complex numbers, and real closed fields like the real numbers; but also p-adic fields with deep applications in number theory).
The basic ideas go back to Tarski's use of "quantifier elimination" but the direction has shifted radically. Tarski's main purpose for this technique was to give a decision routine for elementary algebra. He found an algorithm for taking any formula in the first-order theory of the real field and eliminating the quantifiers one-by-one to get an equivalent but quantifier-free formula without adding any free variables. If the first formula was a sentence then the resulting sentence is trivially either provable or refutable, so this gives a decision routine (albeit far from efficient).
But put it another way: Tarski showed that any subset of the real numbers which is definable at all in the first order theory, is definable by finitely many equations and inequalities. It does not need quantifiers. Every such set is a finite number of intervals (counting an isolated point as an interval, and including unbounded intervals like all real numbers greater than 0).
Of course set theory can define much "wilder" subsets of the real line, including ones with all kinds of difficult properties that an earlier generation called "pathologies"--e.g. non-measurable subsets. Tarski's result shows that all the subsets *definable in* elementary algebra are "tame." Van den Dries noticed that this implies very strong constraints on all the subsets of n-dimensional real space R^n that can be defined in the first order theory, and indeed very nice constraints, and that it all lifts to much more general contexts. In great generality, *definable* sets are "tame."
Van den Dries's ideas grew from model theory but Lawvere and others emphasized the relation to the "tame topology" proposed in Grothendieck's "Esquisse d'un Programme" (Sketch of a Program). You can read the esquisse (in English) in Leila Schneps and Pierre Lochak eds. GEOMETRIC GALOIS ACTIONS.
This became a powerful idea. Very often the specific structures we want to know about in algebra and geometry can be defined within models of suitable first order theories, where "suitable" means that all such definable structures are "tame." Many set-theoretic complications are ruled out by just looking at the first-order definable cases and this has penetrating useful consequences.
So Macintyre sees a time when model theory will be re-named definability theory. In this book van den Dries quotes Hrushovski's proposal that "model theory = the geography of tame mathematics" (p. 38).
This book introduces that perspective including "stability" and "o-minimality" and applications in number theory. You may even want to refer to the more specialized chapters only as needed, while focussing on the general accounts of model theory, classical results on fields, o-minimality, and stability.
This is a more conceptual, unified subject than model theory a la Chang and Keisler. One line on the back of the book harks back to the older view: "Perhaps surprisingly, it is sometimes the most abstract aspects of model theory" that have important applications. From the current viewpoint it could, and should, say instead "Happily, it is often the most conceptual and least technical aspects of model theory..." Again, the massive Chang and Keisler remains indispensable for full mastery of the field, but there has been real progress.
The subject has become clearer and so more suited to a brilliant concise survey like this.
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Stable Groups (Mathematical Surveys and Monographs)
Bruno Poizat
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Hardcover
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ASIN: 0821826859 |
Book Description
This is the English translation of the book originally published in 1987. It is a faithful reproduction of the original, supplemented by a new Foreword and brought up to date by a short postscript. The book gives an introduction by a specialist in contemporary mathematical logic to the model-theoretic study of groups, i.e., into what can be said about groups, and for that matter, about all the traditional algebraic objects.
The author introduces the groups of finite Morley rank (those satisfying the most restrictive assumptions from the point of view of logic), and highlights their resemblance to algebraic groups, of which they are the prototypes. (All the necessary prerequisites from algebraic geometry are included in the book.) Then, whenever possible, generalizations of properties of groups of finite Morley type to broader classes of superstables and stable groups are described.
The exposition in the first four chapters can be understood by mathematicians who have some knowledge of logic (model theory). The last three chapters are intended for specialists in mathematical logic.
Book Description
Dark omens shadow the romance of Edgar, Master of Ravenwood, and Lucy Ashton, daughter of the man who through force dispossessed the Ravenwood family of their ancestral home. Scott's gothic romance weaves the personal and historic in a tale of love and revenge set amidst the political factionalism of Scotland after the Act of Union of 1707. With a text drawn from the "Magnum" edition of 1830, this annotated edition also includes an appendix on relevant Scottish history and a glossary of Scots words and legal terminology.
Download Description
Few have been in my secret while I was compiling these narratives, nor is it probable that they will ever become public during the life of their author. Even were that event to happen, I am not ambitious of the honoured distinction, digito monstrari. I confess that, were it safe to cherish such dreams at all, I should more enjoy the thought of remaining behind the curtain unseen, like the ingenious manager of Punch and his wife Joan, and enjoying the astonishment and conjectures of my audience. Then might I, perchance, hear the productions of the obscure Peter Pattieson praised by the judicious and admired by the feeling, engrossing the young and attracting even the old; while the critic traced their fame up to some name of literary celebrity, and the question when, and by whom, these tales were written filled up the pause of conversation in a hundred circles and coteries. This I may never enjoy during my lifetime; but farther than this, I am certain, my vanity should never induce me to aspire.
Customer Reviews:
Love's Course.......2007-04-10
I read the biography of Anna Cora Mowatt, "Lady of Fashion." As the brightest theatre star of the 1840s-1850s, she starred in a stage version of "The Bride of Lammermoor." In addition to the opera, there were two stage adaptations of Scott's novel. I haven't been able to locate either of the stage versions, but I did check out Scott's book to read the story.
This is a tale that keeps your interest throughout. I found the Scottish dialect a bit hard to wade through although I "ken" understand it for the most part. Oddly, the first chapter starts with the tale of Dick Tinto who apparently relates this story to our narrator. Tinto is referred to in one other place in the novel. However, his story appears attached and unrelated to what comes after.
The tale of Lord Ravenswood and the demise of his family's fortune is an interesting one. Lucy Ashton's attachment to him happens quickly and seems as if it were enchanted. Alice, the old blind woman who foretells the lovers' fate, is a rich and vibrant character. The servant Caleb is hilarious as he manufactures excuses why the best food and accommodations cannot be given to Ravenswood's guests, even to the point of breaking empty bottles as he enters a room and then using that as an excuse for not having wine to serve. Lady Ashton seems to be more controlling than alert, missing all of the signals of her daughter's mental state nor particularly caring about them. The story's outworking after the wedding with Ravenswood's disappearance into the mist is likewise strange, with both he and his horse forever gone. I enjoyed this book, its gothic castles, the hunt, the commonfolk and the political alliances.
The novel written in 1819 holds up remarkably well 188 years later. Scott paces the unfolding of the adventure well, keeping the reader wanting to reach for one more chapter to uncover the next incident. While we never stop rooting for the lovers, we know that love's course never did run smooth! Enjoy!
A classic that remains interesting in the present, while becoming more interesting as a historical piece........2007-03-16
By the end of this novel, I was leaving late for things because I had trouble putting it down, even though I knew how it ended. I cannot say if it is too predictable or not: being a classic people are always giving away the plot, and even Scott did that in his introduction, Even if he hadn't, it was adapted into an opera, which was discussed on a program I saw recently. If you have managed to get to the story without knowing the plot, you may wish to skip the introduction by Scott and anyone else until the end.
I found it not only a good narrative, but an unexpectedly complicated one. Scott seems somewhat ambivalent about many of the issues that he addresses and gives multiple points of view from the aristocrats to the peasantry. Thus, one can see a certain nostalgic glamor to the continuance of an ancient noble house in possession of its estates, the deserving qualities of the rising people who displace them, and also the resentment and poverty of the peasants. It is sometimes humorous and frequently cynical. His ambivalence towards his characters in interesting. This was a historical novel set over 100 years before when it was first written. Scott had as one of his purposes the recording of traditional Scottish customs, and this adds considerably to the interest and charm of the book. There is an appendix in this edition containing a timeline for the novel and Scottish history that I recommend that anyone not familiar with the time and place read first.
I thoroughly enjoyed this novel, although it has features that I know will put off some readers. Fortunately or unfortunately, the novel includes a small number of notes by Scott, designated in the text by numbers. Some are important for understanding, some just seem to afford the opportunity to whimsically throw in the odd tale or song. The editor has added an enormous number of notes, some of them essential, some a bit of a distraction while reading. There is also an extensive, and in my case necessary, glossary of Scots. One of the things that impressed me about the writing is that even with flipping back to the notes and glossary so frequently, the narrative still gripped my interest. Some readers may find this intolerable, I leave it to each to decide their own tastes.
This edition also contains a brief biography and a chronology of Sir Walter Scott. Variations of this novel were published, this is described as the "Magnum Opus" version. A note on the text is included.
I have also been told told, by authentic natives of Scotland, that the language and the people are definitely referred to as Scots and as Scottish or Scotch. Whatever!
A good one to start with.......2001-01-12
Sir Walter Scott was once considered the equal of Shakespeare by some. His influence on 19th century literature was immense. What's more, he still offers good reading. You might not know it from the typical undergraduate British literature survey text, though, where he is likely to be neglected in favor of writers more fashionable today.
I had to read Scott on my own -- fired by the enthusiasm of C. S. Lewis, whose essay on Scott in SELECTED LITERARY ESSAYS is warmly recommended. The first one I read, Kenilworth, wasn't all that good. Better were The Antiquary, Redgauntlet, Rob Roy, The Heart of Midlothian, and Waverley. This novel, The Bride of Lammermoor, is a good one to start with -- being not as long as many of his masterpieces. I suggest the first-time reader skip to the second chapter and start there. Be independent! Find out for yourself why your great-great-great grandparents loved this guy. If you like a warm-hearted storyteller, you should look into Sir Walter.
Gothic chills and local flavour.......2000-03-19
A rather weird novel that does not lack local flavour and even comical characters is the result of Scott's excursion into gothic style of writing. The atmosphere of the novel is perfectly eerie. Falling down residences, a mad old woman, the shadow of death on Lammermoor from the beginning. A feud between to families in which the Ashtons, have taken over all the possessions of the Ravenswoods, forces Edgar, the only offspring of that ill-fated house, to live in the decaying Wolf's Crag. A grim prophecy foretells his end, if he ever should ride to Ravenswood (now inhabited by the Ashton's, among others the gentle Lucy). And, last but not least, he himself senses that he will never by happy. It is no surprise that the dreamer Lucy falls in love with this dark hero after he has saved her and her father from an angry bull. It is clear from the very beginning that this love can only end in despair, madness and death. Which is, in my opinion, not a flaw of the book, but one of the things that make it special. - Even Lucy and Edgar must know that their love will never come to a good end, but yet they follow the path of their destiny; they can not help themselves. It is that sense of doom that makes the instants at the fountain so precious and moving, or the moment where the lightening illuminates the profiles of the lovers in Edgar's derelict castle. The characters try to act, but in one way or the other are manipulated by Lady Ashton. She IS fate, or much more nemesis. Her "victims" don't have a chance. But the book has more to offer than just a tale of stark tragedy. Scott draws vivid pictures of his characters, for example Caleb (Edgar's faithful old servant) - and plays with the his rough humour against the sombre background. Or the strange people of the village and the weird women in the graveyard who must have been characteristic for rural Scotland in Scott's day. All in all it is a capturing book one is not likely to forget so soon.
Indispensible edition of a flawed classic.......1997-11-06
Scott's venture into the gothic genre is problematic, but Bride of Lammermoor is strikingly effective in creating suspense and unease within the framework of a crucial period in Scottish history. The Edinburgh edition's return of the novel to its original pre-Union setting casts fascinating new light on Scott's intentions.
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Bride of Lammermoor
Patrick Montague Smith
Manufacturer: Dutton Adult
ProductGroup: Book
Binding: Hardcover
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ASIN: 0460001299 |
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- Read Scott. Then Listen to Donizetti. Move From THE BRIDE OF LAMMERMOOR to LUCIA DI LAMMERMOOR.
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The Bride Of Lammermoor: The Works Of Sir Walter Scott
Walter, Sir Scott
Manufacturer: Kessinger Publishing
ProductGroup: Book
Binding: Paperback
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ASIN: 076618773X |
Book Description
1905. Sir Walter Scott was a master of diverse talents. He was a man of letters, a dedicated historian and historiographer, a well-read translator of foreign texts, and a talented poet. Deriving most of his material from his native Scotland, its history and its legends, Scott invented and mastered what we know today as the historical novel. Dark omens shadow the romance of Edgar, Master of Ravenwood, and Lucy Ashton, daughter of the man who through force dispossessed the Ravenwood family of their ancestral home. Scott's gothic romance weaves the personal and historic in a tale of love and revenge set amidst the political factionalism of Scotland after the Act of Union of 1707. See the many other works by this author available from Kessinger Publishing.
Customer Reviews:
Read Scott. Then Listen to Donizetti. Move From THE BRIDE OF LAMMERMOOR to LUCIA DI LAMMERMOOR........2007-08-21
Librettists and composers were quick to note how readily the plots and vivid scenes of the poems and novels of Sir Walter Scott lent themselves to reinterpretation as operas. Indeed since 1811 there have been at least 85 operas or musical dramas based on Scott. Only Shakespeare has inspired more. By far the best known and most frequently heard today is Gaetano Donizetti's 1835 LUCIA DI LAMMERMOOR. Five other composers also turned Scott's 1819 THE BRIDE OF LAMMERMOOR into song.
January 25 and 26, 2007 Asheville Lyric Opera and The Opera Company of North Carolina will stage LUCIA DI LAMMERMOOR (see [...]). I am encouraging friends and students of my coming introductory course on Sir Walter Scott to be at Diana Wortham Theatre in the heart of Asheville for this production.
But first they should read the novel.
THE BRIDE OF LAMMERMOOR is one of Walter Scott's five or six best romances, and by common accord his most tightly woven and scripted. It is based on real history, a tragedy whose otherwise depressingly sad ending Sir Walter felt obliged to respect. But that two innocent lovers, Edgar Ravenswood and Lucy Ashton, met such unmerited doom cried out to the young future Cardinal John Henry Newman almost as an affront to the justice of God. Newman felt the same way about Romeo and Juliet and Hamlet's Ophelia. The opera focuses on the love story and for dramatic purposes ignores, compresses or changes anything else in Scott's novel that gives political or historical background, context or motivation.
The background is this in the earliest Scott editions (later shifted a few years ahead in time; my references below are to the first edition). Anne Stuart has been on the thrones of Scotland and England since 1702 and will soon, after 1707, be Queen of the brand new United Kingdom in which Scotland will cease to be an independent nation. Many Scots were scheming that on her anticipated death without children, her nephew James Francis Edward Stuart (The Old Pretender) would succeed to the throne.
Scott's novel is set in Lammermoor, in the southeast of Scotland. Wolfscrag, a lonely tower above "the German Sea" is the last remaining property of the once powerful, ancient noble family of Ravenswood. Not many miles away is its old castle and intervening square miles of farms and woods now in the hands of an anti-Royalist upstart Sir William Ashton, a political trimmer and lawyer who has legally but unfairly dispossessed Sir Alan Ravenswood. A convinced Presbyterian, Sir William as local magistrate also approved efforts to break up the illegal Episcopalian burial service for the broken hearted Lord of Ravenswood. The son, Edgar Ravenswood, vows revenge but falls in love with Lucy Ashton, Sir William's daughter. Both Edgar and Sir William attempt a reconciliation.
Lucy's mother Eleanor, a haughty Douglas, is off visiting London and friends of Queen Anne. In that permissive atmosphere Edgar and Lucy secretly promise each other by tokens and in writing to be true to each other and to marry when they can. Eleanor, catching wind of developments, rushes home and forces Lucy to marry an amiable rich heir of Eleanor's choosing.
Odds being strong that many readers of this review have not yet read THE BRIDE OF LAMMERMOOR, I will speak no more of the small steps over the intervening year that lead almost inevitably to Lucy's stabbing her unwanted husband on their coerced wedding night and her collapse into madness -- all forcefully staged by Donizetti.
Religion, politics and superstition also play huge roles in this novel (rigorously ignored in the opera). Not for nothing do some scholars call Sir Walter Scott father not just of the historical novel but of the political novel as well. And THE BRIDE OF LAMMERMOOR shows how great men and women of Scotland heartlessly move Edgar Ravenswood and Lucy Ashton across a chessboard of high politics. As for religion, Lady Eleanor's trump card against her daughter's pledge to Edgar is a text from NUMBERS XXX: 2 -5 forbidding a daughter to honor a pledge unless her father consents (which the henpecked Sir William would like to do but dares not in opposition to his consort).
This novel is intensely Scottish and Sir Walter says: "this would not be a Scottish story, unless it manifested a tinge of Scottish superstition" (Vol. II. Ch. 9). There are at least four witches actively in play, several legends and dire prophecies. There are signs and omens.
And in the person of impoverished Edgar's steward, Caleb Balderstone, Scott has created one of his four or five greatest comic figures. Caleb lies, bluffs and pretends to the world that his young master is wealthy, powerful and revered. Caleb pretends, for instance, toward novel's end, that Wolfscrag is burning down, so that he can later explain the poverty-induced absence of portraits, furniture and tapestry. Rebuked by his usually indulgent master, Caleb retorts in broad lowland Scots: "Fir for shame, your honour! ... it fits an auld carle like me weel eneugh to tell lees for the credit of the family, but it wadna beseem the like o' your honour's sell" (Vol. II. Ch.12).
Read the novel. Then listen to the Deutschegrammophon DVD of Joan Sutherland singing Lucia at the Met on November 13, 1982. Time permitting, come to Western North Carolina in January 2008 and watch it all come together live at Asheville Civic Opera.
It does not get any better than this: Scott plus Donizetti.
-OOO-
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BRIDE OF LAMMERMOOR
SCOTT
Manufacturer: BLACK
ProductGroup: Book
Binding: Hardcover
ASIN: B000SAFDHW |
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