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An introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and Markovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls "a rich lode of applications and research topics." 1957 edition. 37 figures.

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The construction principles of Celtic art were re-discovered in the middle of the 20th century by George Bain. Until his writing, the intricate knots, interlacings, and spirals used in illuminating The Book of Kells and in decorating craftwork and jewelry seemed almost impossible, "the work of angels." In this pioneering work, George Bain shows how simple principles, no more difficult than those used in needlecraft, were used to create some of the finest artistic works ever seen. He also explains how you can use these principles in re-creating artifacts and in creating your own Celtic designs for art and craft work or even for recreational use. Step-by-step procedures carefully introduce the simple rules and methods of Celtic knot work and the well-known designs from the great manuscripts and stone work. Later chapters build up to complex knot work, spiral work, and key pattern designs, with special coverage of alphabets and the stylized use of animals, humans, and plants. Altogether over 225 different patterns are presented for your use, with hundreds of modification suggestions, 110 historical and modern artifacts showing designs in use, a great number of letters including six complete alphabets and 25 decorative initials, and a number of animal and human figures used in the original Celtic works. Artists, students, craftspeople, even children can work with these patterns and instructions for creating dynamic designs for use in leather work, in embroidery and other needle work, in metalwork, jewelry making, card design, borders, panels, illuminations, and in countless other ways. Mathematicians will find a great deal of pleasure in the geometric principles on which the patterns are based. Art historians and others interested in studying Celtic art will find a great number of outstanding art works and the best presentation in English for understanding Celtic design.   

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Manual of the Grasses of the United States, Volume One

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This work is actually the definitive encyclopedia of United States grass life. Compiled from the U.S. National Herbarium collection, the largest of its kind in the world, it is the only complete manual of U.S. grasses available and one of the basic reference works on U.S. plant life. It catalogs and describes in detail all 1,398 numbered species in 169 numbered genera found in this country, plus 120 species in 16 genera of the so-called waifs. Professor Hitchcock is the former Chief Botanist in charge of systematic agrostology for the U.S. Department of Agriculture, by whom the work was originally published, and an internationally known authority.The heart of the book is its detailed descriptions of the family of grasses, the two main subfamilies, the tribes, genera, and species. Quick finding keys are provided for the identification of tribes and genera. Each of the species is given thorough botanical description, including various aspects of its morphology  size, shape, form of culms, blades, panicles, spikes, and flowers  and height, proper planting season, and range of distribution are noted. The Manual also outlines the common uses to which grasses are put and discusses in general terms their distribution, classification, nomenclature, and common names. The 1,199 drawings make identification of any grass species found in the United States a virtual certainty. The appended synonymy of alternate names for each species provides an authoritative taxonomy, eliminating confusion.The nature lover with no more technical equipment than a keen eye can use this manual with profit, for a glossary of botanical terms is included. Naturalists, botanists, agriculturists, and horticulturists will find it valuable as a field and research guide to virtually all the grasses that grow in this country.

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A. S. Hitchcock U.S. Dept. of Agriculture, A. S. Hitchcock

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The demands of tuning (attaining the perfect scale) and temperament (the compromises necessary for composing in every key) have challenged musicians from the earliest civilizations onward. This guide surveys these longstanding problems, devoting a chapter to each principal theory and offering a running account of the complete history of tuning and temperament. Organized chronologically, the book features a helpful glossary and numerous illustrative tables, and it requires minimal background in music theory. This new reissue is currently the only edition in print of a much-quoted classic. 9 figures. 180 tables.

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Ludwig van Beethoven (17701827), the protagonist of freedom for music, disentangled music from the control of the ruling class. In publishing his music and writing for the rising classes, Beethoven claimed freedom and expressed the emotions of the new rulers, the artists. The Eroica, Fidelio, and the piano works express the emotions of the new rulers  the intense love, the need for companionship of people, the forces that conspired to defeat the artist, and the strength and superiority of the artist in overcoming the weaknesses. The letters of Beethoven are the principal nonmusical expression of his personality in its relationship with the world of his time.In what he called the "dry letters of the alphabet," Beethoven depicted his fears, his loves, and his friendly relations: his fears of deafness and of corrupted texts by pirating printers; his loves, Bettina Brentano and Giulietta Guicciardi; and his friendly relations with Baron Zmeskall, Frau Nannette Streicher, and the music publishers Steiner and Company. He praises the poetry of Goethe and Schiller but condemns Goethe for his obeisance toward royalty. He solicits help during his perpetual trouble with his health and with his servants. He castigates publishers, sets prices for his works, and calculates letters of dedication. He expresses his love for his nephew, Carl, but documents the trouble that Carl was causing him by taking up his precious time. And although Beethoven liked to decorate the letters with musical openings and closings and an occasional song to the receiver, he increasingly signed his letters, "In haste."The 457 letters collected here are the most important of the letters of the spirit that was to shape and move a century. Explanatory notes comment upon works, on persons mentioned, and on the puns of which Beethoven was fond. The letters chronicle his business, his needs, his humor and bitterness, and his philosophy. They will give many insights into Beethoven's methods, his influences, his moods, and the conditions under which the master worked.

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Manual of the Grasses of the United States, Volume Two

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This work is actually the definitive encyclopedia of United States grass life. Compiled from the U.S. National Herbarium collection, the largest of its kind in the world, it is the only complete manual of U.S. grasses available and one of the basic reference works on U.S. plant life. It catalogs and describes in detail all 1,398 numbered species in 169 numbered genera found in this country, plus 120 species in 16 genera of the so-called waifs. Professor Hitchcock is the former Chief Botanist in charge of systematic agrostology for the U.S. Department of Agriculture, by whom the work was originally published, and an internationally known authority.The heart of the book is its detailed descriptions of the family of grasses, the two main subfamilies, the tribes, genera, and species. Quick finding keys are provided for the identification of tribes and genera. Each of the species is given thorough botanical description, including various aspects of its morphology  size, shape, form of culms, blades, panicles, spikes, and flowers  and height, proper planting season, and range of distribution are noted. The Manual also outlines the common uses to which grasses are put and discusses in general terms their distribution, classification, nomenclature, and common names. The 1,199 drawings make identification of any grass species found in the United States a virtual certainty. The appended synonymy of alternate names for each species provides an authoritative taxonomy, eliminating confusion.The nature lover with no more technical equipment than a keen eye can use this manual with profit, for a glossary of botanical terms is included. Naturalists, botanists, agriculturists, and horticulturists will find it valuable as a field and research guide to virtually all the grasses that grow in this country.

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A. S. Hitchcock U.S. Dept. of Agriculture, A. S. Hitchcock

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"There is not one page of this enchanting book which does not contain something to interest the common reader as well as the serious student. Regarded simply as a history of flowers, it adds to the joys of the country."  B. E. Todd, Spectator.If you want to know how pleurisy root, lungwort, and abscess root got their names, how poison ivy used to treat rheumatism, or how garlic guarded against the Bubonic Plague, consult A Modern Herbal. This 20th-century version of the medieval Herbal is as rich in scientific fact and folklore as its predecessors and is equally encyclopedic in coverage. From aconite to zedoary, not an herb, grass, fungus, shrub or tree is overlooked; and strange and wonderful discoveries about even the most common of plants await the reader.Traditionally, an herbal combined the folk beliefs and tales about plants, the medicinal properties (and parts used) of the herbs, and their botanical classification. But Mrs. Grieve has extended and enlarged the tradition; her coverage of asafetida, bearberry, broom, chamomile, chickweed, dandelion, dock, elecampane, almond, eyebright, fenugreek, moss, fern, figwort, gentian, Hart's tongue, indigo, acacia, jaborandi, kava kava, lavender, pimpernel, rhubarb, squill, sage, thyme, sarsaparilla, unicorn root, valerian, woundwort, yew, etc.  more than 800 varieties in all  includes in addition methods of cultivation; the chemical constituents, dosages, and preparations of extracts and tinctures, unknown to earlier herbalists; possible economic and cosmetic properties, and detailed illustrations, from root to bud, of 161 plants.Of the many exceptional plants covered in Herbal, perhaps the most fascinating are the poisonous varieties  hemlock, poison oak, aconite, etc.  whose poisons, in certain cases, serve medical purposes and whose antidotes (if known) are given in detail. And of the many unique features, perhaps the most interesting are the hundreds of recipes and instructions for making ointments, lotions, sauces, wines, and fruit brandies like bilberry and carrot jam, elderberry and mint vinegar, sagina sauce, and cucumber lotion for sunburn; and the hundreds of prescriptions for tonics and liniments for bronchitis, arthritis, dropsy, jaundice, nervous tension, skin disease, and other ailments. 96 plates, 161 illustrations.

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There is a knitting book as dependable as your own private instructor, as complete, as explicit, and equally as helpful . . . Mary Thomas's Knitting Book. It's a veritable encyclopedia of knitting, clearly and definitively explaining and illustrating every method, operation and stitch, and a good number of the patterns you are ever likely to need or use. After an engaging history of the craft and its implements, Miss Thomas carefully lays the foundation of knitting in the opening chapters  how to hold needles, wind yarn, gauge stitches, control tension, etc.  and builds gradually upon it in the following sections. These explain in lucid progression every operation in common knitting, from basic knit stitch and purl, casting on and casting off, shaping by decreases and increases to turning, triangular shapes and mitres, and knitting on the diagonal or bias. For the reader who has mastered these fundamental procedures, Miss Thomas devotes the remainder of the book to fancy knitting stitches and techniques, including color knitting by stranding and weaving; pattern weaving; knitting woven, by frame with its complement of stitches (plain, raised, rib, etc.), looped, beaded, embroidered by chart, using cross stitch, honeycomb, etc.; and making patterns for garments and working out their details (armholes, belts, buttonholes, collars, hems, necklines, pockets et al). To put what the reader learns into practice, she offers instructions and patterns for making various Shetland shawls, gloves, and socks. More than 250 technique diagrams clearly illustrate every operation and pattern as to position of hands, yarn, and needle, so the knitter will have no trouble in following along. For all knitters, whether beginner or adept, a chapter of helpful knitting hints on blocking, picking up dropped stitches, lengthening, knitting up, mending, taking-back (correcting), etc. completes these invaluable and personalized lessons.Unabridged republication of original (1938) edition.

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This handy guide provides numerous insights and shortcuts to drawing and sketching effectively. Describing mandatory skills for beginning and advanced students, the text covers such subjects as diminution, foreshortening, convergence, shade and shadow, and other visual principles of perspective drawing.Accompanying a concise and thoughtfully written text are more than 150 simply drawn illustrations that depict a sense of space and depth, demonstrate vanishing points and eye level, and explain such concepts as appearance versus reality; perspective distortion; determining heights, depths, and widths; and the use of circles, cylinders, and cones.Artists, architects, designers, and engineers will find this book invaluable in creating works with convincing perspective.

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This book contains the fruits of centuries of experience and invention in knitting and is quite possibly the best single manual of knitting patterns ever written. Turning its pages, you will see the patterns grow from simple to more elaborate. You will find this to be the best arrangement for instructional purposes as well as a demonstrations of the orderly and scientific methods on which knitting patterns are based. You will be astonished at the great beauty and variety of these patterns, and you will come to realize the potential of knitting, in practiced hands, as one of the finest of crafts.The author begins with basics, with the distinction between knit and purl sides of the fabric and the use of simple black-and-white charts to present patterns. She then introduces a new motif or design in each chapter. Charts, diagrams, and photographs are used liberally along with the text to illustrate each pattern and steps in the creation of each, with special symbols to indicate critical points, so that you can guard against going astray. The patterns range from cross and cross-over motifs through slip-stitch patterns, eyelet patterns, faggot and lace faggot stitch, bias fabrics, lace knitting, embossed motifs and patterns, medallion knitting, picot point knitting, and filet lace. Concluding chapters are devoted to seamless garments and accessories, modern garments, and ornamental uses of increasing and decreasing. There are lists of French and German knitting terms and an index of textures.Special attention is given throughout to explaining the how and why of each pattern, and the properties of each in terms of horizontal and vertical stretching so that selection of patterns can be made practically as well as aesthetically. The beginner will find this book an excellent guide and instruction manual, and the experienced knitter will find it an almost inexhaustible encyclopedia of patterns, methods, and suggestions.

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Written by a famous American painter and teacher, whose landscapes are found in many of the world's most noted museums, this book is known as one of the art student's most helpful guides. It provides a wealth of advice on the choice of subject; it tells what to look for and aim for, and explains the mysteries of color, atmospheric conditions, and other phenomena to be found in nature. Through his profound understanding of the physical nature of landscapes and his highly developed artistic sense, John Carlson is able to explain both the whys and the hows of the various aspects of landscape painting. Among the subjects covered are angles and consequent values (an insightful concept necessary for strong overall unity of design), aerial and linear perspective, the painting of trees, the emotional properties of line and mass in composition, light, unity of tone, choice of subject, and memory work. In the beginning chapters, the author tells how to make the best of canvas, palette, colors, brushes, and other materials and gives valuable advice about texture, glazing, varnishing, bleaching, retouching, and framing. Thirty-four reproductions of Mr. Carlson's own work and 58 of his explanatory diagrams are shown on pages adjoining the text. As Howard Simon says in the introduction: "Crammed into its pages are the thoughts and experiences of a lifetime of painting and teaching. Undoubtedly it is a good book for the beginner, but the old hand at art will appreciate its honesty and broadness of viewpoint. It confines itself to the mechanics of landscape painting but, philosophically, it roams far and wide. . . . This is a book to keep, to read at leisure, and to look into for the solution of problems as they arise, when the need for an experienced hand is felt."

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This little book, written at the height of his career by Josef Lhevinne, the "inward poet of the piano," is a clear statement of principles based on his lifelong experience in performance and teaching. Lhevinne was, with Rachmaninoff, Schnabel, and Hoffman, one of the great modern masters, and was the first artist invited to teach at the newly formed Julliard Graduate School of Music.Technique, through essential, must be subordinate to musical understanding. Complete knowledge of scales, apprehended not mechanically but musically; understanding of the uses of rests and silence, which Mozart considered the greatest effect in music; a feeling for rhythm and training of the ear; these are the basic elements of a thorough grounding in musicianship and are accordingly emphasized in the opening chapters.The heart of the book is devoted to the attainment of a beautiful tone. Anyone who has heard Lhevinne play or has listened to one of his recordings will know how great were his achievements in that area. The secret lay, at least in part, in the technique he called "the arm floating in air," and in the use of the wrists as natural shock absorbers. The achievement of varieties of tone, of the singing, ringing tone, of brilliancy, of delicacy, and of power are all explained in terms of a careful analysis of the ways in which the fingers, hand, wrist, arm, and indeed the whole body function in striking the keys. There are further remarks about how to get a clear staccato and an unblurred legato, about the dangers of undue emphasis on memorization and the need for variety in practicing, and special comments on the use of the pedal, which should be employed with as much precision as the keys.Throughout, specific musical examples are presented as illustrations. The author draws not only upon his own experiences and methods, but upon the examples of Anton Rubenstein and of his teacher, Safonoff, for this remarkably lucid and concise formulation of basic principles.

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Even the average knitter can now begin to knit in modern lace patterns  "Celandine," "Mosaic," "Rose Leaf," "Candlelight," "Coronet," "Valentine," "Azalea," "Primula," "Sun Ray," "English Crystal," "Springtime," "Three of Hearts"  all by well-known modern lace designer Marianne Kinzel. What is especially attractive about Mrs. Kinzel's approach is not only her fine knitted lace designs but also the comparatively short time and low cost involved in accomplishing each project.Marianne Kinzel, well known to knitters in the United Kingdom and the United States, has long been looked to for her gift for clear presentation and even more so for her ability in devising original designs. She begins with a chapter on the fundamentals of lace knitting, covering everything the average knitter needs to know to begin working in lace. Other chapters give detailed instructions for projects in two-needle, round, and square techniques. Over 25 distinctive lace projects are presented, including luncheon sets, tray and table cloths, curtains, cushion covers, chair backs, and doilies. Instructions are presented both in the traditional written method and in the chart-and-symbol method. There are keys to the charts in English, French, and German, lavish and helpful illustrations, and sound practical advice on knitting techniques, finishing, and laundering. There are also instructions on altering the patterns to your own special needs. Perfect for the beginning lace knitter or the advanced professional, Marianne Kinzel's lace patterns make well-suited gifts and items for around the home.

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The volume presents two book by Walter Gieseking, foremost pianist of his generation, and his teacher for five years, Karl Leimer, that have long been sought after by students and teachers looking for a radical approach toward developing not only finger-technique but expression-technique. Emphasis throughout is on listening to one's self and proper understanding as the basis of proper technique for the piano.In book one, originally titled The Shortest Way to Pianistic Perfection, Gieseking and Leimer work with a series of piano works  a study from Lebert and Stark, Bach's Two- and Three-Part Inventions in C, and Beethoven's Sonata in F Minor, Op. 2, No. 1. Before beginning to play, the student is asked to visualize each piece through silent reading. Through Leimer's instruction in this area the student soon discovers how to approach each piece as not merely a series of notes to memorize but as a coherent musical structure to understand. Following are instructions on natural interpretation, with consideration of touch, relaxation, and proper emphasis in the practice. Also given are notes on such topics as etudes, scales, broken chords, the trill, and tranquility.In book two, Rhythmics, Dynamics, Pedal and Other Problems of Piano Playing, Leimer carries his method of visualization further with a study of the Allemande from Bach's French Suite in E Major. Following are further exercises and practices for developing other pianistic technique with reference to works of other composers. Specific exercises which cover rhythmics, dynamics, and phrasing are designed so that they will benefit not only the pianist but also performers on other instruments. Extensive chapters on variety of touch and the pedal give a great number of techniques and exercises for extending the expressive and dynamic range.

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Terence Reese, "the world's best bridge player and best bridge writer" (The New York Times), turns his attention in this book to you, the bright beginner. He gives a complete guide to the game with sample bidding and sample game play and coverage of everything the beginner needs, from point count bidding to finesses, to make bridge the exciting, competitive game it is.Mr. Reese isn't content with presenting rules the beginner will later abandon. Instead he builds up the game in simple steps with chapters on opening bids of one, responses, defensive overcalls, opening bids of more than one, play and defense in no trump, play and defense in suit, scoring, and so on, until the game is taught as you can expect to play it against strong competition. In the course of the book you will learn the common terms used in bridge, the fundamentals of offensive and defensive bidding and play, the reasons why bridge strategies work, and how to use such popular conventions as the Blackwood and the Stayman. Altogether you will have had experience evaluating 130 normal bidding hands and playing through 18 sample games. An index and summary of bidding at the end also make the book useful as an instant reference for later use.Both the bright beginner and the player who has had some experience will want to use this book to learn the fundamentals of bridge and increase his ability to establish best possible bid and play. For a further competitive advantage and even more bridge fun, you will also want to read Reese's other bridge books, Bidding a Bridge Hand and Play Bridge with Reese.

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Special Functions for Scientists and Engineers

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Clear and comprehensive, this text provides undergraduates with a straightforward guide to special functions. It is equally suitable as a reference volume for professionals, and readers need no higher level of mathematical knowledge beyond elementary calculus. Topics include the solution of second-order differential equations in terms of power series; gamma and beta functions; Legendre polynomials and functions; Bessel functions; Hermite, Laguerre, and Chebyshev polynomials; Gegenbauer and Jacobi polynomials; and hypergeometric and other special functions. Three appendices offer convenient tabulation of principal results, and a generous supply of worked examples and problems includes some hints and solutions. 1968 edition. 25 figures.

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This is the complete orchestral and vocal score of Mozart's Don Giovanni, considered by many to be the greatest opera ever written. This edition contains all the music Mozart wrote for Don Giovanni, both for the original version performed in Prague (1787) and the alterationsDon Ottavio's aria "Dalla sua pace," Elvira's aria (and its transposition to D Major) "Mi tradi quell'alma ingrata," Zerlina and Leporello's duet "Per queste tue manine," the cut in the finale  made for the first Viennese performance six months later, as well as the concert ending of the overture.The editors, Georg Schunemann and Kurt Soldan, worked directly from Mozart's autograph manuscript and from early copies made under Mozart's supervision, correcting many errors that had persisted since Mozart's time. An extensive commentary lists all vague or controversial elements the editors encountered in the score. In addition the complete Italian libretto and stage directions by Lorenzo Da Ponte and a German translation of the vocal text by Georg Schunemann have also been included. Do not confuse this with a piano rendering; it is the full orchestral score. In addition to its obvious uses for study, this score is also an indispensable associate for anyone listening to the music. In no other manner can the listener or student keep full awareness of the many elements that make up this opera.

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Best Ghost Stories of Algernon Blackwood

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A woman of snow . . . a midnight caller keeping his promise . . . forests where Nature is deliberate and malefic . . . enchanted houses . . . these are the beings and ideas that flood through this collection of ghost stories by Algernon Blackwood (1869-1951). Altogether thirteen stories, gathered from the entire corpus of Blackwood's work, are included: stories of such sheer power and imagination that it is easy to see why he has been considered the foremost British supernaturalist of the twentieth century. Blackwood's ability to create an atmosphere of unrelieved horror and sustain it to the end of the story is almost unsurpassed. "The Willows"  which has been called by H. P. Lovecraft the finest supernatural story  is a typical example of Blackwood's art: slowly and surely Blackwood draws the reader into a world of shadows, nuances, and unearthly terror. Blackwood was also a master at evoking feelings of mysticism and cosmic experience; dealing with such ideas as interpenetrating levels of existence and pantheistic elemental powers, he expanded the content of supernatural literature enormously. But even the more traditional elements of horror stories such as ghosts and haunted houses are handled with such energy and feeling that they rise far above their predecessors. Drawing on serious Oriental thought, modern psychology, and philosophy, Algernon Blackwood introduced a sophistication to the horror story that  with few exceptions  it was devoid of before. The results are stories that are not only guaranteed to chill, but stories that have something to say to the intelligent reader.

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Arms, Uniforms and Equipment of the Union and Confederacy

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This comprehensive reference will be invaluable to anyone requiring accurate data on the Civil War period. Indispensable for identifying, describing, and understanding the use of more than 800 items, the text is arranged alphabetically by topic, with subjects ranging from artillery accouterments, heavy cannon, boats, and barracks equipment to bridge materials, a charcoal water filter, brass name stencils (to label personal equipment), and an enormous variety of weapons. Material is cross-referenced for quick location of individual entries. "Everything an interested reader would want to know . . . A must-have book."  Antiques & Auction News. Over 350 rare illustrations.

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The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.