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Problema y solucion M70 de las paginas 58 y 59 del libro A FIRST COURSE IN LINEAR ALGEBRA

xviii, 462 p. 25 cm

xviii, 462 p. 25 cm

We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the semigroup. The main result is that for every bound $C$ there exist, up to isomorphism, only finitely divisorial ideals $I$ such that $\mu(I)\le C$. It follows that there exist only finitely many Cohen--Macaulay divisor classes. Moreover we determine the minimal depth of all divisorial ideals and the behaviour of $\mu$ and depth in ``arithmetic progressions'' in the divisor class group. The results are generalized to more general systems of linear inequalities whose homogeneous versions define the semigroup in a not necessarily irredundant way. The ideals arising this way can also be considered as defined by the non-negative solutions of an inhomogeneous system of linear diophantine equations. We also give a more ring-theoretic approach to the theorem on minimal number of generators of divisorial ideals: it turns out to be a special instance of a theorem on the growth of multigraded Hilbert functions.

By properly specializing the parameters irreducible modules of maximal dimension for the De Concini-Kac version of the Drinfeld-Jimbo quantum algebra in type $A$ may be transformed into modules over Lusztig's infinitesimal quantum algeba. Thus obtained modules have a simple socle and a simple head, and share the same dimension as the infinitesimal Verma modules. Despite these common features we find that they are never isomorphic to infinitesimal Verma modules unless they are irreducible. The same carry over to the modular setup for the special linear groups in positive characteristic.

This course contains the notebooks for the Numerical Linear Algebra elective in USF's MSAN program, summer 2017 Numerical Linear Algebra for Coders This course is focused on the question: How do we do matrix computations with acceptable speed and acceptable accuracy? This course was taught in the University of San Francisco's Masters of Science in Analytics program, summer 2017 (for graduate students studying to become data scientists). The course is taught in Python with Jupyter Notebooks, using libraries such as Scikit-Learn and Numpy for most lessons, as well as Numba (a library that compiles Python to C for faster performance) and PyTorch (an alternative to Numpy for the GPU) in a few lessons. Accompanying the notebooks is a playlist of lecture videos, available on YouTube . If you are ever confused by a lecture or it goes too quickly, check out the beginning of the next video, where I review concepts from the previous lecture, often explaining things from a new perspective or with different illustrations, and answer questions. Getting Help You can ask questions or share your thoughts and resources using the Computational Linear Algebra category on our fast.ai discussion forums . Table of Contents The following listing links to the notebooks in this repository, rendered through the nbviewer service. Topics Covered: 0. Course Logistics ( Video 1 ) My background Teaching Approach Importance of Technical Writing List of Excellent Technical Blogs Linear Algebra Review Resources 1. Why are we here? ( Video 1 ) We start with a high level overview of some foundational concepts in numerical linear algebra. - Matrix and Tensor Products - Matrix Decompositions - Accuracy - Memory use - Speed - Parallelization & Vectorization 2. Topic Modeling with NMF and SVD ( Video 2 and Video 3 ) We will use the newsgroups dataset to try to identify the topics of different posts. We use a term-document matrix that represents the frequency of the vocabulary in the documents. We factor it using NMF, and then with SVD. - Topic Frequency-Inverse Document Frequency (TF-IDF) - Singular Value Decomposition (SVD) - Non-negative Matrix Factorization (NMF) - Stochastic Gradient Descent (SGD) - Intro to PyTorch - Truncated SVD 3. Background Removal with Robust PCA ( Video 3 , Video 4 , and Video 5 ) Another application of SVD is to identify the people and remove the background of a surveillance video. We will cover robust PCA, which uses randomized SVD. And Randomized SVD uses the LU factorization. - Load and View Video Data - SVD - Principal Component Analysis (PCA) - L1 Norm Induces Sparsity - Robust PCA - LU factorization - Stability of LU - LU factorization with Pivoting - History of Gaussian Elimination - Block Matrix Multiplication 4. Compressed Sensing with Robust Regression ( Video 6 and Video 7 ) Compressed sensing is critical to allowing CT scans with lower radiation-- the image can be reconstructed with less data. Here we will learn the technique and apply it to CT images. - Broadcasting - Sparse matrices - CT Scans and Compressed Sensing - L1 and L2 regression 5. Predicting Health Outcomes with Linear Regressions ( Video 8 ) Linear regression in sklearn Polynomial Features Speeding up with Numba Regularization and Noise 6. How to Implement Linear Regression ( Video 8 ) How did Scikit Learn do it? Naive solution Normal equations and Cholesky factorization QR factorization SVD Timing Comparison Conditioning & Stability Full vs Reduced Factorizations Matrix Inversion is Unstable 7. PageRank with Eigen Decompositions ( Video 9 and Video 10 ) We have applied SVD to topic modeling, background removal, and linear regression. SVD is intimately connected to the eigen decomposition, so we will now learn how to calculate eigenvalues for a large matrix. We will use DBpedia data, a large dataset of Wikipedia links, because here the principal eigenvector gives the relative importance of different Wikipedia pages (this is the basic idea of Google's PageRank algorithm). We will look at 3 different methods for calculating eigenvectors, of increasing complexity (and increasing usefulness!). - SVD - DBpedia Dataset - Power Method - QR Algorithm - Two-phase approach to finding eigenvalues - Arnoldi Iteration 8. Implementing QR Factorization ( Video 10 ) Gram-Schmidt Householder Stability Examples Why is this course taught in such a weird order? This course is structured with a top-down teaching method, which is different from how most math courses operate. Typically, in a bottom-up approach, you first learn all the separate components you will be using, and then you gradually build them up into more complex structures. The problems with this are that students often lose motivation, don't have a sense of the "big picture", and don't know what they'll need. Harvard Professor David Perkins has a book, Making Learning Whole in which he uses baseball as an analogy. We don't require kids to memorize all the rules of baseball and understand all the technical details before we let them play the game. Rather, they start playing with a just general sense of it, and then gradually learn more rules/details as time goes on. If you took the fast.ai deep learning course, that is what we used. You can hear more about my teaching philosophy in this blog post or this talk I gave at the San Francisco Machine Learning meetup . All that to say, don't worry if you don't understand everything at first! You're not supposed to. We will start using some "black boxes" or matrix decompositions that haven't yet been explained, and then we'll dig into the lower level details later. To start, focus on what things DO, not what they ARE. To restore the repository, download the bundle fastai-numerical-linear-algebra_-_2017-07-21_17-20-28.bundle and run: git clone fastai-numerical-linear-algebra_-_2017-07-21_17-20-28.bundle -b master Source: https://github.com/fastai/numerical-linear-algebra Uploader: fastai Upload date: 2017-07-21

Universidade Federal do ABC (UFABC) MCTB001 - Álgebra Linear (AlgLin) 1q'21 - Turmas A2 e B2 Noturno - campus Santo André Prof. Pedro Lauridsen Ribeiro Aula 1 (2.2.21) - informações sobre o funcionamento do curso. Motivação: o que são espaços vetoriais e qual a sua importância? Origem geométrica: vetores de deslocamento num espaço de pontos (espaço afim). Soma vetorial e seus axiomas. Multiplicação por escalares = fatores de escala naturais, inteiros e racionais.

The Poisson brackets for non-linear sigma models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra.

We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation method is the `atomic superposition and electron delocalization molecular orbitals theory' (ASED), using the Mulliken charge density. Very crucial algorithm is the generalized shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace extended to non-orthogonal basis set. The most important techniques for applications are the shifted equation and the seed switching method, which make the computational cost be reduced much. We, then, present some applications to electronic structure calculations with MD simulation. The applications are given to the fracture propagation in nano-scale Si crystals and the proton transfer in water.

In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including the semiring of nonnegative real numbers and all idempotent semirings. We discuss also the computational complexity of problems in interval idempotent linear algebra. In the traditional Interval Analysis problems of this kind are generally NP-hard. In the note we consider matrix equations over positive semirings; in this case the computational complexity of the problem is polynomial. Idempotent and other positive semirings arise naturally in optimization problems. Many of these problems turn out to be linear over appropriate idempotent semirings. In this case, the system of equations X=AX+B appears to be a natural analog of a usual linear system in the traditional linear algebra over fields. B. A. Carre showed that many of the well-known algorithms of discrete optimization are analogous to standard algorithms of the traditional computational linear algebra.

In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including the semiring of nonnegative real numbers and all idempotent semirings. We discuss also the computational complexity of problems in interval idempotent linear algebra. In the traditional Interval Analysis problems of this kind are generally NP-hard. In the note we consider matrix equations over positive semirings; in this case the computational complexity of the problem is polynomial. Idempotent and other positive semirings arise naturally in optimization problems. Many of these problems turn out to be linear over appropriate idempotent semirings. In this case, the system of equations X=AX+B appears to be a natural analog of a usual linear system in the traditional linear algebra over fields. B. A. Carre showed that many of the well-known algorithms of discrete optimization are analogous to standard algorithms of the traditional computational linear algebra.

pages cm

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Vector spaces and applications -- Linear transformations and their matrices -- Systems of linear equations -- Determinants: a classical approach -- Determinants: a nonclassical approach -- Structure of operators -- Chart of theorems and definitions -- Appendix A. Mathematical induction (an informal approach) -- Appendix B. Complex numbers

Maths optional book for upsc

Maths optional book for upsc

Maths optional book for upsc

Maths optional book for upsc

14

Linear Algebra Review By Professor Dave

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1Lilac Fairy Book

By Andrew Lang

Andrew Lang's Fairy Books or Andrew Lang's "Coloured" Fairy Books are a twelve-book series of fairy tale collections. Although Andrew Lang did not collect the stories himself from the oral tradition, the extent of his sources (who had collected them originally), made them an immensely influential collection, especially as he used foreign-language sources, giving many of these tales their first appearance in English. As acknowledged in the prefaces, although Lang himself made most of the selections, his wife and other translators did a large portion of the translating and telling of the actual stories. Many of them were illustrated by Henry J. Ford. Lancelot Speed also did some illustrations. (Summary from Wikipedia)

2Blue Fairy Book

By Andrew Lang

Andrew Lang's Blue Fairy Book (1889) was a beautifully produced and illustrated edition of fairy tales that has become a classic. This was followed by many other collections of fairy tales, collectively known as Andrew Lang's Fairy Books. (Wikipedia)

3Yellow Fairy Book

By Andrew Lang

"Andrew Lang's Fairy Books or Andrew Lang's "Coloured" Fairy Books are a twelve-book series of fairy tale collections. Although Andrew Lang did not collect the stories himself from the oral tradition, the extent of his sources (who had collected them originally), made them an immensely influential collection, especially as he used foreign-language sources, giving many of these tales their first appearance in English. As acknowledged in the prefaces, although Lang himself made most of the selections, his wife and other translators did a large portion of the translating and telling of the actual stories." (summary from Wikipedia)

4Red Fairy Book

By Andrew Lang

<i>The Red Fairy Book</i> is the second in a series of twelve books known as <i>Andrew Lang's Fairy Books</i> or <i>Andrew Lang's "Coloured" Books</i>. The series was immensely popular and proved of great influence in children's literature, increasing the popularity of fairy tales over tales of real life. (Summary adapted from Wikipedia)

5Green Fairy Book

By Andrew Lang

Andrew Lang's Fairy Books or Andrew Lang's "Coloured" Fairy Books constitute a twelve-book series of fairy tale collections. Although Andrew Lang did not collect the stories himself from the oral tradition, the extent of his sources, who had collected them originally (with the notable exception of Madame d'Aulnoy), made them an immensely influential collection, especially as he used foreign-language sources, giving many of these tales their first appearance in English. As acknowledged in the prefaces, although Lang himself made most of the selections, his wife and other translators did a large portion of the translating and telling of the actual stories.<br><br>"The irony of Lang's life and work is that although he wrote for a profession—literary criticism; fiction; poems; books and articles on anthropology, mythology, history, and travel ... he is best recognized for the works he did not write."<br /><br /> Many of the books were illustrated by Henry J. Ford, Lancelot Speed, and G. P. Jacomb-Hood also contributed some illustrations.

6Crimson Fairy Book

By Andrew Lang

The Crimson Fairy Book contains thirty-six stories collected from around the world and edited by Andrew Lang. Many tales in this book are translated, or adapted, from those told by mothers and nurses in Hungary; others are familiar to Russian nurseries; the Servians are responsible for some; a rather peculiarly fanciful set of stories are adapted from the Roumanians; others are from the Baltic shores; others from sunny Sicily; a few are from Finland, and Iceland, and Japan, and Tunis, and Portugal. No doubt many children will like to look out these places on the map, and study their mountains, rivers, soil, products, and fiscal policies, in the geography books. The peoples who tell the stories differ in colour; language, religion, and almost everything else; but they all love a nursery tale. The stories have mainly been adapted or translated by Mrs. Lang, a few by Miss Lang and Miss Blackley. (Summary from the preface)

7Short History of Scotland

By Andrew Lang

A Short History of Scotland is a concise introduction to the history of Scotland from Roman times to the last Jacobite rebellion, written by the author of a much longer Scottish history. (Summary by Sibella Denton.)

8Arabian Nights Entertainments

By Andrew Lang

The Arabian Nights is a collection of Perso-Arabic folk tales and other stories. The collection, or at least certain stories drawn from it (or purporting to be drawn from it), became widely known in the West from the 18th century, after it was translated from the Arabic — first into French and then into English and other European languages. The first English language edition, based on Galland's French rather than the original Arabic, rendered the title as The Arabian Nights' Entertainment - and this, or simply The Arabian Nights, has been the title by which it has been best known to English-speaking people ever since. (Summary from Wikipedia)

9Antiquary

By Andrew Lang and Sir Walter Scott

Illegitimacy, false identity, and bankruptcy are the major elements of Sir Walter Scott's 1816 novel, The Antiquary. Set in the period of the French Revolution, the novel's hero, Lovel, struggles to gain repute and the hand of his beloved despite his uncertain parentage. During these pursuits, he befriends the title's antiquary, Johnathan Oldbuck, who finds Lovel a captive audience to his scholarly studies and a tragic likeness to his own disappointments in love. Readers will discover whether Lovel's acts of bravery and courage ultimately earn him the birth and fortunes of a nobleman. (Summary by S. Kovalchik)

10Orange Fairy Book

By Andrew Lang

Andrew Lang's Fairy Books or Andrew Lang's "Coloured" Fairy Books constitute a twelve-book series of fairy tale collections. Although Andrew Lang did not collect the stories himself from the oral tradition, the extent of his sources, who had collected them originally (with the notable exception of Madame d'Aulnoy), made them an immensely influential collection, especially as he used foreign-language sources, giving many of these tales their first appearance in English. As acknowledged in the prefaces, although Lang himself made most of the selections, his wife and other translators did a large portion of the translating and telling of the actual stories.<br><br>Many of the books were illustrated by Henry J. Ford. Lancelot Speed, and G. P. Jacomb Hood also contributed some illustrations. (Summary by Wikipedia)

11Pink Fairy Book

By Andrew Lang

All people in the world tell nursery tales to their children, and the stories are apt to be like each other everywhere. A child who has read the Blue and Red and Yellow Fairy Books will find some old friends with new faces in the Pink Fairy Book. Courage, youth, beauty, kindness, have many trials, but they always win the battle; while witches, giants, unfriendly cruel people, are on the losing hand. So it ought to be, and so, on the whole, it is and will be; and that is all the moral of fairy tales. We cannot all be young, alas! and pretty, and strong; but nothing prevents us from being kind, and no kind man, woman, or beast or bird, ever comes to anything but good in these oldest fables of the world. (Summary of the Author's Preface by Elliott Miller)

12He

By Andrew Lang and Walter Herries Pollock

This book is a parody of the famous swashbuckling novel, She, by H. Rider Haggard. (summary by Neeru Iyer)<br><br>You will not think, therefore, that the respectful Liberty we have taken with your Wondrous Tale... indicates any lack of Loyalty to our Lady Ayesha.<br><br>Her beauties are beyond the reach of danger from Burlesque, nor does her form flit across our humble pages. (taken from the Dedication)<br /><br /> The characters of Editor and Publisher, who make comments throughout the story were read by: Editor – <a href="http://librivox.org/reader/3588">Neeru Iyer</a> and Publisher – <a href="http://librivox.org/reader/2506">Julie VW</a>

13Grey Fairy Book

By Andrew Lang

The tales in the Grey Fairy Book are derived from many countries — Lithuania, various parts of Africa, Germany, France, Greece, and other regions of the world. They have been translated and adapted by Mrs. Dent, Mrs. Lang, Miss Eleanor Sellar, Miss Blackley, and Miss Hang. 'The Three Sons of Hali' is from the last century 'Cabinet des Fees,' a very large collection. The French author may have had some Oriental original before him in parts; at all events he copied the Eastern method of putting tale within tale, like the Eastern balls of carved ivory. The stories, as usual, illustrate the method of popular fiction. A certain number of incidents are shaken into many varying combinations, like the fragments of coloured glass in the kaleidoscope. Probably the possible combinations, like possible musical combinations, are not unlimited in number, but children may be less sensitive in the matter of fairies than Mr. John Stuart Mill was as regards music. (Summary from the preface)

This is a children's version of Jonathan Swift's novel <i>Gulliver's Travels</i>, from the <i>Told to the Children Series</i> (published in 1910). The children's adventure story covers Gulliver's visits to the lands of Lilliput and Brobdingnag. (Summary by Laurie Anne Walden)

15Olive Fairy Book

By Andrew Lang

Andrew Lang’s Olive Fairy Book (1907) was a beautifully produced and illustrated edition of fairy tales that has become a classic. This was followed by many other collections of fairy tales, collectively known as Andrew Lang’s Fairy Books. (Summary by Wikipedia)

16Brown Fairy Book

By Andrew Lang

Andrew Lang’s Brown Fairy Book (1904) was a beautifully produced and illustrated edition of fairy tales that has become a classic. This was one of many other collections of fairy tales, collectively known as Andrew Lang’s Fairy Books. (Summary by Wikipedia)

17Violet Fairy Book

By Andrew Lang

Andrew Lang’s Violet Fairy Book (1901) was a beautifully produced and illustrated edition of fairy tales that has become a classic. This was one of many other collections of fairy tales, collectively known as Andrew Lang’s Fairy Books. (Summary by Wikipedia)

Joan of Arc is a folk heroine of France and a Roman Catholic saint. Claiming divine guidance, she led the French army to several important victories during the Hundred Years' War, which paved the way for the coronation of Charles VII of France. Captured by her enemies, she was sold to the English and put on trial for charges of "insubordination and heterodoxy". She was burned at the stake for heresy when she was 19 years old. Twenty-five years after her execution, an inquisitorial court examined the trial, pronounced her innocent, and declared her a martyr. Joan of Arc was beatified in 1909 and canonized in 1920. She is one of the patron saints of France. Most of what is known today of her story comes from the detailed court records of her trials. (Summary by timothyFR)

19Letters to Dead Authors

By Andrew Lang

With twenty two letters, addressed to various already deceased authors, Andrew Lang discusses literary subjects with his usual humour and acidity. The impulse for the writing of the letters came, almost as a joke, from the editor of the 'St. James's Gazette,' and sixteen of the letters collected in the volume appeared first in that journal. According to the author, "some of the Letters are written rather to suit the Correspondent than to express the writer's own taste or opinions"; in all of them, though, the reader will find the charming wit of their author. (Summary by Leni)

LibriVox volunteers bring you 16 readings of <em>Romance</em> by Andrew Lang, probably best known as Edward Elgar's song <em>My Love Dwelt in a Northern Land</em>. Interestingly, Lang initially refused permission for his words to be used as lyrics, and Elgar's wife Alice wrote alternative words <em>Afar, amidst the Sunny Isles</em> for the song. However, Lang later relented and gave permission for his poem to be used. <br/><br />The poem was initially published in The Century Magazine, May 1882, and this is the version recorded here. Later collections of Lang's poetry omit the third verse. (Summary by Ruth Golding)

21Stories from the Faerie Queen

By Jean Lang and Edmund Spenser

A major work by Spenser, The Faerie Queen, was published between 1590 and 1596. As an allegorical work, it can be read on many levels. According to Jeanie Lang, Spenser always looked for the beautiful and the good when he wrote. Lang said, "There are many stories in The Faerie Queen, and out of these all I have told you only eight." The eight are "Una and the Lion," "St. Gergoe and the Dragon," "Britomart and the Magic Mirror," "The Quest of Sir Gregory," "Pastorella," "Cambell and Triamond," "Marinell the Sea-Nymph's Son," and "Flormell and the Witch." - Summary by Bill Boerst

22Old Friends, Essays in Epistolary Parody

By Andrew Lang

"Every fancy which dwells much with the unborn and immortal characters of Fiction must ask itself, Did the persons in contemporary novels never meet? In so little a world their paths must often have crossed, their orbits must have intersected, though we hear nothing about the adventure from the accredited narrators. In historical fiction authors make their people meet real men and women of history—Louis XI., Lazarus, Mary Queen of Scots, General Webbe, Moses, the Man in the Iron Mask, Marie Antoinette; the list is endless. But novelists, in spite of Mr. Thackeray’s advice to Alexandre Dumas, and of his own example in “Rebecca and Rowena,” have not introduced each other’s characters" (from the Introduction). In this volume, Andrew Lang shows, what a letter from one fictional character to another might look like.

23Tales of King Arthur and the Round Table (version 2)

By Andrew Lang

The tales of King Arthur and his Knights are of Celtic origin. The Celts were the people who occupied Britain at the time when the history of the country opens, and a few words are necessary to explain why the characters in the stories act and speak as though they belonged to a later age. These stories are adapted from the Book of Romance by ANDREW LANG.<br /><br /> It is believed that King Arthur lived in the sixth century, just after the Romans withdrew from Britain, and when the Britons, left to defend themselves against the attacks of the marauding Saxons, rose and defeated them at Mount Badon, securing to themselves peace for many years. It was probably about this time that King Arthur and his company of Knights performed the deeds which were to become the themes of stories and lays for generations afterwards.<br /><br /> In olden times, it was the custom of minstrels and story-tellers to travel through the land from court to court, telling of tales of chivalry and heroism, and for many centuries the tales of King Arthur formed the stock from which the story-teller drew.<br /><br /> In this way the stories came to be handed down from father to son, in Brittany (whose people are of the same family as the Welsh) as well as in Wales and England, and by this means alone were they prevented from being lost. But in the reigns of Henry II. and Richard I., they were set down on paper, and so became literature. Before this, however, a British writer had written out some of the tales, and from him as well as from the lips of the bards and story-tellers of their own generation, the writers in the time of Henry II. were able to collect their information. One of the most famous of the books compiled by old English writers was the “Historia Britonum,” which was written (in Latin) by Geoffrey, Bishop of Asaph. It contained an account of a war which King Arthur waged in Western Europe, but made no mention of the Holy Grail.<br /><br /> From this and other books of romances compiled in England, and very largely, too, from books of French romances, Sir Thomas Malory obtained the material for his “Morte d’Arthur,” which was written in 1470. This is the most famous of the early books of Arthurian legend, and it is from the “Morte d’Arthur” that most of the stories in this book are taken. Some, however, are taken from the “High History of the Holy Graal,” translated from the French by Dr. Sebastian Evans. The language throughout has been modified with a view to making the legends more easy of study. - Summary by The introduction and BC

24Tales Of King Arthur And The Round Table

By Andrew Lang

The tales of King Arthur and his Knights are of Celtic origin. The Celts were the people who occupied Britain at the time when the history of the country opens… It is believed that King Arthur lived in the sixth century, just after the Romans withdrew from Britain… the stories came to be handed down from father to son, in Brittany (whose people are of the same family as the Welsh) as well as in Wales and England… [story-tellers altered the stories to suit their times down through the centuries] …and so in their altered and historically inaccurate form they have reached us at the present day. …Sir Thomas Malory obtained the material for his “Morte d’Arthur,” which was written in 1470. This is the most famous of the early books of Arthurian legend, and it is from the “Morte d’Arthur” that most of the stories in this book are taken…. The language throughout has been modified with a view to making the legends more easy of study. - Summary by Book Introduction and david wales

25Tales of Troy: Ulysses the Sacker of Cities

By Andrew Lang

These are short stories about the life of Ulysses, the stealing of Helen, Paris, battles, Trojan horses, and more! - Summary by Maggie Travers

26Strange Story Book

By Leonora Blanche Lang

A collection of stories compiled by the widow of the renowned children's short-story collector, Andrew Lang. She describes this as the final installment of his series of fairy stories and includes some of those stories he had not included in other collections. In the preface, she pays tribute to her husband, saying he liked old things more than new, he loved all beasts' because they were beasts', fairies, cricket and dancing. He longed to visit far away places, but hated to travel. But most of all he befriended children wherever he went and they shared stories with him. Only his own children mocked him. - Summary by Lynne Thompson

27Strange Story Book (version 2)

By Leonora Blanche Lang

This is the last book in the The Andrew Lang "Color" Fairy Books series published after his death by his wife. She wrote the stories and he had edited them before his demise. It is a collection of stories that are a bit different than the Fairy Books: still colorful and well written but telling tales about decidedly odd topics. A word of <font color="red">Caution: </font> please read the stories before your children do, some of them contain some violent imagery. - Summary by Linda Andrus

28Summer's Ending

By Andrew Lang

Andrew Lang was a Scottish poet, novelist, literary critic, and contributor to the field of anthropology. He is best known as a collector of folk and fairy tales. The Andrew Lang lectures at the University of St Andrews are named after him. - Summary by Wikipedia