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A Compact Study of Numbers by William Thomas Miller Pdf
Individuals and groups reading the Scriptures for their own enrichment can find appropriate guides for Genesis and Exodus. Numbers is another matter. The complexities of ritual laws, holy days, moral codes, and conflicts experienced by Moses and the people during their forty years in the wilderness form a daunting maze. Average readers, especially Christians, are often unsure of the inner logic of the regulations or of how to apply the sound theology found therein. This compact study starts with Numbers, following the story from exodus to the wilderness. The format is Socratic, asking as many step-by-step questions as seems reasonable and providing the answers at the back to encourage note taking and discussion beforehand. The forty years of strife depict the deep spiritual stresses experienced by the Chosen People (and by God), and can serve our own understanding for surviving challenges as a people called by God. Another lesson is the significant role of ancient Jewish laypeople within their system of ritual and prayer. They did much more than simply watch priests handle altar sacrifices and incense. A better understanding of that ancient teamwork in worship can aid our own modern worship customs.
A Compact Study of Leviticus by William Thomas Miller Pdf
Beginners scanning Leviticus will find much detail about rituals and sinful situations, but little enlightening context or rationale. This study explores how scholars imagine that these rituals and moral laws made sense to those living back then, even though many of these early rituals and customs have been discontinued or replaced by consensus with alternative forms of worship. The authors seem to be unquestioningly devout, and quite realistic about life at the same time. Everyone shared in rituals of faith at home, at shrines, or in Jerusalem; everyone honored the proper food and eligibility regulations, and everyone was called to the common code of justice. Likewise, most everyone knew at least the temptation to shirk religious duties; they understood the lure of trying to contact other gods, ones more lenient or at least easier to understand; and they could be inclined to look the other way at improper romances, or quick but dishonest chances to get a bigger slice of the pie. The Covenant was not a deal made by saints. It was a cry for help from sinners, a cry for help for which they had not earned the right. The same is true for us believers even now.
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.
Itpzf}JlOV, li~oxov uoq>ZUJlCJ. 7:WV Al(JX., llpoj1. AE(Jj1. The first part of this volume is based on a course taught at Princeton University in 1961-62; at that time, an excellent set ofnotes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by ChevaIley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very welt It contained abrief but essentially com plete account of the main features of c1assfield theory, both local and global; and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I inc1uded such a treatment of this topic. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. In fact, I have adhered to it rather c10sely at some critical points.
Compact Manifolds with Special Holonomy by Dominic D. Joyce Pdf
This is a combination of a graduate textbook on Reimannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It contains much new research and many new examples.
In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual interested in exploring the vast universe of numbers.
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.
Handbook of Topological Fixed Point Theory by Robert F. Brown,Massimo Furi,L. Gorniewicz,Boju Jiang Pdf
This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory. This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
Classes of Linear Operators Vol. I by Israel Gohberg,Seymor Goldberg,Marinus Kaashoek Pdf
After the book "Basic Operator Theory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first.
THE COMMUNE OF LONDON AND OTHER STUDIES by J. H. ROUND M.A. Pdf
The paper which gives its title to this volume of unpublished studies deals with a subject of great interest, the origin of the City Corporation. In my previous work, ‘Geoffrey de Mandeville’ (1892), and especially in the Appendix it contains on ‘The early administration of London,’ I endeavoured to advance our knowledge of the government and the liberties of the City in the 12th century. In the present volume the paper entitled “London under Stephen” pursues the enquiry further. I have there argued that the “English Cnihtengild” was not the governing body, and have shown that it did not, as is alleged, embrace a religious life by entering Holy Trinity Priory en masse. The great office of “Justiciar of London,” created, as I previously held, by the charter of Henry I., is now proved, in this paper, to have been held by successive citizens in the days of Stephen. The communal movement, which, even under Stephen, seems to have influenced the City, attained its triumph under Richard I.; and the most important discovery, perhaps, in these pages is that of the oath sworn to the Commune of London. From it we learn that the governing body consisted at the time of a Mayor and “Échevins,” as in a continental city, and[x] that the older officers, the Aldermen of the Wards, had not been amalgamated, as has been supposed, with the new and foreign system. The latter, I have urged, is now represented by the Mayor and Common Council. That this communal organization was almost certainly derived from Normandy, and probably from Rouen, will, I think, be generally admitted in the light of the evidence here adduced. This conclusion has led me to discuss the date of the “Établissements de Rouen,” a problem that has received much attention from that eminent scholar, M. Giry. I have also dwelt on the financial side of London’s communal revolution, and shown that it involved the sharp reduction of the ‘firma’ paid by the City to the Crown, the amount of which was a grievance with the citizens and a standing subject of dispute. The strand connecting the other studies contained in this volume is the critical treatment of historical evidence, especially of records and kindred documents. It is possible that some of the discoveries resulting from this treatment may not only illustrate the importance of absolute exactitude in statement, but may also encourage that searching and independent study of ‘sources’ which affords so valuable an historical training, and is at times the means of obtaining light on hitherto perplexing problems. The opening paper (originally read before the Society of Antiquaries) is a plea for the more scientific study of the great field for exploration presented by our English place-names. Certain current beliefs on the settlement of the English invaders are based, it is here urged, on nothing but the rash conclusions[xi] of Kemble, writing, as he did, under the influence of a now abandoned theory. In the paper which follows, the value of charters, for the Norman period, is illustrated, some points of ‘diplomatic’ investigated, and the danger of inexactitude revealed. Finance, the key to much of our early institutional history, is dealt with in a paper on “The origin of the Exchequer,” a problem of long standing. On the one hand, allowance is here made for the personal equation of the author of the famous ‘Dialogus de Scaccario,’ and some of his statements critically examined, with the result of showing that he exaggerates the changes introduced under Henry I., by the founder of his own house, and that certain alleged innovations were, in truth, older than the Conquest. On the other, it is shown that his treatise does, when carefully studied, reveal the existence of a Treasury audit, which has hitherto escaped notice. Further, the office of Chamberlain of the Exchequer is traced back as a feudal serjeanty to the days of the Conqueror himself, and its connection with the tenure of Porchester Castle established, probably, for the first time. The geographical position of Porchester should, in this connection, be observed. In two papers I deal with Ireland and its Anglo-Norman conquest. The principal object in the first of these is to show the true character of that alleged golden age which the coming of the invaders destroyed. It is possible, however, of course, that a “vast human shambles” may be, in the eyes of some, an ideal condition for a country. Mr. Dillon, at least, has consistently described the Soudan, before our conquest,[xii] as “a comparatively peaceful country.”[1] In the second of these papers I advance a new solution of the problem raised by the alleged grant of Ireland, by the Pope, to Henry II. As to this fiercely contested point, I suggest that, on the English side, there was a conspiracy to base the title of our kings to Ireland on a Papal donation of the sovereignty of the island, itself avowedly based on the (forged) “donation of Constantine.” No such act of the Popes can, in my opinion, be proved. Even the “Bull Laudabiliter,” which, in the form we have it, is of no authority, does not go so far as this, while its confirmation by Alexander III. is nothing but a clumsy forgery. The only document sent to Ireland, to support his rights, by Henry II. was, I here contend, the letter of Alexander III. (20th September, 1172), approving of what had been done. That he sent there the alleged bull of Adrian, and that he did so in 1175, are both, I urge, although accepted, facts without foundation.[2] The method adopted in this paper of testing the date hitherto adopted, and disproving it by the sequence of events, is one which I have also employed in “The Struggle of John and Longchamp (1191).” The interest of this latter paper consists in[xiii] its bearing on the whole question of historic probability, and on the problem of harmonising narratives by four different witnesses, as discussed by Dr. Abbott in his work on St. Thomas of Canterbury. This is, perhaps, the only instance in which I have found the historic judgment and the marvellous insight of the Bishop of Oxford, if I may venture to say so, at fault; and it illustrates the importance of minute attention to the actual dates of events. Another point that I have tried to illustrate is the tendency to erect a theory on a single initial error. In “The Marshalship of England” I have shown that the belief in the existence of two distinct Marshalseas converging on a single house rests only on a careless slip in a coronation claim (1377). A marginal note scribbled by Carew, under a misapprehension, in the days of Elizabeth, is shown (p. 149) to be the source of Professor Brewer’s theory on certain Irish MSS. Again, the accepted story of the Cnihtengild rests only on a misunderstanding of a mediæval phrase (p. 104). Stranger still, the careless reading of a marginal note found in the works of Matthew Paris has led astray the learned editors of several volumes in the Rolls Series, and has even been made, as I have shown in “the Coronation of Richard I.,” the basis of a theory that a record of that event formerly existed, though now wanting, in the Red Book of the Exchequer.
Number Theory with an Emphasis on the Markoff Spectrum by Andrew Pollington,William Moran Pdf
Presenting the proceedings of a recently held conference in Provo, Utah, this reference provides original research articles in several different areas of number theory, highlighting the Markoff spectrum.;Detailing the integration of geometric, algebraic, analytic and arithmetic ideas, Number Theory with an Emphasis on the Markoff Spectrum contains refereed contributions on: general problems of diophantine approximation; quadratic forms and their connections with automorphic forms; the modular group and its subgroups; continued fractions; hyperbolic geometry; and the lower part of the Markoff spectrum.;Written by over 30 authorities in the field, this book should be a useful resource for research mathematicians in harmonic analysis, number theory algebra, geometry and probability and graduate students in these disciplines.
Author : A. A. Ashour,A.-S. F. Obada Publisher : World Scientific Page : 412 pages File Size : 45,9 Mb Release : 2001 Category : Mathematics ISBN : 9789812810243
Mathematics and the 21st Century by A. A. Ashour,A.-S. F. Obada Pdf
The Conference on "Mathematics and the 21st Century" was held in Cairo, Egypt during the period 15-20 January 2000. The conference's sessions consisted of plenary lectures and topical sessions. Some of the plenary lectures covered general fields such as: rewriting the history of mathematics; education of mathematics; relation between mathematics and sciences; and mathematical aspects of transportation.