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Author: Percy A. Macmahon
Publisher: Forgotten Books
ISBN: 9780265854563
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Excerpt from Combinatory Analysis, Vol. 2 The ordinary partitions of Section VII are regarded, from this point of View, as essentially belonging to space of one dimension with a graphical representation in two dimensions. One generalization, taken up in Sections IX and X, considers partitions which appertain essentially to space of two dimensions, with a graphical representation in three dimensions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Percy A. Macmahon
Publisher: Forgotten Books
ISBN: 9780265854563
Category : Mathematics
Languages : en
Pages : 360
Get Book Here
Book Description
Excerpt from Combinatory Analysis, Vol. 2 The ordinary partitions of Section VII are regarded, from this point of View, as essentially belonging to space of one dimension with a graphical representation in two dimensions. One generalization, taken up in Sections IX and X, considers partitions which appertain essentially to space of two dimensions, with a graphical representation in three dimensions. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Percy Alexander MacMahon
Publisher:
ISBN:
Category : Combinations
Languages : en
Pages : 174
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Book Description
Author: Percy Alexander Macmahon
Publisher:
ISBN: 9781331941842
Category : Mathematics
Languages : en
Pages : 328
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Book Description
Excerpt from Combinatory Analysis, Vol. 1 The object of this work is, in the main, to present to mathematicians an account of theorems in combinatory analysis which are of a perfectly general character, and to shew the connexion between them by as far as possible bringing them together as parts of a general doctrine. It may appeal also to others whose reading has not been very extensive. They may not improbably find here some new points of view and suggestions which may prompt them to original investigation in a fascinating subject. Little attempt has been hitherto made either to make a general attack upon the territory to be won or to coordinate and arrange the ground that has been already gained. The combinatory analysis as considered in this work occupies the ground between algebra, properly so called, and the higher arithmetic. The methods employed are distinctly algebraical and not arithmetical The essential connecting link between algebra and arithmetic is found in the circumstance that a particular case of algebraical multiplication involves arithmetical addition. Thus the multiplication of a and a, where a, x and y are numerical magnitudes, involves the addition of the magnitudes x and y When these are integers we have the addition which is effective in combinatory analysis. This link was forged by Euler for use in the theory of the partitions of numbers. It is used here for the most general theory of combinations of which the partition of numbers is a particular case. The theory of the partition of numbers belongs partly to algebra and partly to the higher arithmetic. The former aspect is treated here. It is remarkable that in the international organization of the subject-matter of mathematics "Partitions" is considered to be a part of the Theory of Numbers, which is an alternative name for the Higher Arithmetic, whereas it is essentially a subdivision of Combinatory Analysis which is not considered to be within the purview of the Theory of Numbers. The fact is that up to the point of determining the real and enumerating Generating Functions the theory is essentially algebraical, and it is only when the actual evaluation of the coefficients in the generating functions is taken up that the methods and ideas of the Higher Arithmetic may become involved. Much has been accomplished in respect of various combinations of entities between which there are no similarities. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: P. A. Macmahon
Publisher: Forgotten Books
ISBN: 9781528581226
Category : Mathematics
Languages : en
Pages : 82
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Book Description
Excerpt from An Introduction to Combinatory Analysis My grateful thanks are due to Professor J. E. A. Steggall, m.a. For much helpful criticism during the composition of the book. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Macmahon P. A.
Publisher:
ISBN: 9780243787418
Category :
Languages : en
Pages :
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Author: Percy A. Macmahon
Publisher: Forgotten Books
ISBN: 9781330390580
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Excerpt from Combinatory Analysis, Vol. 2 Volume I of this work will not be found to overlap Netto's Combinatorik to any considerable extent. The latter excellent treatise treats for the most part of combinations of objects which are all different, and deals with many special investigations of interest concerning them. It is particularly good in the historical treatment, and the reader who desires a comprehensive account of combinatory analysis should read the Combinatorik, as well as the present book. Investigations by, amongst other writers, Weyrauch, Longchamp, Tait, Cantor, Terquem, Weiss, Metzler, Sprague, Scheck, Schroder, Steiner, Reiss, Moore, De Vries, Heffter, Kirkman, Lucas, are given by Netto, which are valuable, but are not within the scope of the task undertaken here. This has in view the presentation of processes of great generality, and of new ideas, which have not up to the present time found a place in any book in any language. This second volume commences with a detailed account of what is known concerning the algebra of the Theory of Partitions of Numbers, the point of view being that of Euler, and the first Section overlaps the Combinatorik to some extent. It does not include the investigations of Sylvester and Cayley in regard to expressions for the general coefficients in the enumerating generating functions. These are omitted as being arithmetical rather than algebraical. The reader is recommended to consult the original memoirs, and also a short account in the work of Netto. New ideas will be found in Section VII in regard to: (i) the transformation of certain series by a graphical method; (ii) the discussion of Ramanujan's important identities; (iii) the transformation of certain generating functions by means of symmetric functions; (iv) the connexion of the theory of partitions with other combinatory theories. The most important part of the volume, Sections VIII et seq., arises from basing the theory of partitions upon the theory of Diophantine inequalities. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author: Percy Alexander Macmahon
Publisher: Andesite Press
ISBN: 9781296758295
Category :
Languages : en
Pages : 366
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Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Percy Alexander MacMahon
Publisher: Nabu Press
ISBN: 9781295231485
Category :
Languages : en
Pages : 366
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Book Description
This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Author:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages : 88
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Book Description
Author: Percy Alexander Macmahon
Publisher: Andesite Press
ISBN: 9781297639449
Category :
Languages : en
Pages : 80
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Book Description
This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
