[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-51730-en":3,"doc-seo-51730-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},51730,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","An Introduction To The Modern Theory Of Equations","A scholarly mathematics text introducing the modern theory of equations through a pedagogical progression from elementary properties to advanced structural ideas. The preface highlights an intentional selection of topics, omitting invariants and covariants to make space for substitution elements and substitution groups, domains of rationality, and their application to equations. The author emphasizes clarity via numerous classroom-oriented exercises and acknowledges foundational results associated with mathematicians such as Abel, Galois, and Kronecker.","# AN INTRODUCTION TOTHE MOIERNTHEORY OF EQUATIONS\n\nAN INTRODUCTION TO  \n# THE MODERN\n\nTHEORY OF EQUATIONS  \nFLORIAN CAJORI,PH.D.  \nPROFRBSOR OF MATHEMATICS AT CoLORADO COLLEGE  \nNemork  \nTHE MACMILLAN COMPANYLONDON:MACMILLAN &CO.LrD,1904  \n4ZI righd rserved  \nCoPYRIGHT,1904,By THE MACMILLAN CUMPANY.  \nSet up and electrotyped Published October,I904  \n# PREFACE\n\nTHE main difference between this text and others on thesame subject,published in the English language,consists inthe selection of the material.In proceeding from the ele-mentary to the more advanced properties of equations,thesubject of invariants and covar1ants is here omitted,to makeroom for a discussion of the elements of substitut1ons andsubstitution-gioups,of domans of rationality,and of theirapplication to equations.  Thereby the reader acqures somefamiliarity with the fundamental results on tlhe theory ofequations,reached by(auss,Abel,Galois,and Kronecker.  \nThe Galos theory of equations is usually found by thebeginner to be qute difficult of comprehension.In the pres-ent text the effort is imade to render the subject more concreteby the insertion of numerous exercises.If,in the work ofthe class room,this text be found to possess any superiority,1t will be due largely to these exereises.Most of them aremy own;some are taken from the treatises named below.  \nIn the mode of presentation I can claim no originality.The following texts have been used in the preparation of thisbook:  \nBACHMANN,P.Kreistheilung Leipzig,1872.  \nBrRNSIDE,W.Theory of (1oups.Cambridge,1897.  \nBuRNSIDE,w.S,and PANTOx,A.W.Theory of Equations,Vol.I,1899;Vol.II,1901.  \nDiCK8ON,I.E.Theory of Algebraic Equations.New York,1903.EABTON,B.S.The Constructve Development of Group-Theory.Phila-delphia,1902.  \nEncyklopadie der Mathematischen Wussenschaften.  \nPREFACE  \nGALoTs,D'EvARISTE,Euores mathématiques,avec une introduction par  \nM.EMILE PICARD.Paris,1897.  \nKLEIN, F. Vorlesungen über das Ikosaeder. Leipzig, 1884.  \nMATTHIessen, L. Grundzüge der Antiken u. Modernen Algebra. Leipzig 1872zig,1878.  \nNETTO,E.Theory of Substitution8,translated by F.N.CoLE,AnnArbor,1892  \nNETTO,E.Vorlesungen uber Algebra.Leipzig,Vol.I,1896;Vol.II,1900  \nPETERSEx,J.Theorle der Algebrazschen Glezchungen.Kopenhagen,1878.  \nPIERPONT,J.Galozs'Theory on Algebraic Equatzons.Salem,1900.SALMON,G.Modern lugler Algebra.Jublin,1876.  \nSERRET,J.A.Handbuch der Hoheren Algebra.Deutsche Uebers.v.  \nG.WERTIIEIM,Lelpzig,1878.  \nToDHUNTER,I.Theory of Equations London,1880.  \nVoGT,H.Resoluton 1lgébrique des Equatuons.Paris,1895.  \nWEBER,H.Lehrbuch der Algebra.  Braunschweig,Vol.I,1898;Vol.II,1896  \nWEBER，H. Encyklopädie der Elementaren Algebra und Analysis.Leipzig,1903.  \nOf these books,some have been used more than others.Inthe elementary parts I have been influenced by the excellenttreatment found in the first volume of Burnside and Panton.In the presentation of the Galois theory I have followed thefirst volume of Weber's admrable Lehrbuch der Algebra.Nextto these,special mention of indebtedness is due to Bachmann,Netto,Serret,and Pierpont.  \nI desire also to express my thanks to Miss Edith P.Hub-bard,of the Cutler Academy,Miss Adelaide Denis,of the Col-orado Springs High School,and Mr.R.E.Powers,of Denver,for valuable suggestions and assistance in the reading of theproofs,and to Mr.W.N.Birchby,who has furnished solutionsto a large number of problems.  \nFLORIAN CAJORI.  \n# TABLE OF CONTENTS\n\n## CHAPTER I\n\nPAG,E  \nSoME ELEMENTARY PROPERTIES oF EQUATIONs,§§1-26  \n## CHAPTER II\n\nELEMENTABY TRANSFORMATIOxs ok EQUATIONs,§27-36 .   .  31  \n## CHAPTER III\n\n.   .   .  43  \nLoCATION OF THE Roo1s OF AN EQUATION,§§37-51  \n## CHAPTER IV\n\nAPPROXIMATION TO THE RooTs oF NUMERICAL EQUATIONs,S§52-58  60  \n## CHAPTER V\n\nTHE ALGEBRAIC SoLUTIOx OF TIE CuBIC AND QUARTIC,§§59-62  68  \n## CHAPTER VI\n\nSoLUTION OF BINOMIAL EQUATIONS AND RECIPROCAL EQUATIONS,§§63-67 .   .   ·   ·   ·  \n## CHAPTER VII\n\nSYMMETRIC FuNCTIONs OF THE RooTs,§§68-71 .   ·  ·  .  84  \nBumATo₀","cbCaib8u5eYMBaxa","https://ap.wps.com/l/cbCaib8u5eYMBaxa","pdf",13405588,1,264,"English","en",105,"# CHAPTER I\n## Some Elementary Properties of Equations (§§1-26)\n# CHAPTER II\n## Elementary Transformations of Equations (§§27-36)\n# CHAPTER III\n## Location of the Roots of an Equation (§§37-51)\n# CHAPTER IV\n## Approximation to the Roots of Numerical Equations (§§52-58)\n# CHAPTER V\n## The Algebraic Solution of the Cubic and Quartic (§§59-62)\n# CHAPTER VI\n## Solution of Binomial Equations and Reciprocal Equations (§§63-67)\n# CHAPTER VII\n## Symmetric Functions of the Roots (§§68-71)","[{\"question\":\"What main topic does this book introduce?\",\"answer\":\"The book presents an introduction to the modern theory of equations, moving from basic properties toward deeper methods used in solving and analyzing equations.\"},{\"question\":\"Why does the author omit invariants and covariants?\",\"answer\":\"The preface states that invariants and covariants are omitted to make room for a discussion of substitution elements and substitution groups, domains of rationality, and their applications to equations.\"},{\"question\":\"How does the book aim to make the Galois theory easier to understand?\",\"answer\":\"It uses numerous exercises to render the subject more concrete, with an emphasis on classroom usefulness and guided 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main topic does this book introduce?","Question",{"text":75,"@type":76},"The book presents an introduction to the modern theory of equations, moving from basic properties toward deeper methods used in solving and analyzing equations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does the author omit invariants and covariants?",{"text":80,"@type":76},"The preface states that invariants and covariants are omitted to make room for a discussion of substitution elements and substitution groups, domains of rationality, and their applications to equations.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the book aim to make the Galois theory easier to understand?",{"text":84,"@type":76},"It uses numerous exercises to render the subject more concrete, with an emphasis on classroom usefulness and guided 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