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Product Identifiers
PublisherSpringer New York
ISBN-100387953450
ISBN-139780387953458
eBay Product ID (ePID)1949063
Product Key Features
Number of PagesXxii, 450 Pages
LanguageEnglish
Publication NameGlimpses of Algebra and Geometry
SubjectGeometry / General, Number Theory, Algebra / General, Mathematical Analysis
Publication Year2002
FeaturesRevised
TypeTextbook
Subject AreaMathematics
AuthorGabor Toth
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Weight39.2 Oz
Item Length9.3 in
Item Width7 in
Additional Product Features
Edition Number2
Intended AudienceScholarly & Professional
LCCN2001-049269
ReviewsFrom the reviews of the second edition: "Toth's 'Glimpses' offer selected material that connect algebra and geometry ... . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein's famous work on the quintic and the icosahedron." (Günter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004) "The book is intended - and really manages it - to fill undergraduates with enthusiasm to reach the graduate level. ... the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. ... information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte für Mathematik, Vol. 141 (2), 2004) "The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. ... there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. ... the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003) "This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. ... Each of the chapters is a good read and the book adds up to a wholly appealing entity. ... It can be warmly recommended ... . I can well imagine that teachers ... as well as scientists ... will benefit from this carefully worked-out textbook." (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003), From the reviews of the second edition: "Totha's a?Glimpsesa? offer selected material that connect algebra and geometry a? . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Kleina's famous work on the quintic and the icosahedron." (G'nter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004) "The book is intended a? and really manages it a? to fill undergraduates with enthusiasm to reach the graduate level. a? the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. a? information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte f'r Mathematik, Vol. 141 (2), 2004) "The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. a? there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. a? the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003) "This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. a? Each of the chapters is a good read and the book adds up to a wholly appealing entity. a? It can be warmly recommended a? . I can well imagine that teachers a? as well as scientists a? will benefit from this carefully worked-out textbook." (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003), From the reviews of the second edition: "Toth's 'Glimpses' offer selected material that connect algebra and geometry … . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein's famous work on the quintic and the icosahedron." (Günter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004) "The book is intended and really manages it to fill undergraduates with enthusiasm to reach the graduate level. … the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. … information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte für Mathematik, Vol. 141 (2), 2004) "The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. … there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. … the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003) "This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. … Each of the chapters is a good read and the book adds up to a wholly appealing entity. … It can be warmly recommended … . I can well imagine that teachers … as well as scientists … will benefit from this carefully worked-out textbook." (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003), From the reviews of the second edition: "Toth's 'Glimpses' offer selected material that connect algebra and geometry ... . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein's famous work on the quintic and the icosahedron." (Günter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004) "The book is intended - and really manages it - to fill undergraduates with enthusiasm to reach the graduate level. ... the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. ... information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte für Mathematik, Vol. 141 (2), 2004) "The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. ... there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. ... the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003) "This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. ... Each of the chapters is a good read and the book adds up to a wholly appealing entity. ... It can be warmly recommended ... . I can well imagine that teachers ... as well as scientists ... willbenefit from this carefully worked-out textbook." (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003), From the reviews of the second edition:"Toth's 'Glimpses' offer selected material that connect algebra and geometry … . This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein's famous work on the quintic and the icosahedron." (Günter M. Ziegler, Zentralblatt MATH, Vol. 1027, 2004)"The book is intended and really manages it to fill undergraduates with enthusiasm to reach the graduate level. … the author presents various topics of number theory, geometry and algebra and at the same time shows their connection resp. interplay, thus making the study lively and fascinating for the reader. … information on advanced websites and films show how carefully the author has done his job. So this second edition hopefully will not be the last one." (G. Kowol, Monatshefte für Mathematik, Vol. 141 (2), 2004)"The text covers a wide range of topics and gives a taste of advanced material in number theory, geometry and algebra, particularly where these fields overlap. … there are plenty of references for the interested reader who wishes to pursue a particular topic in greater depth. … the accessibility of the format and the flow of the material combine to create an entertaining and informative work. I recommend the text as a good read for mathematicians of all specialities. " (Stephen Lucas, The Australian Mathematical Society Gazette, Vol. 30 (4), 2003)"This is the second, much revised and augmented edition of the book originally published in 1998. It intends to close the gap between undergraduate and graduate studies in number theory, classical geometry and modern algebra. … Each of the chapters is a good read and the book adds up to a wholly appealing entity. … It can be warmly recommended … . I can well imagine that teachers … as well as scientists … will benefit from this carefully worked-out textbook." (J. Lang, Internationale Mathematische Nachrichten, Vol. 57 (192), 2003)
Dewey Edition21
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal512/.12
Table Of Content"A Number Is a Multitude Composed of Units"--Euclid.- "... There Are No Irrational Numbers at All"--Kronecker.- Rationality, Elliptic Curves, and Fermat's Last Theorem.- Algebraic or Transcendental?.- Complex Arithmetic.- Quadratic, Cubic, and Quartic Equations.- Stereographic Projection.- Proof of the Fundamental Theorem of Algebra.- Symmetries of Regular Polygons.- Discrete Subgroups of Iso (R2).- Möbius Geometry.- Complex Linear Fractional Transformations.- "Out of Nothing I Have Created a New Universe"--Bolyai.- Fuchsian Groups.- Riemann Surfaces.- General Surfaces.- The Five Platonic Solids.- Finite Möbius Groups.- Detour in Topology: Euler-Poincaré Characteristic.- Detour in Graph Theory: Euler, Hamilton, and the Four Color Theorem.- Dimension Leap.- Quaternions.- Back to R3!.- Invariants.- The Icosahedron and the Unsolvable Quintic.- The Fourth Dimension.
Edition DescriptionRevised edition
SynopsisThe purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between number theory, classical geometry and modern algebra in a clear and easily understandable style. Over 160 computer-generated images, accessible to readers via the World Wide Web, facilitate an understanding of mathematical concepts and proofs even further., Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http: //mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problem, viii 2. As a natural continuation of the section on the Platonic solids, a detailed and complete classi'cation of ?nite Mobius ¨ groupsal ' a Klein has been given with the necessary background material, such as Cayley's theorem and the Riemann-Hurwitz relation. 3. Oneofthemostspectaculardevelopmentsinalgebraandge- etry during the late nineteenth century was Felix Klein's theory of the icosahedron and his solution of the irreducible quintic in termsofhypergeometricfunctions.Aquick,direct,andmodern approach of Klein's main result, the so-called Normalformsatz, has been given in a single large section. This treatment is in- pendent of the material in the rest of the book, and is suitable for enrichment and undergraduate/graduate research projects. All known approaches to the solution of the irreducible qu- tic are technical; I have chosen a geometric approach based on the construction of canonical quintic resolvents of the equation of the icosahedron, since it meshes well with the treatment of the Platonic solids given in the earlier part of the text. An - gebraic approach based on the reduction of the equation of the icosahedron to the Brioschi quintic by Tschirnhaus transfor- tions is well documented in other textbooks. Another section on polynomial invariants of ?nite Mobius ¨ groups, and two new appendices, containing preparatory material on the hyper- ometric differential equation and Galois theory, facilitate the understanding of this advanced material., Previous edition sold 2000 copies in 3 years; Explores the subtle connections between Number Theory, Classical Geometry and Modern Algebra; Over 180 illustrations, as well as text and Maple files, are available via the web facilitate understanding: http://mathsgi01.rutgers.edu/cgi-bin/wrap/gtoth/; Contains an insert with 4-color illustrations; Includes numerous examples and worked-out problems, This book is intended for a "bridge course" facilitating the transition between undergraduate and graduate studies. The new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz"., Glimpses of Algebra and Geometry is intended for a "Bridge Course" that facilitates the transition between undergraduate and graduate studies. This new edition includes innumerable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Mobius groups a la Klein, and a quick, direct, and modern approach to Felix Klein's "Normalformsatz."
LC Classification NumberQA299.6-433
