MOMENTAN AUSVERKAUFT
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Product Identifiers
PublisherSpringer New York
ISBN-100387942904
ISBN-139780387942902
eBay Product ID (ePID)540186
Product Key Features
Number of PagesXii, 184 Pages
Publication NameElements of Algebra : Geometry, Numbers, Equations
LanguageEnglish
Publication Year1994
SubjectGeometry / General, Number Theory, Algebra / General
TypeTextbook
AuthorJohn C. Stillwell
Subject AreaMathematics
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover
Dimensions
Item Height0.2 in
Item Weight36 Oz
Item Length9.2 in
Item Width6.1 in
Additional Product Features
Edition Number3
Intended AudienceScholarly & Professional
LCCN94-010085
Dewey Edition20
Reviews"...The book is written in a very clear and pleasing style. Each of the 9 chapters of the book concludes with a section called "Discussions", which contains very interesting and valuable historical information and comments on the topics presented in the respective chapter. We strongly recommend this nice volume not only to beginners but also to experts."--MATHEMATICAL REVIEWS
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal512/.02
Table Of Content1. Algebra and Geometry.- 2. The Rational Numbers.- 3. Numbers in General.- 4. Polynomials.- 5. Fields.- 6. Isomorphisms.- 7. Groups.- 8. Galois Theory of Unsolvability.- 9. Galois Theory of Solvability.- References.
SynopsisThis book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation - both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others., Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge- bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart., Algebra is abstract mathematics - let us make no bones about it - yet it is also applied mathematics in its best and purest form. It is not abstraction for its own sake, but abstraction for the sake of efficiency, power and insight. Algebra emerged from the struggle to solve concrete, physical problems in geometry, and succeeded after 2000 years of failure by other forms of mathematics. It did this by exposing the mathematical structure of geometry, and by providing the tools to analyse it. This is typical of the way algebra is applied; it is the best and purest form of application because it reveals the simplest and most universal mathematical structures. The present book aims to foster a proper appreciation of algebra by showing abstraction at work on concrete problems, the classical problems of construction by straightedge and compass. These problems originated in the time of Euclid, when geometry and number theory were paramount, and were not solved until th the 19 century, with the advent of abstract algebra. As we now know, alge bra brings about a unification of geometry, number theory and indeed most branches of mathematics. This is not really surprising when one has a historical understanding of the subject, which I also hope to impart.
LC Classification NumberQA150-272
