Hilton, Peter 19232010
Overview
Works:  163 works in 958 publications in 5 languages and 18,892 library holdings 

Genres:  Conference papers and proceedings Popular works Bibliography 
Roles:  Author, Editor, Honoree, Translator, Other, Contributor 
Classifications:  QA611, 510 
Publication Timeline
.
Most widely held works by
Peter Hilton
A mathematical tapestry : demonstrating the beautiful unity of mathematics by
Peter Hilton(
)
20 editions published in 2010 in English and held by 1,531 WorldCat member libraries worldwide
"This easytoread book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paperfolding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain handson experience constructing these models and to discover for themselves the patterns and relationships they unearth"
20 editions published in 2010 in English and held by 1,531 WorldCat member libraries worldwide
"This easytoread book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, combinatorial geometry, and group theory. Using a systematic paperfolding procedure it is possible to construct a regular polygon with any number of sides. This remarkable algorithm has led to interesting proofs of certain results in number theory, has been used to answer combinatorial questions involving partitions of space, and has enabled the authors to obtain the formula for the volume of a regular tetrahedron in around three steps, using nothing more complicated than basic arithmetic and the most elementary plane geometry. All of these ideas, and more, reveal the beauty of mathematics and the interconnectedness of its various branches. Detailed instructions, including clear illustrations, enable the reader to gain handson experience constructing these models and to discover for themselves the patterns and relationships they unearth"
General cohomology theory and Ktheory by
Peter Hilton(
)
32 editions published between 1971 and 1973 in English and held by 1,305 WorldCat member libraries worldwide
These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of Ktheory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences
32 editions published between 1971 and 1973 in English and held by 1,305 WorldCat member libraries worldwide
These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of Ktheory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences
Topological topics : articles on algebra and topology presented to Professor P.J. Hilton in celebration of his sixtieth birthday by
I. M James(
)
15 editions published in 1983 in English and held by 1,144 WorldCat member libraries worldwide
Professor Peter Hilton is one of the best known mathematicians of his generation. He has published almost 300 books and papers on various aspects of topology and algebra. The present volume is to celebrate the occasion of his sixtieth birthday. It begins with a bibliography of his work, followed by reviews of his contributions to topology and algebra. These are followed by eleven research papers concerned with various topics of current interest in algebra and topology. The articles are contributed by some of the many mathematicians with whom he has worked at one time or another. This book will
15 editions published in 1983 in English and held by 1,144 WorldCat member libraries worldwide
Professor Peter Hilton is one of the best known mathematicians of his generation. He has published almost 300 books and papers on various aspects of topology and algebra. The present volume is to celebrate the occasion of his sixtieth birthday. It begins with a bibliography of his work, followed by reviews of his contributions to topology and algebra. These are followed by eleven research papers concerned with various topics of current interest in algebra and topology. The articles are contributed by some of the many mathematicians with whom he has worked at one time or another. This book will
A course in homological algebra by
Peter Hilton(
Book
)
48 editions published between 1970 and 2012 in 3 languages and held by 1,066 WorldCat member libraries worldwide
This classic book provides a broad introduction to homological algebra, including a comprehensive set of exercises. Since publication of the first edition homological algebra has found a large number of applications in many different fields. Today, it is a truly indispensable tool in fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In this new edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. The background assumes little more than knowledge of the algebraic theories groups and of vector spaces over a field
48 editions published between 1970 and 2012 in 3 languages and held by 1,066 WorldCat member libraries worldwide
This classic book provides a broad introduction to homological algebra, including a comprehensive set of exercises. Since publication of the first edition homological algebra has found a large number of applications in many different fields. Today, it is a truly indispensable tool in fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In this new edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. The background assumes little more than knowledge of the algebraic theories groups and of vector spaces over a field
A comprehensive textbook of classical mathematics; a contemporary interpretation by
H. Brian Griffiths(
Book
)
37 editions published between 1970 and 1979 in English and held by 828 WorldCat member libraries worldwide
Arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree
37 editions published between 1970 and 1979 in English and held by 828 WorldCat member libraries worldwide
Arithmetic of the integers, linear algebra, an introduction to group theory, the theory of polynomial functions and polynomial equations, and some Boolean algebra. It could be supplemented, of course, by material from other chapters. Again, Course 5 (Calculus) aiscusses the differential and integral calculus more or less from the beginnings of these theories, and proceeds through functions of several real variables, functions of a complex variable, and topics of real analysis such as the implicit function theorem. We would, however, like to make a further point with regard to the appropriateness of our text in course work. We emphasized in the Introduction to the original edition that, in the main, we had in mind the reader who had already met the topics once and wished to review them in the light of his (or her) increased knowledge and mathematical maturity. We therefore believe that our book could form a suitable basis for American graduate courses in the mathematical sciences, especially those prerequisites for a Master's degree
Studies in modern topology by
Peter Hilton(
Book
)
17 editions published in 1968 in English and Undetermined and held by 817 WorldCat member libraries worldwide
17 editions published in 1968 in English and Undetermined and held by 817 WorldCat member libraries worldwide
Homology theory, an introduction to algebraic topology by
Peter Hilton(
Book
)
53 editions published between 1960 and 2008 in English and held by 809 WorldCat member libraries worldwide
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject
53 editions published between 1960 and 2008 in English and held by 809 WorldCat member libraries worldwide
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject
Mathematical reflections : in a room with many mirrors by
Peter Hilton(
Book
)
22 editions published between 1996 and 2012 in English and Italian and held by 771 WorldCat member libraries worldwide
The purpose of this book is to show what mathematics is about, how it is done, and what it is good for. The relaxed and informal presentation conveys the joy of mathematical discovery and insight and makes it clear that mathematics can be an exciting and engrossing activity. Frequent questions lead the reader to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that serve to illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascal's Triangle and paper folding  two topics where geometry, number theory, and algebra meet and interact; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught; these ideas are referred to throughout the text, whenever mathematical strategy and technique are at issue. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics (for mathematics students or for prospective or inservice mathematics teachers) or as enrichment for other courses. It can also be read with pleasure on its own by anyone interested in the intellectually intriguing aspects of mathematics
22 editions published between 1996 and 2012 in English and Italian and held by 771 WorldCat member libraries worldwide
The purpose of this book is to show what mathematics is about, how it is done, and what it is good for. The relaxed and informal presentation conveys the joy of mathematical discovery and insight and makes it clear that mathematics can be an exciting and engrossing activity. Frequent questions lead the reader to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that serve to illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both "pure" and "applied" mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascal's Triangle and paper folding  two topics where geometry, number theory, and algebra meet and interact; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught; these ideas are referred to throughout the text, whenever mathematical strategy and technique are at issue. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics (for mathematics students or for prospective or inservice mathematics teachers) or as enrichment for other courses. It can also be read with pleasure on its own by anyone interested in the intellectually intriguing aspects of mathematics
Structural stability, the theory of catastrophes, and applications in the sciences : proceedings of the conference held at
the Battelle Seattle Research Center, 1975 by
Peter Hilton(
Book
)
25 editions published in 1976 in English and held by 653 WorldCat member libraries worldwide
25 editions published in 1976 in English and held by 653 WorldCat member libraries worldwide
Symposium on Algebraic Topology by
Peter Hilton(
Book
)
34 editions published between 1971 and 2008 in English and Undetermined and held by 643 WorldCat member libraries worldwide
34 editions published between 1971 and 2008 in English and Undetermined and held by 643 WorldCat member libraries worldwide
Localization in group theory and homotopy theory, and related topics by
Peter Hilton(
Book
)
36 editions published between 1974 and 2008 in English and German and held by 623 WorldCat member libraries worldwide
36 editions published between 1974 and 2008 in English and German and held by 623 WorldCat member libraries worldwide
An introduction to homotopy theory by
Peter Hilton(
Book
)
35 editions published between 1953 and 1972 in English and held by 616 WorldCat member libraries worldwide
Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibrespaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cellcomplexes and their application to homotopy groups of complexes
35 editions published between 1953 and 1972 in English and held by 616 WorldCat member libraries worldwide
Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibrespaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cellcomplexes and their application to homotopy groups of complexes
A course in modern algebra by
Peter Hilton(
Book
)
27 editions published between 1974 and 1989 in English and Undetermined and held by 604 WorldCat member libraries worldwide
27 editions published between 1974 and 1989 in English and Undetermined and held by 604 WorldCat member libraries worldwide
Localization of nilpotent groups and spaces by
Peter Hilton(
Book
)
20 editions published between 1975 and 2016 in English and Dutch and held by 523 WorldCat member libraries worldwide
Notas de mathematica, 55
20 editions published between 1975 and 2016 in English and Dutch and held by 523 WorldCat member libraries worldwide
Notas de mathematica, 55
Introduction to the theory of categories and functors by
Ionel Bucur(
Book
)
14 editions published between 1968 and 1970 in English and held by 522 WorldCat member libraries worldwide
14 editions published between 1968 and 1970 in English and held by 522 WorldCat member libraries worldwide
New directions in applied mathematics : papers presented April 25/26, 1980, on the occasion of the Case centennial celebration by
Peter Hilton(
Book
)
25 editions published between 1981 and 1982 in English and Undetermined and held by 511 WorldCat member libraries worldwide
It is close enough to the end of the century to make a guess as to what the Encyclopedia Britannica article on the history of mathematics will report in 2582: "We have said that the dominating theme of the Nineteenth Century was the development and application of the theory of functions of one variable. At the beginning of the Twentieth Century, mathematicians turned optimistically to the study off unctions of several variables. But wholly unexpected difficulties were met, new phenomena were discovered, and new fields of mathematics sprung up to study and master them. As a result, except where development of methods from earlier centuries continued, there was a recoil from applications. Most of the best mathematicians of the first twothirds of the century devoted their efforts entirely to pure mathe matics. In the last third, however, the powerful methods devised by then for higherdimensional problems were turned onto applications, and the tools of applied mathematics were drastically changed. By the end of the century, the temporary overemphasis on pure mathematics was completely gone and the traditional interconnections between pure mathematics and applications restored. "This century also saw the first primitive beginnings of the electronic calculator, whose development in the next century led to our modern methods of handling mathematics
25 editions published between 1981 and 1982 in English and Undetermined and held by 511 WorldCat member libraries worldwide
It is close enough to the end of the century to make a guess as to what the Encyclopedia Britannica article on the history of mathematics will report in 2582: "We have said that the dominating theme of the Nineteenth Century was the development and application of the theory of functions of one variable. At the beginning of the Twentieth Century, mathematicians turned optimistically to the study off unctions of several variables. But wholly unexpected difficulties were met, new phenomena were discovered, and new fields of mathematics sprung up to study and master them. As a result, except where development of methods from earlier centuries continued, there was a recoil from applications. Most of the best mathematicians of the first twothirds of the century devoted their efforts entirely to pure mathe matics. In the last third, however, the powerful methods devised by then for higherdimensional problems were turned onto applications, and the tools of applied mathematics were drastically changed. By the end of the century, the temporary overemphasis on pure mathematics was completely gone and the traditional interconnections between pure mathematics and applications restored. "This century also saw the first primitive beginnings of the electronic calculator, whose development in the next century led to our modern methods of handling mathematics
Homotopy theory and duality by
Peter Hilton(
Book
)
24 editions published between 1959 and 1967 in English and held by 495 WorldCat member libraries worldwide
24 editions published between 1959 and 1967 in English and held by 495 WorldCat member libraries worldwide
Nilpotente Gruppen und nilpotente Räume : nachdiplomvorlesung gehalten am MathematikDepartement ETH Zürich 1981/82 by
Peter Hilton(
Book
)
24 editions published in 1984 in German and English and held by 462 WorldCat member libraries worldwide
24 editions published in 1984 in German and English and held by 462 WorldCat member libraries worldwide
Mathematical vistas : from a room with many windows by
Peter Hilton(
Book
)
15 editions published between 2000 and 2011 in English and held by 433 WorldCat member libraries worldwide
The goal of Mathematical Vistas is to stimulate the interest of bright people in mathematics. The book consists of nine related mathematical essays which will intrigue and inform the curious reader. In order to offer a broad spectrum of exciting developments in mathematics, topics are treated at different levels of depth and thoroughness. Some chapters can be understood completely with little background, others can be thought of as appetizers for further study. A number of BREAKS are included in each chapter. These are problems designed to test the reader's understanding of the material thus far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently
15 editions published between 2000 and 2011 in English and held by 433 WorldCat member libraries worldwide
The goal of Mathematical Vistas is to stimulate the interest of bright people in mathematics. The book consists of nine related mathematical essays which will intrigue and inform the curious reader. In order to offer a broad spectrum of exciting developments in mathematics, topics are treated at different levels of depth and thoroughness. Some chapters can be understood completely with little background, others can be thought of as appetizers for further study. A number of BREAKS are included in each chapter. These are problems designed to test the reader's understanding of the material thus far in the chapter. This book is a sequel to the authors's popular book "Mathematical Reflections" and can be read independently
Symmetry by
Hans Walser(
Book
)
7 editions published between 2000 and 2001 in English and held by 430 WorldCat member libraries worldwide
"This English edition has been prepared, with the author's cooperation, to make it available to Englishspeaking students of mathematics. The treatment is informal and the text is enriched by the presence of very illuminating diagrams. Questions are posed at fairly frequent intervals and the answers to those questions appear at the end of each chapter."
7 editions published between 2000 and 2001 in English and held by 430 WorldCat member libraries worldwide
"This English edition has been prepared, with the author's cooperation, to make it available to Englishspeaking students of mathematics. The treatment is informal and the text is enriched by the presence of very illuminating diagrams. Questions are posed at fairly frequent intervals and the answers to those questions appear at the end of each chapter."
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Related Identities
 Pedersen, Jean Other
 Instituto de Pesquisas Matemáticas de Universidade de São Paulo
 Holton, Derek Allan 1941
 James, I. M. (Ioan Mackenzie) 1928 Author Editor
 Stammbach, Urs
 Donmoyer, Sylvie Illustrator
 Battelle Seattle Research Center Organizer of meeting Editor
 Griffiths, H. Brian (Hubert Brian) Author
 Wylie, S. (Shaun) 19132009 Other
 Wu, YelChiang 1939
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Associated Subjects
Abelian groups Algebra Algebra, Homological Algebraic topology Catastrophes (Mathematics) Categories (Mathematics) Cryptography CW complexes Differentiable dynamical systems Duality theory (Mathematics) Engineering Enigma cipher system France Functor theory Geometrical models Geometry Geometry, Differential GeometryStudy and teaching Great Britain Group theory Hilton, Peter, Homology theory Homotopy theory Ktheory Localization theory Mathematical recreations Mathematics MathematicsStudy and teaching Nilpotent groups Oscillations Paper work Physics PolyhedraModels Secret service Stability Symmetric functions Symmetry Topological spaces Topology Underground movements, War Wake, Nancy, World War (19391945)
Alternative Names
Hilton, P.
Hilton, P. 19232010
Hilton, P. Dž.
Hilton, P. J.
Hilton, P.J., 19232010
Hilton, P. J. ((Peter J.))
Hilton, P. J. (Peter John), 1923
Hilton, P. J. (Peter John), 19232010
Hilton, P. (Peter), 1923
Hilton, Peter.
Hilton Peter 1923....
Hilton, Peter 19232010
Hilton, Peter J.
Hilton, Peter J. 19232010
Hilton, Peter John
Hilton, Peter John, 1923
Peter Hilton britischer Mathematiker
Peter Hilton britisk matematikar
Peter Hilton britisk matematiker
Peter Hilton Brits wiskundige (19232010)
Peter Hilton brittisk matematiker
Peter Hilton matemático británico
Peter Hilton matematico e crittografo inglese
Peter Hilton mathématicien britannique
Xi'erdun, 19232010
Хилтон, П. Дж..
Хилтон, П. Дж., 19232010
Хилтон, Питер.
Хилтон, Питер, 19232010
پیتر هیلتون
ピーター・ヒルトン
希尔顿, 19232010
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