Background
Hilton, Peter John was born on April 7, 1923 in London. Son of Mortimer and Elizabeth (Freedman) Hilton.
(This classic work is now available in an unabridged paper...)
This classic work is now available in an unabridged paperback edition. Hilton and Wu's unique approach brings the reader from the elements of linear algebra past the frontier of homological algebra. They describe a number of different algebraic domains, then emphasize the similarities and differences between them, employing the terminology of categories and functors. Exposition begins with set theory and group theory, and continues with coverage categories, functors, natural transformations, and duality, and closes with discussion of the two most fundamental derived functors of homological algebra, Ext and Tor.
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(Category Theory, Homology Theory and Their Applications. ...)
Category Theory, Homology Theory and Their Applications. Proceedings of the Conference Held at the Seattle Research of the Battelle Memorial Institute, June 24 - July 19, 1968: Volume 3
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(These notes constitute a faithful record of a short cours...)
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 K-theory 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.
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(arithmetic of the integers, linear algebra, an introducti...)
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.
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(Category Theory, Homology Theory and Their Applications. ...)
Category Theory, Homology Theory and Their Applications. Proceedings of the Conference Held at the Seattle Research Center of the Battelle Memorial Institute, June 24 - July 19, 1968: Volume 1
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(Hardcover: 281 pages Publisher: Addison Wesley Publishing...)
Hardcover: 281 pages Publisher: Addison Wesley Publishing Company (January 1983) Language: English ISBN-10: 0201057131 ISBN-13: 978-0201057133 Product Dimensions: 9.6 x 7.8 x 0.7 inches Shipping Weight: 1.6 pounds
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( Homological algebra has found a large number of applica...)
Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to the field, the authors address a number of select topics and describe their applications, illustrating the range and depth of their developments. A comprehensive set of exercises is included.
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(This account of algebraic topology is complete in itself,...)
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.
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(A relaxed and informal presentation conveying the joy of ...)
A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers 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 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; Pascals Triangle and paper folding; 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. 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 or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics.
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(Since the introduction of homotopy groups by Hurewicz in ...)
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, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cell-complexes and their application to homotopy groups of complexes.
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Hilton, Peter John was born on April 7, 1923 in London. Son of Mortimer and Elizabeth (Freedman) Hilton.
Master of Arts, Oxford (England) University, England, 1948; Doctor of Philosophy, Oxford (England) University, 1950; Doctor of Philosophy, Cambridge (England) University, England, 1952; HHD (honorary), Northern Michigan U., 1977; Doctor of Science (honorary), Memorial U. Newfoundland, Canada, 1983; Doctor of Science (honorary), University Autonoma Barcelona, Spain, 1989.
Lecturer, Manchester U., England, 1948-1952;
senior lecturer, Manchester U., 1956-1958;
lecturer, Cambridge U., 1952-1955;
Mason professor pure mathematics, Birmingham U., England, 1958-1962;
professor mathematics, Cornell Univercity, 1962-1971;
professor mathematics, U. Washington, 1971-1973;
Beaumont professor, Case Western Reserve U., 1973-1982;
distinguished professor, State University of New York, Binghamton, 1982-1993;
emeritus, State University of New York, Binghamton, since 1993;
distinguished professor, U. Control Florida, Orlando, since 1993. Guest professor Swiss Federal Institute Technology, Zurich, 1966-1967, 81-82, 88-89, Courant Institute Mathematics Sciences, New York University, 1967-1968, Ohio State University, 1977, U. Autonoma, Barcelona, 1989, University de Lausanne, 1996. Mahler lecturer Australian Mathematics Society, 1997.
Visiting fellow Battelle Seattle Research Center, 1970-1971,fellow, since 1971. Co-chairman Cambridge Conference on School Mathematics 1965. Chairman of Commission applied mathematics training National Research Council, since 1977.
Secretary International Commission Mathematics Instruction, 1979-1982.
( Homological algebra has found a large number of applica...)
(Hardcover: 281 pages Publisher: Addison Wesley Publishing...)
(arithmetic of the integers, linear algebra, an introducti...)
(Since the introduction of homotopy groups by Hurewicz in ...)
(These notes constitute a faithful record of a short cours...)
(This account of algebraic topology is complete in itself,...)
(A relaxed and informal presentation conveying the joy of ...)
(This classic work is now available in an unabridged paper...)
(Category Theory, Homology Theory and Their Applications. ...)
(Category Theory, Homology Theory and Their Applications. ...)
Member American Mathematics Society, Mathematics Association American (1st vice president 1978-1980), Canada Mathematics Society, Math Society Belgium (honorary), London Mathematics Society, Cambridge Philosophical Society, Brazilian Academy Sciences (honorary).
Married Margaret Mostyn, September 14, 1949. Children: Nicholas, Timothy.