Background
Golan, Jonathan Samuel was born on May 29, 1942 in Milwaukee. Son of Ezriel and Naomi Ruth (Bernstein) Golan. arrived in Israel, 1967.
(There is no branch of mathematics, however abstract, whic...)
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" Golan, 1992, first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .
http://www.amazon.com/gp/product/0792357868/?tag=2022091-20
(This volume provides a comprehensive and up-to-date surve...)
This volume provides a comprehensive and up-to-date survey of research on torsion theories defined on module categories over noncommutative rings and their use in the localization of rings and modules. The text places special emphasis on the results of the last ten years. Among the topics covered are: the structures on modules defined relative to a fixed torsion theory, the several endofunctors of the category of modules defined by a torsion theory, the structure of the frame of all torsion theories over a given module category and its use in characterizing rings, behavior of various torsion theories of special types, decompositions and dimensions of modules defined by torsion theories, and local cohomology relative to a torsion theory.
http://www.amazon.com/gp/product/0582998085/?tag=2022091-20
(There is no branch of mathematics, however abstract, whic...)
There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world. - Nikolai Ivanovich Lobatchevsky This book is an extensively-revised and expanded version of "The Theory of Semirings, with Applicationsin Mathematics and Theoretical Computer Science" Golan, 1992, first published by Longman. When that book went out of print, it became clear - in light of the significant advances in semiring theory over the past years and its new important applications in such areas as idempotent analysis and the theory of discrete-event dynamical systems - that a second edition incorporating minor changes would not be sufficient and that a major revision of the book was in order. Therefore, though the structure of the first «dition was preserved, the text was extensively rewritten and substantially expanded. In particular, references to many interesting and applications of semiring theory, developed in the past few years, had to be added. Unfortunately, I find that it is best not to go into these applications in detail, for that would entail long digressions into various domains of pure and applied mathematics which would only detract from the unity of the volume and increase its length considerably. However, I have tried to provide an extensive collection of examples to arouse the reader's interest in applications, as well as sufficient citations to allow the interested reader to locate them. For the reader's convenience, an index to these citations is given at the end of the book .
http://www.amazon.com/gp/product/9048152526/?tag=2022091-20
(This monograph is a continuation of several themes presen...)
This monograph is a continuation of several themes presented in my previous books 146, 149. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak 185: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.
http://www.amazon.com/gp/product/0792358341/?tag=2022091-20
(This book is an extensively revised version of my textboo...)
This book is an extensively revised version of my textbook "¥esodot HaAlgebra HaLiniarit" (The Foundations of Linear Algebra) used at many universities in Israel. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors. Therefore, I assume that the student already has a certain amount of mathematical background - including set theory, mathematical induction, basic analytic geometry, and elementary calculus - as wellas a modicum of mathematical sophistication. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en rolled in an introductory computer science course. Therefore, consideration of the more computational aspects of linear algebra - such as the solution of systems of linear equations and the calculation of eigenvalues - is delayed until all students are assumed able to write computer programs for this purpose. Beginning with Chap ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it.
http://www.amazon.com/gp/product/9048145929/?tag=2022091-20
( Semiring theory stands with a foot in each of two mathe...)
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.
http://www.amazon.com/gp/product/9048163102/?tag=2022091-20
(This book is an extensively revised version of my textboo...)
This book is an extensively revised version of my textbook "¥esodot HaAlgebra HaLiniarit" (The Foundations of Linear Algebra) used at many universities in Israel. It is designed for a comprehensive one-year course in linear algebra (112 lecture hours) for mathematics majors. Therefore, I assume that the student already has a certain amount of mathematical background - including set theory, mathematical induction, basic analytic geometry, and elementary calculus - as wellas a modicum of mathematical sophistication. My intention is to provide not only a solid basis in the abstract theory of linear algebra, but also to provide examples of the application of this theory to other branches ofmathematics and computer science. Thus, for example, the introduction of finite fields is dictated by the needs of students studying algebraic coding theory as an immediate followup to their linear algebra studies. Many of the students studying linear algebra either are familiar with the care and feeding of computers before they begin their studies or are simultaneously en rolled in an introductory computer science course. Therefore, consideration of the more computational aspects of linear algebra - such as the solution of systems of linear equations and the calculation of eigenvalues - is delayed until all students are assumed able to write computer programs for this purpose. Beginning with Chap ter VII, there is an implicit assumption that the student has access to a personal computer and knows how to use it.
http://www.amazon.com/gp/product/0792336143/?tag=2022091-20
(This monograph is a continuation of several themes presen...)
This monograph is a continuation of several themes presented in my previous books 146, 149. In those volumes, I was concerned primarily with the properties of semirings. Here, the objects of investigation are sets of the form RA, where R is a semiring and A is a set having a certain structure. The problem is one of translating that structure to RA in some "natural" way. As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. Another special case is the creation of "idempotent analysis" and similar work in optimization theory. Unlike the case of the previous work, which rested on a fairly established mathematical foundation, the approach here is much more tentative and docimastic. This is an introduction to, not a definitative presentation of, an area of mathematics still very much in the making. The basic philosphical problem lurking in the background is one stated suc cinctly by Hahle and Sostak 185: ". . . to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?" The conflicting definitions proposed by various researchers in search of a resolution to this conundrum show just how difficult this problem is to see in a proper light.
http://www.amazon.com/gp/product/9048152704/?tag=2022091-20
mathematics and computer science educator
Golan, Jonathan Samuel was born on May 29, 1942 in Milwaukee. Son of Ezriel and Naomi Ruth (Bernstein) Golan. arrived in Israel, 1967.
Bachelor, University Wisconsin, 1964. Master of Arts, University California, Berkeley, 1965. Doctor of Philosophy, Hebrew University, Jerusalem, Israel, 1971.
Visiting professor mathematics, U. Florida, Gainesville, 1971-1972; visiting professor mathematics, McGill University, Montreal, Quebec, Canada, 1972-1973; visiting professor mathematics, Indiana U., Bloomington, 1978-1979; visiting professor mathematics, George Mason U., Fairfax, Virginia, 1983-1984; visiting professor mathematics, U. Idaho, since 1997; professor mathematics, U. Haifa, Israel, since 1973.
(This volume provides a comprehensive and up-to-date surve...)
(This book is an extensively revised version of my textboo...)
(This book is an extensively revised version of my textboo...)
(There is no branch of mathematics, however abstract, whic...)
(There is no branch of mathematics, however abstract, whic...)
(This monograph is a continuation of several themes presen...)
(This monograph is a continuation of several themes presen...)
( Semiring theory stands with a foot in each of two mathe...)
( Semiring theory stands with a foot in each of two mathe...)
(Book by Golan, Jonathan S.)
Member American Mathematics Society, Mathematics Association American, Israel Mathematics Union.
Married Hemda Mousaieff, September 10, 1968. Children: Aharon, Elitsur, Yael.