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His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec tions could, of course, not be made sharply, there are several overlaps. 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To tie them together, and to place them in context, I have supplemented them by a series of brief essays sketching their historieal background (as I see it). In addition to these I have listed some subsequent papers by others which have further developed some of my key ideas. The papers on universal algebra, lattice theory, and general topology collected in the present volume concern ideas which have become familiar to all working mathematicians. It may be helpful to make them readily accessible in one volume. I have tried in the introduction to each part to state the most significant features of ea ch paper reprinted there, and to indieate later developments. The background that shaped and stimulated my early work on universal algebra, lattice theory, and topology may be of some interest. As a Harvard undergraduate in 1928-32, I was encouraged to do independent reading and to write an original thesis. 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Each of these four groups of papers is introduced by a review of the contents and significance, respectively of the impact of these papers. The first volume contains, in addition, an autobiography, a complete list of publications, a list of doctoral students and four unpublished essays on mathematics in general: a) A report on the University of Leningrad b) On the work of the mathematical mind c) Proofs in Mathematics d) About Mathematical books. The report on the University of Leningrad, written in the late '40's, is a unique historical document which is still of current interest for several reasons. It is of interest for professional reasons since it contains a com- plete description of a mathematics majors' curriculum through his entire course of studies. From it one can see both the changes and invariants of course material as well as the students' course load. Then one can also see the consequences of admittedly extreme political intervention in uni- versity affairs. 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It has been an honor to have been entrusted with the editorial work for these seleeta. I am grateful to the writers of the various commentaries for their illuminating contributions and to Richard Askey for solid advice.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52143369715985,"sku":"NLS9781461284116","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461284116.jpg?v=1757584167"},{"product_id":"collected-mathematical-papers-book-n-jacobson-9781461282143","title":"Collected Mathematical Papers","description":"This collection contains all my published papers, both research and expository, that were published from 1934 to 1988. The research papers arranged in chronological order appear in Volume I and II and in the first part of Volume III. The expository papers, which are mainly reports presented at conferences, appear in chronological order in the last part of Volume III. Volume I covers the period 1910 to 1947, the year I moved to Yale, Volume II covers the period 1947 to 1965 when I became Chairman of the Department at Yale and Volume III covers the period from 1965 to 1989, which goes beyond my assumption of an emeritus status in 1981. I have divided the time interval covered in each volume into subintervals preceded by an account of my personal history during this period, and a commentary on the research papers published in the period. I have omitted commentaries on the expository papers and have sorted out the commentaries on the research papers according to the principal fields of my research. my recollections, checked against written The personal history has been based on documentation in my file of letters as well as diaries. One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A. W. 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The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi­ cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif­ ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52143820308753,"sku":"NLS9781461253433","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461253433.jpg?v=1757586137"},{"product_id":"hassler-whitney-collected-papers-volume-i-book-james-eelles-9781461277408","title":"Hassler Whitney Collected Papers Volume I","description":"We present here the mathematical papers of Hassler Whitney. This collection contains all the published papers, with the exception of some short announcements that Whitney did not wish to be included. We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem. The papers are presented under some broad categories: graphs. and combinatorics, differentiable functions and singularities, analytic spaces, manifolds, bundles and characteristic classes, topology and algebraic topology, geometric integration theory. Whitney intended to write an introduction to this collection. Unfortunately he left us no manuscript at the time of his death, May 10, 1989. We had discussed the possibility of using his paper Moscow 1935 - Topology moving toward America, written for the Centennial of the American Mathematical Society, as part of his introduction to this collection, an idea which he much liked. We therefore include this paper, which contains personal information as well as mathematical reflections, as Whitney's own introduction to these volumes. Whitney's mathematical style, like his personal style, was that of an explorer and pioneer. One of the pictures included in these volumes shows him as a mountain climber. In mathematics, he preferred to work on undeveloped areas: break new ground and build foundations. During the last twenty years of his life he concentrated his efforts on developing an educational system that builds on the natural tendency in children to be explorers.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144016163089,"sku":"NLS9781461277408","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461277408.jpg?v=1757587018"},{"product_id":"kurt-otto-friedrichs-book-cs-morawetz-9781461253815","title":"Kurt Otto Friedrichs","description":"In 1981 I was approached by Klaus Peters to assist in publishing a selection of the papers of Kurt Otto Friedrichs. With some coaxing on my part the selection was made mainly by Friedrichs despite his frequent modest grumble that it did not make sense to include that paper as X had subsequently improved either the result or the proof.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144060727569,"sku":"NLS9781461253815","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461253815.jpg?v=1757587226"},{"product_id":"kurt-otto-friedrichs-book-cs-morawetz-9781461253846","title":"Kurt Otto Friedrichs","description":"The work presented in this report originated in connection with a research project in magneto-hydrodynamics conducted by Professor H. Grad at the Institute of Mathematical Sciences at New York Univer sity; the report was completed while the author was a consultant at Los Alamos Scientific Laboratory. The report contains an expository analysis of the mathematical structure of magneto-hydrodynamic theory; specifically, of the theory of the interaction of magnetic fields with conducting compressible fluids. One of the major aims is to emphasize the remarkably close parallelism between this theory and ordinary gas dynamics. While hydromagnetic shocks and small disturbance waves have been treated before, it seems that hydromagnetic 'simple waves are here treated for the first time. In a typical example it is shown that - as in gas dynamics - simple one-dimensional flow problems can be solved with the aid of shocks and simple waves. Throughout the exposition a familiarity with the basic notions of gas dynamics - covered e.g. by the first three chapters of Super sonic low and Shock Waves - is presupposed. The bibliography refers only to those papers which are concerned with the subjects treated. No reference is made to a number of sig nificant contributions to hydromagnetics concerned with subjects - such as astro- and geophysical applications, effect of turbulence, stabil ity questions - which are not covered in this report.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144245178641,"sku":"NLS9781461253846","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461253846.jpg?v=1757588026"},{"product_id":"hassler-whitney-collected-papers-book-james-eelles-9781461277415","title":"Hassler Whitney Collected Papers","description":"We present here the mathematical papers of Hassler Whitney. This collection contains all the published papers, with the exception of some short announcements that Whimey did not wish to be included. We also include the introduction to his book Geometric Integration Theory, and one previously unpublished manuscript on the four-color problem. The papers are presented under some broad categories: graphs and combinatorics, differentiable functions and singularities, analytic spaces, manifolds, bundles and characteristic classes, topology and algebraic topology, geometric integration theory. Whimey intended to write an introduction to this collection. Unfortunately he left us no manuscript at the time of his death, May 10, 1989. We had discussed the possibility of using his paper Moscow 1935 - Topology moving toward America, written for the Centennial of the American Mathematical Society, as part of his introduction to this collection, an idea which he much liked. We therefore include this paper. which contains personal information as well as mathematical reflections. as Whimey's own introduction to these volumes. Whimey's mathematical style, like his personal style. was that of an explorer and pioneer. Ooe of the pictures included in these volumes shows him as a mountain climber. 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One of these was a diary I kept of my trip to the USSR in 1961; the others were diaries Florie (Florence) kept during other major visits abroad. I have also consulted Professor A. W. Tucker on historical details on Princeton during the 1930's.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144376742161,"sku":"NLS9781461282150","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461282150.jpg?v=1757588624"},{"product_id":"gabor-szegoe-collected-papers-book-gabor-szeg-9781461257875","title":"Gabor Szegoe: Collected Papers","description":"1. 1. Definition of L-forms. In the years 1907-1911 O. Toeplitz [21, 22, 23, 24]* studied a class of quadratic forms whose matrix is of the follO\\\\\"ing type: (Ll) C-2 C_I Co C-n-I Cn-I The elements Cn are given complex constants. Toeplitz designated these forms as L-forms and investigated in detail their relation to the analytic function defined in a neighborhood of the unit circle by the Laurent series 2; C z\", n = n - 00, . . . , 00; this series is assumed to be convergent in a certain circular ring rl \u0026lt; I z I \u0026lt; r2, rl \u0026lt; 1 \u0026lt; r2. It is obvious that these matrices are connected with the infinite cyclic group, just as the finite cyclic matrix CO CI C2 C Co CI n r (1. 2) Cn-I C Co n L. c, c, Co is associated with the finite cyclic group. The main result of Toeplitz is that the spectrum of the L-form is identical with the complex values the Laurent series assumes on the unit circle I z I = 1. 1. 2. Hermitian forms. The case C = en is of particular importance; the n matrix (1. 1) is in this case a Hermitian one and the associated Laurent series i8 represents a real function f(8) on the unit circle z = e , -'II\" ~ 8 \u0026lt; '11\".","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144396796177,"sku":"NLS9781461257875","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781461257875.jpg?v=1757588725"},{"product_id":"gian-carlo-rota-on-analysis-and-probability-book-jean-dhombres-9781461274025","title":"Gian-Carlo Rota on Analysis and Probability","description":"Rota's early work was in analysis, more specifically, in operator theory, differ  ential equations, ergodic theory, and probability theory. 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Before the I World War he started to study mathematics at Tomsk university but then went to the front to ?ght as a volunteer. In 1946 he continued his study at Voroshilovgrad (now Lugansk) Pedagogical Institute and at the same time taught mathematics at a secondary school. In 1950 Shirshov was accepted as a graduate student at the Moscow State University under the supervision of A. G. Kurosh. In 1953 he has successfully defended his Candidate of Science thesis (analog of a Ph. D. ) Some problems in the theory of nonassociative rings and algebras and joined the Department of Higher Algebra at the Moscow State University. In 1958 Shirshov was awarded the Doctor of Science degree for the thesis On some classes of rings that are nearly associative. In 1960 Shirshov moved to Novosibirsk (at the invitations of S. L. Sobolev and A. I. 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From 1960 to 1973 he was a deputy director of the Institute and till his last days he led the research in the theory of algebras at the Institute.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52147242860817,"sku":"NLS9783764388577","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52762246218001,"sku":"NIN9783764388577","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764388577.jpg?v=1757599899"},{"product_id":"selected-papers-of-norman-levinson-book-ja-nohel-9780817638627","title":"Selected Papers of Norman Levinson","description":"The deep and original ideas of Norman Levinson have had a lasting impact on fields as diverse as differential \u0026amp; integral equations, harmonic, complex \u0026amp; stochas­ tic analysis, and analytic number theory during more than half a century. Yet, the extent of his contributions has not always been fully recognized in the mathematics community. For example, the horseshoe mapping constructed by Stephen Smale in 1960 played a central role in the development of the modern theory of dynami­ cal systems and chaos. The horseshoe map was directly stimulated by Levinson's research on forced periodic oscillations of the Van der Pol oscillator, and specifi­ cally by his seminal work initiated by Cartwright and Littlewood. In other topics, Levinson provided the foundation for a rigorous theory of singularly perturbed dif­ ferential equations. He also made fundamental contributions to inverse scattering theory by showing the connection between scattering data and spectral data, thus relating the famous Gel'fand-Levitan method to the inverse scattering problem for the Schrodinger equation. He was the first to analyze and make explicit use of wave functions, now widely known as the Jost functions. Near the end of his life, Levinson returned to research in analytic number theory and made profound progress on the resolution of the Riemann Hypothesis. Levinson's papers are typically tightly crafted and masterpieces of brevity and clarity. It is our hope that the publication of these selected papers will bring his mathematical ideas to the attention of the larger mathematical community.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52333065077009,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52333065568529,"sku":"NLS9780817638627","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817638627.jpg?v=1758153587"},{"product_id":"mathematics-from-leningrad-to-austin-volume-2-book-rudolph-a-lorentz-9780817639228","title":"Mathematics from Leningrad to Austin, Volume 2","description":"The works of George G. 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This condition, relating the time and spatial discretizations for finite difference schemes, is now universally employed in the simulation of solutions of equations describing propagation phenomena. His example of a linear equation with no solution (1957), with its attendant consequence that most equations have no solution, was not merely an unexpected fact, but changed the viewpoint of the entire field. Lewy made pivotal contributions in many other areas, for example, the regu- larity theory of elliptic equations and systems, the Monge-Ampere Equation, the Minkowski Problem, the asymptotic analysis of boundary value problems, and sev- eral complex variables. He was among the first to study variational inequalities. In much of his work, his underlying philosophy was that simple tools of function theory could help us understand the essential concepts embedded in an issue, although at a cost in generality. This was extremely successful.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52410031735057,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52410032259345,"sku":"NLS9780817635237","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817635237.jpg?v=1758776658"},{"product_id":"hans-lewy-selecta-book-david-kinderlehrer-9780817635244","title":"Hans Lewy Selecta","description":"The work of Hans Lewy (1904--1988) has had a profound influence in  the direction of applied mathematics and partial differential  equations, in particular, from the late 1920s.  Two of the particulars  are well known. The Courant--Friedrichs--Lewy condition (1928), or CFL  condition, was devised to obtain existence and approximation results.  This condition, relating the time and spatial discretizations for  finite difference schemes, is now universally employed in the  simulation of solutions of equations describing propagation phenomena.  Lewy's example of a linear equation with no solution (1957), with its  attendant consequence that most equations have no solution, was not  merely an unexpected fact, but changed the viewpoint of the entire  field.     Lewy made pivotal contributions in many other areas, for example,  the regularity theory of elliptic equations and systems, the Monge--  AmpSre Equation, the Minkowski Problem, the asymptotic analysis of  boundary value problems, and several complex variables. He was among  the first to study variational inequalities. In much of his work, his  underlying philosophy was that simple tools of function theory could  help one understand the essential concepts embedded in an issue,  although at a cost in generality. This approach was extremely  successful.     In this two-volume work, most all of Lewy's papers are presented,  in chronological order. They are preceded by several short essays  about Lewy himself, prepared by Helen Lewy, Constance Reid, and David  Kinderlehrer, and commentaries on his work by Erhard Heinz, Peter Lax,  Jean Leray, Richard MacCamy, Fran?ois Treves, and Louis Nirenberg.  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These papers are divided into four fields. father wrote from The first volume contains the papers on 1) Summability and Number Theory and 2) Interpolation. The second volume contains the fields 3) Real and Functional Analysis and 4) Approximation Theory. Each of these four groups of papers is introduced by a review of the contents and significance, respectively of the impact of these papers. The first volume contains, in addition, an autobiography, a complete list of publications, a list of doctoral students and four unpublished essays on mathematics in general: a) A report on the University of Leningrad b) On the work of the mathematical mind c) Proofs in Mathematics d) About Mathematical books. The report on the University of Leningrad, written in the late '40's, is a unique historical document which is still of current interest for several reasons. It is of interest for professional reasons since it contains a com- plete description of a mathematics majors' curriculum through his entire course of studies. From it one can see both the changes and invariants of course material as well as the students' course load. Then one can also see the consequences of admittedly extreme political intervention in uni- versity affairs. Today we use the term politically correct, but in those times being politically correct was a matter of life and death.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52425867985169,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52425868607761,"sku":"NLS9780817637101","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817637101.jpg?v=1759156032"},{"product_id":"selected-papers-of-norman-levinson-book-john-nohel-9780817639792","title":"Selected Papers of Norman Levinson","description":"Norman Levinson (1912-1975) was a mathematician of international repute. This collection of his selected papers bears witness to the profound influence Levinson had on research in mathematical analysis with applications to problems in science and technology. 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With some reluctance Friedrichs has agreed to help in making the selection although in the initial stages only one paper [47-2] was in his opinion worthy of being included. With some coaxing on my part the selection was made mainly by Friedrichs despite his frequent modest grumble that it did not make sense to include \"that\" paper as \"X\" had subsequently improved either the result or the proof. Later P.D. Lax and L. Nirenberg identified appropriate papers and, perhaps not so remarkably, there was almost complete overlap. The vast majority of the papers are in partial differential equations and spectral theory where Friedrichs had the greatest impact. For these Peter Lax and Tosio Kato have written the commentaries. Friedrichs made fundamental contributions in the theory of asymptotics; two papers, including Friedrichs' Gibbs Lecture, have been reviewed by W. Wasow. The very profound contributions Friedrichs made to applied mathematics are represented by some papers in elasticity, mainly written with J.J. Stoker and now reviewed by F. John and in magneto-hydrodynamics where Friedrichs' original notes have been reproduced and his contributions to the subject reviewed by Harold Weitzner. 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For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VI, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52426304880913,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52426305274129,"sku":"NLS9780817632663","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780817632663.jpg?v=1759157343"},{"product_id":"g-w-stewart-book-misha-e-kilmer-9780817649678","title":"G.W. Stewart","description":"Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. 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This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. G.W. 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