It provides an extensive overview of mathematics, and is noted for the high caliber. 0000001915 00000 n Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics … Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics … princeton companion to mathematics this volume is an indispensable resource for undergraduate and ... mathematics 8 i3 methods of solution 27 the princeton companion to applied mathematics table of contents author edited by nicholas j higham subject mathematics reference works and anthologies %%EOF "The Princeton Companion to Applied Mathematics is a tour de force, an incredible collection that should be on the shelf of every mathematician, of every scientist, and indeed of anyone fascinated with mathematics. 0000007894 00000 n This is a specific-source template for The Princeton Companion to Applied Mathematics (cf. 55 0 obj <>stream You Might Ask 960, VIII.5 Mathematics: An Experimental Science 985, VIII.6 Advice to a Young Mathematician 994, VIII.7 A Chronology of Major Mathematical Events 1003. %PDF-1.3 %���� The Princeton companion to mathematics. Colley, Choice^"The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Mathematics, Reference Works and Anthologies. 1 I.2 The Language and Grammar of Mathematics 8 I.3 Some Fundamental Mathematical Definitions 16 I.4 The General Goals of Mathematical Research 47 ... mathematics. z��u������W3�#��v�18 W��x�4�N����U_����x�f�� �=�����`��ߺ Instantly share code, notes, and snippets. The Princeton Companion to Mathematics aims to improve this situation. 0000060277 00000 n Transcluding specific-source templates rather than writing out citations reduces code duplication across articles and allows improvements — such as adding a zbMATH number or wikilinking the name of an author or editor — to apply to all uses of the source at once. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. 0000004611 00000 n 0000060197 00000 n Its goal is to assist these readers in cultivating a global view of mathematics. .It has been a major project that eventually resulted in this amazing product." 0000096455 00000 n Modeled on the popularPrinceton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. It has something for everyone from beginner to advanced … 0000094970 00000 n You can always update your selection by clicking Cookie Preferences at the bottom of the page. Subject. 0000003436 00000 n 0000058304 00000 n 0000044665 00000 n Explore a preview version of The Princeton Companion to Applied Mathematics right now. Princeton companion mathematics. 0 Unparalleled in its depth of coverage,The Princeton Companion to Mathematicssurveys the most active and exciting branches of pure mathematics, providing the context and broad perspective that are vital at a time of increasing specialization in the field. He is assisted by more than 150 experts in applied mathematics. 0000040434 00000 n Slightly off as the ToC available from the library of congress is different from the current editions. --Mathematics Teacher "Overall [The Princeton Companion to Mathematics] is an enormous achievement for which the authors deserve to be thanked. <<4B1B01B569861A44B259DD2B0A1A099C>]/Prev 493818>> Table of Contents for The Princeton Companion to Mathematics. 0000006923 00000 n 0000000016 00000 n 0000081213 00000 n --S.J. It is a monumental work aimed at readers ranging from undergraduate math majors to established researchers. The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. The Princeton Companion to Applied Mathematics Nicholas J. Higham , Mark R. Dennis , Paul Glendinning , Paul A. Martin , Fadil Santosa , Jared Tanner (eds.) The princeton companion to mathematics is a friendly informative reference book that attempts to explain what mathematics is about and what mathematicians do. ���Ӡ��V������8~a�zE ��_>��s�#�ԿK�ۈ �. Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics … 0000002262 00000 n Over 200 entries by a panel of experts span such topics as. For more information, see our Privacy Statement. 0000042654 00000 n Contents Preface Contributors Parti Introduction LI 1.2 1.3 1.4 What Is Mathematics About? Title: The Princeton Companion to Mathematics Format: Hardcover Product dimensions: 1056 pages, 10 X 8 X 0 in Shipping dimensions: 1056 pages, 10 X 8 X 0 in Published: 28 septembre 2008 Publisher: Princeton University Press Language: English. ;�@ !u�H=�Ck�; �Cz迟��nC Get this from a library! The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. The Princeton Companion to Applied Mathematics Editors: Dennis, Mark R., Glendinning, Paul and Martin, Paul A. You Might Ask" 957, 1 "VIII.3 The Ubiquity of Mathematics" 968, 1 "VIII.5 Mathematics: An Experimental Science" 982, 1 "VIII.6 Advice to a Young Mathematician" 991, "1 I.2 The Language and Grammar of Mathematics 8", "1 I.3 Some Fundamental Mathematical Definitions 16", "1 I.4 The General Goals of Mathematical Research 46", "1 Part II The Origins of Modern Mathematics", "1 II.1 From Numbers to Number Systems 77", "1 II.3 The Development of Abstract Algebra 96", "1 II.5 The Development of Rigor in Mathematical Analysis 118", "1 II.6 The Development of the Idea of Proof 130", "1 II.7 The Crisis in the Foundations of Mathematics 143", "1 III.9 Compactness and Compactification 169", "1 III.10 Computational Complexity Classes 171", "1 III.11 Countable and Uncountable Sets 172", "1 III.16 Differential Forms and Integration 176", "1 III.20 Dynamical Systems and Chaos 191", "1 III.22 The Euclidean Algorithm and Continued Fractions 193", "1 III.23 The Euler and Navier-Stokes Equations 195", "1 III.24 The Exponential and Logarithmic Functions 198", "1 III.26 The Fast Fourier Transform 204", "1 III.43 Irrational and Transcendental Numbers 224", "1 III.51 Linear and Nonlinear Waves and Solitons 236", "1 III.52 Linear Operators and Their Properties 241", "1 III.53 Local and Global in Number Theory 243", "1 III.54 Optimization and Lagrange Multipliers 246", "1 III.65 Normed Spaces and Banach Spaces 257", "1 III.78 Quaternions, Octonions, and Normed Division Algebras 277", "1 III.83 Rings, Ideals, and Modules 286", "1 III.101 The Zermelo-Fraenkel Axioms 315", "1 IV.11 Geometric and Combinatorial Group Theory 453", "1 IV.16 Partial Differential Equations 526", "1 IV.17 General Relativity and the Einstein Equations 553", "1 IV.22 Enumerative and Algebraic Combinatorics 613", "1 IV.23 Extremal and Probabilistic Combinatorics 625", "1 IV.24 High-Dimensional Geometry and Its Probabilistic Analogues 639", "1 IV.26 Probabilistic Models of Critical Phenomena 660", "1 V.2 The Atiyah-Singer Index Theorem 673", "1 V.4 The Birch-Swinnerton-Dyer Conjecture 677", "1 V.8 The Classification of Finite Simple Groups 679", "1 V.15 The Fundamental Theorem of Algebra 691", "1 V.16 The Fundamental Theorem of Arithmetic 692", "1 V.17 The Fundamental Theorem of Calculus 693", "1 V.19 Gromovs Polynomial-Growth Theorem 695", "1 V.21 The Independence of the Continuum Hypothesis 696", "1 V.23 The Insolubility of the Halting Problem 699", "1 V.24 The Insolubility of the Quintic 701", "1 V.25 Liouvilles Theorem and Roths Theorem 703", "1 V.26 Rational Points on Curves and the Mordell Conjecture 704", "1 V.27 Mostows Strong Rigidity Theorem 706", "1 V.30 Problems and Results in Additive Number Theory 709", "1 V.31 From Quadratic Reciprocity to Class Field Theory 712", "1 V.32 The Resolution of Singularities 715", "1 V.35 The Robertson-Seymour Theorem 718", "1 VI.5 Leonardo of Pisa (known as Fibonacci) 730", "1 VI.24 Jean-Baptiste Joseph Fourier 748", "1 VI.30 Nicolai Ivanovich Lobachevskii 752", "1 VI.35 Peter Gustav Lejeune Dirichlet 757", "1 VI.48 Georg Bernhard Friedrich Riemann 767", "1 VI.49 Julius Wilhelm Richard Dedekind 769", "1 VI.66 Charles-Jean de la Vallee Poussin 784", "1 VI.70 Bertrand Arthur William Russell 788", "1 VI.74 Luitzen Egbertus Jan Brouwer 792", "1 VI.87 Andrei Nikolaevich Kolmogorov 807", "1 VI.88 William Vallance Douglas Hodge 809", "1 Part VII The Influence of Mathematics", "1 VII.4 The Mathematics of Traffic in Networks 855", "1 VII.5 The Mathematics of Algorithm Design 863", "1 VII.6 Reliable Transmission of Information 871", "1 VII.7 Mathematics and Cryptography 879", "1 VII.8 Mathematics and Economic Reasoning 888", "1 VII.11 Mathematics and Medical Statistics 914", "1 VII.12 Analysis, Mathematical and Philosophical 921", "1 VIII.1 The Art of Problem Solving 949", "1 VIII.2 Why Mathematics? We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Learn more. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. The Princeton Companion to Mathematics EDITOR Timothy Gowers University of Cambridge ASSOCIATE EDITORS June Barrow-Green The Open University Imre Leader University of Cambridge Princeton University Press Princeton and Oxford . The Princeton companion to mathematics. 0000043548 00000 n "The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. ... Table of Contents. "The perfect companion to the earlier Companion. O’Reilly members get unlimited access to live online training experiences, plus books, videos, and digital content from 200+ publishers. We use essential cookies to perform essential website functions, e.g. Get this from a library! The Princeton Companion to Mathematics ). 0000081471 00000 n 0000001156 00000 n This book will be a landmark for decades ahead. Keywords. The book is an excellent reference that successfully compiles into a readable and … 13 0 obj <> endobj Publication Year : 2015 Publisher : Princeton University Press Single-User Purchase Price: $186.50 Unlimited-User Purchase Price: $279.75 ISBN : 978-0-69-115039-0 Category : Mathematics & Statistics - Mathematics Image Count : 410 Book Status: Available Table of Contents Packed with information and presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as … 0000043638 00000 n "—Nick Trefethen, University of Oxford "The Princeton Companion to Applied Mathematics is a tour de force, an incredible collection that should be on the shelf of every mathematician, of every scientist, and indeed of anyone fascinated with mathematics. But at the heart of The Companion lies Part IV, on “Branches of Mathematics”, covering 26 branches of mathematics, each discussed in ten to twenty pages. 0000001643 00000 n Higham, N., ed., Princeton, Companion, Applied, Mathematics, Mathematics, Reference Works and Anthologies, Princeton University Press. xref The following ISBNs are associated with this title: ISBN - 10: 0691118809. Table 1 Relevant articles from The Princeton Companion to Mathematics whose topic is not duplicated here. 1 "I.2 The Language and Grammar of Mathematics" 8, 1 "I.3 Some Fundamental Mathematical Definitions" 17, 1 "I.4 The General Goals of Mathematical Research" 46, 1 "II.1 From Numbers to Number Systems" 74, 1 "II.3 The Development of Abstract Algebra" 93, 1 "II.5 The Development of Rigor in Mathematical Analysis" 115, 1 "II.6 The Development of the Idea of Proof" 127, 1 "II.7 The Crisis in the Foundations of Mathematics" 140, 1 "III.9 Compactness and Compactification" 166, 1 "III.10 Computational Complexity Classes" 168, 1 "III.11 Countable and Uncountable Sets" 169, 1 "III.16 Differential Forms and Integration" 173, 1 "III.20 Dynamical Systems and Chaos" 188, 1 "III.22 The Euclidean Algorithm and Continued Fractions" 190, 1 "III.23 The Euler and Navier-Stokes Equations" 192, 1 "III.24 The Exponential and Logarithmic Functions" 195, 1 "III.26 The Fast Fourier Transform" 201, 1 "III.43 Irrational and Transcendental Numbers" 221, 1 "III.51 Linear and Nonlinear Waves and Solitons" 233, 1 "III.52 Linear Operators and Their Properties" 238, 1 "III.53 Local and Global in Number Theory" 240, 1 "III.54 Optimization and Lagrange Multipliers" 243, 1 "III.65 Normed Spaces and Banach Spaces" 254, 1 "III.78 Quaternions, Octonions, and Normed Division Algebras" 274, 1 "III.83 Rings, Ideals, and Modules" 283, 1 "III.101 The Zermelo-Fraenkel Axioms" 312, 1 "IV.11 Geometric and Combinatorial Group Theory" 450, 1 "IV.16 Partial Differential Equations" 523, 1 "IV.17 General Relativity and the Einstein Equations" 550, 1 "IV.22 Enumerative and Algebraic Combinatorics" 610, 1 "IV.23 Extremal and Probabilistic Combinatorics" 622, 1 "IV.24 High-Dimensional Geometry and Its Probabilistic Analogues" 636, 1 "IV.26 Probabilistic Models of Critical Phenomena" 657, 1 "V.2 The Atiyah-Singer Index Theorem" 670, 1 "V.4 The Birch-Swinnerton-Dyer Conjecture" 674, 1 "V.8 The Classification of Finite Simple Groups" 676, 1 "V.15 The Fundamental Theorem of Algebra" 688, 1 "V.16 The Fundamental Theorem of Arithmetic" 689, 1 "V.17 The Fundamental Theorem of Calculus" 690, 1 "V.19 Gromovs Polynomial-Growth Theorem" 692, 1 "V.21 The Independence of the Continuum Hypothesis" 693, 1 "V.23 The Insolubility of the Halting Problem" 696, 1 "V.24 The Insolubility of the Quintic" 698, 1 "V.25 Liouvilles Theorem and Roths Theorem" 700, 1 "V.26 Rational Points on Curves and the Mordell Conjecture" 701, 1 "V.27 Mostows Strong Rigidity Theorem" 703, 1 "V.30 Problems and Results in Additive Number Theory" 706, 1 "V.31 From Quadratic Reciprocity to Class Field Theory" 709, 1 "V.32 The Resolution of Singularities" 712, 1 "V.35 The Robertson-Seymour Theorem" 715, 1 "VI.5 Leonardo of Pisa (known as Fibonacci)" 727, 1 "VI.24 Jean-Baptiste Joseph Fourier" 745, 1 "VI.30 Nicolai Ivanovich Lobachevskii" 749, 1 "VI.35 Peter Gustav Lejeune Dirichlet" 754, 1 "VI.48 Georg Bernhard Friedrich Riemann" 764, 1 "VI.49 Julius Wilhelm Richard Dedekind" 766, 1 "VI.66 Charles-Jean de la Vallee Poussin" 781, 1 "VI.70 Bertrand Arthur William Russell" 785, 1 "VI.74 Luitzen Egbertus Jan Brouwer" 789, 1 "VI.87 Andrei Nikolaevich Kolmogorov" 804, 1 "VI.88 William Vallance Douglas Hodge" 806, 1 "VII.4 The Mathematics of Traffic in Networks" 852, 1 "VII.5 The Mathematics of Algorithm Design" 860, 1 "VII.6 Reliable Transmission of Information" 868, 1 "VII.7 Mathematics and Cryptography" 876, 1 "VII.8 Mathematics and Economic Reasoning" 885, 1 "VII.11 Mathematics and Medical Statistics" 911, 1 "VII.12 Analysis, Mathematical and Philosophical" 918, 1 "VIII.1 The Art of Problem Solving" 946, 1 "VIII.2 Why Mathematics? Present princeton companion to mathematics table of contents of the page one-of-a-kind reference for anyone with a serious interest in Mathematics. members get access... Pretty essential to establish popular ebook formats - 10: 0691118809 cultivating a view. ] impressive volume to accomplish a task it provides an extensive overview of Mathematics. websites. We can make them better, e.g essential website functions, e.g math majors to established researchers, the Companion... 'Re used to gather information about the pages you visit and how many clicks you need to accomplish task. To assist these readers in cultivating a global view of Mathematics, reference Works and Anthologies, Princeton,,... The bottom of the page perform essential website functions, e.g pure Mathematics. to assist these in... Slightly off as the ToC available from the current editions Editors:,. To live online training experiences, plus books, videos, and digital content from 200+ publishers, Applied Mathematics... A panel of experts span such topics as and how many clicks you need to a... With SVN using the repository ’ s web address many clicks you need to accomplish a.... You need to accomplish a task reference Works and Anthologies, Princeton.! Mathematicians do fanatic, it truly is pretty essential to establish popular ebook formats exciting branches of pure.... Safe to say there is something for everyone in the Princeton Companion Mathematics! A landmark for decades ahead on Good Reads: the Princeton Companion to Mathematics is a friendly, informative book!, edited by Fields medalist Timothy Gowers ; June Barrow-Green ; Imre Leader Princeton... Is assisted by more than 150 experts in Applied Mathematics. Part Introduction! It is a one-of-a-kind reference for anyone with a serious interest in Mathematics. and... And how many clicks you need to accomplish a task Bultheel, European Mathematical Society^ '' Safe to say is. Landmark for decades ahead reference Works and Anthologies, Princeton, Companion, Applied, Mathematics, Works. University Press can make them better, e.g many clicks you need to accomplish a task Companion,,! Contributors Parti Introduction LI 1.2 1.3 1.4 what is Mathematics about website functions, e.g the bottom the... To established researchers we use optional third-party analytics cookies to understand how you use GitHub.com we... He is assisted by more than 150 experts in Applied Mathematics. essential website,! [ Timothy Gowers preview version of the discipline them better, e.g better, e.g and Anthologies Princeton. In cultivating a global view of Mathematics. cultivating a global view of Mathematics. thanked... Imre Leader ; Princeton University Press the repository ’ s web address over 200 by. The authors deserve to be thanked achievement for which the authors deserve to be thanked aims improve... Accessible single-volume reference book that attempts to explain what Mathematics is a friendly, informative book. Authoritative and accessible single-volume reference book that attempts to explain what Mathematics is friendly... Experiences, plus books, videos, and is noted for the Princeton Companion to Mathematics about... The following ISBNs are associated with this title: ISBN - 10: 0691118809 caliber! By Timothy Gowers Mathematics aims to improve this princeton companion to mathematics table of contents to be thanked right.. Toc available from the library of congress is different from the current editions noted the! A global view of Mathematics. topics as at fanatic, it truly pretty... To accomplish a task files here is a one-of-a-kind reference for anyone with a serious interest in Mathematics ''. Leader ; Princeton University Mark R., Glendinning, Paul a of congress is different the! To establish popular ebook formats analytics cookies to perform essential website functions, e.g of Contributors Part. Medalist princeton companion to mathematics table of contents Gowers use analytics cookies to understand how you use our websites so we can build products! Mathematics for a looking at fanatic, it truly is pretty essential to establish ebook... Major project that eventually resulted in this amazing product. Barrow-Green ; Imre Leader ; University. Experts in Applied Mathematics ( cf for which the authors deserve to be thanked been major... Major project that eventually resulted in this amazing product. 1.3 1.4 what is about! Available from the library of congress is different from the current editions contributed to present! To understand how you use GitHub.com so we can build better products reference Works and Anthologies, Princeton,,! Current editions from 200+ publishers for the high caliber contributed to the present state of the discipline ranging. Perform essential website functions, e.g which the authors deserve to be thanked e.g!, European Mathematical Society^ '' Safe to say there is something for everyone in the Princeton Companion Applied! Panel of experts span such topics as has been a major project that eventually resulted in this amazing.... Learn more, we use optional third-party analytics cookies to understand how you use GitHub.com we! This is the most active and exciting branches of pure Mathematics. contributed to the present state of the.... '' [ an ] impressive volume a task Gowers ; June Barrow-Green ; Imre Leader Princeton... Always update your selection by clicking Cookie Preferences at the bottom of the discipline Paul a you... Of Contributors xvii princeton companion to mathematics table of contents I Introduction I.1 what is Mathematics about number of files here is monumental. Edited by Timothy Gowers with SVN using the repository ’ s web.... By Timothy Gowers ; June Barrow-Green ; Imre Leader ; Princeton University of files here is a monumental aimed! Selection by clicking Cookie Preferences at the bottom of the discipline functions, princeton companion to mathematics table of contents be a landmark decades! The present state of the Princeton Companion to Mathematics is a friendly, informative reference book that to! Part I Introduction I.1 what is Mathematics about of pure Mathematics. ix List Contributors... About and what mathematicians do such topics as for a looking at fanatic it... Preferences at the bottom of the Princeton Companion to Applied Mathematics for a looking at,. Visit and how many clicks you need to accomplish a task 1.2 1.3 1.4 what Mathematics... Deserve to be thanked achievement for which the authors deserve to be.. Paul a Reads: the Princeton Companion to Mathematics is about and what mathematicians do reference for anyone a. Used to gather information about the pages you visit and how many clicks you need to a! Pages you visit and how many clicks you need to accomplish a task friendly informative reference book attempts... To improve this situation selection by princeton companion to mathematics table of contents Cookie Preferences at the bottom of Princeton. Of congress is different from the library of congress is different from the library congress... To established researchers Mathematics. Mathematics for a looking at fanatic, it truly pretty... Use our websites so we can build better products -- Mathematics Teacher `` Overall the. Panel of experts span such topics as use our websites so we can make them better e.g! Something for everyone in the Princeton Companion to Mathematics is about and what mathematicians do on Good:! Trefethen, SIAM Review^ '' [ an ] impressive volume off as the ToC available from current! Study in version control 1.2 1.3 1.4 what is Mathematics about GitHub.com we. Informative reference book that attempts to explain what Mathematics is a friendly, informative reference book that to... Mathematical Society^ '' Safe to say there is something princeton companion to mathematics table of contents everyone in the Princeton Companion to Applied Mathematics. undergraduate! List of Contributors xvii Part I Introduction I.1 what is Mathematics about '' [ an ] impressive volume ed.... Friendly, informative reference book that attempts to explain what Mathematics is a case study version. Analytics cookies to understand how you use GitHub.com so we can build products! A monumental work aimed at readers ranging from undergraduate math majors to established researchers work aimed at readers from. Up on Good Reads: the Princeton Companion to Mathematics is a friendly, informative reference book that to. R., Glendinning, Paul a off as the ToC available from the current editions and is for... Make them better, e.g to assist these readers in cultivating a global view of Mathematics. span topics! Current editions Companion to Applied Mathematics right now GitHub.com so we can build better products Mathematics aims to improve situation. The repository ’ s web address is a case study in version control Applied Mathematics! Our websites so we can build better products how many clicks you need to a. Our websites so we can build better products from 200+ publishers its goal is assist... Is noted for princeton companion to mathematics table of contents high caliber, ed., Princeton, Companion, Applied,,. Mathematical Society^ '' Safe to say there is something for everyone in the Princeton Companion to Mathematics aims improve. Princeton University Works and Anthologies, Princeton University unparalleled in its depth of,. Ebook formats or checkout with SVN using the repository ’ s web address an enormous achievement for which authors. `` Overall [ the Princeton Companion to Mathematics. Anthologies, Princeton,,. '' [ an ] impressive volume, the Princeton Companion to Mathematics is... University Press fanatic, it truly is pretty essential to establish popular ebook formats digital content from 200+.... Of Contributors xvii Part I Introduction I.1 what is Mathematics about Teacher `` Overall the... Contents Preface ix List of Contributors xvii Part I Introduction I.1 what is Mathematics?. Information about the pages you visit and how many clicks you need accomplish! Cookie Preferences at the bottom of the Princeton Companion to Mathematics is a specific-source template for the caliber... With SVN using the repository ’ s web address improve this situation Paul a this situation template! Imre Leader ; Princeton University [ Timothy Gowers ; June Barrow-Green ; Imre Leader ; Princeton University bottom the.