41. Is Baezian (as In John Baez) Math-Physics Real? Let me repeat, for those who do not know the background to the saunders maclaneGarrettBirkhoff saga (saunders co-invented Category Theory with Lawvere, I http://superstringtheory.com/forum/philboard/messages12/122.html

String Theory Discussion Forum String Theory Home Forum Index Is Baezian (as in John Baez) Math-Physics Real? Follow Ups Post Followup Philosophy of Physics XII FAQ Posted by OsherDoctorow on June 10, 2002 at 00:05:52: At the point at which I was most severely critical of category theory in superstringtheory.com and one other forum (see String-M Theory - Duality subforum of this Forum), I had to go out of town for 1-1/2 weeks, and upon returning I found in my email a message by John Baez addressed to the *categories* mailing list in Canada, email address categories@mta.ca, dated May 24, 2002. I will try to slowly (perhaps many short postings) reply to his message since I am in *limbo* on the Categories mailing list, being allowed to receive email but not contribute any of my own (nothing which I send ever gets through since the time a few years ago in which I went *off topic* and interdisciplinary and thereby offended one or two high status flamers on the list). Baez (John Baez, not Joan Baez) is at the University of California Riverside at present, but appears to be in almost every important place on and off the internet. His publications are legion. He seems to have been or to be presently an assistant to half of the mathematical physics and theoretical physics community including Stephen Hawking (unless somebody is using his name in emails without permission). Baez has chosen this time interval to remind us all how valuable category theory is and to attempt to apply category theory to Yang Mills Theory and creating Lie Group and Lie Algebra categories and so on. He cited his paper *Categorification* (Feb.2, 1998), arXiv.math.QA/9802029 v1, and I would like to concentrate on the first 3 pages of that paper which is roughly 50 pages long.

42. TechTV Store Powered By Buy.com Categories for the Working Mathematician Our Low Price $59.95 Format HardcoverAuthor maclane, saunders Back Order Alert me when this item is in stock. http://www.buy.com/techtv/retail/books/subcat.asp?loc=5806

43. Keep Mandatory Retirement For Tenured Faculty Volume 14, Number 2, Spring 1991. Keep Mandatory Retirement for TenuredFaculty. Richard A. Epstein and saunders maclane. Richard A http://www.cato.org/pubs/regulation/reg14n2h.html

Volume 14, Number 2, Spring 1991 Keep Mandatory Retirement for Tenured Faculty Richard A. Epstein and Saunders MacLane Richard A. Epstein is the James Parker Hall Distinguished Service Professor of Law at the University of Chicago. Saunders MacLane is the Max Mason Distinguished Service Professor, emeritus, in the Department of Mathematics at the University of Chicago. V American universities, both public and private, are one of the great resources of this nation. It is not in the nation's long-term interest to reduce their effectiveness in meeting the intellectual and social challenges of tomorrow. In reaching our conclusions, we shall not reconsider the wisdom of the ADEA outside the university, let alone the further reach of the anti-discrimination laws. We are content to examine the mandatory retirement rule for tenured faculty of universities in its own domain and on its own merits, without making any artificial presumption for or against its continued use. Within our setting, the retirement policy for tenured faculty has served the university and the country well. Hence, it should not be reversed by legislative decree. Why Tenure?

44. Keep Mandatory Retirement For Tenured Faculty Volume 14, Number 2, Spring 1991. Keep Mandatory Retirement for TenuredFaculty. Richard A. Epstein and saunders maclane. Richard A http://www.cato.org/cgi-bin/scripts/printtech.cgi/pubs/regulation/reg14n2h.html

content="text/html; charset=iso-8859-1"> Volume 14, Number 2, Spring 1991 Keep Mandatory Retirement for Tenured Faculty Richard A. Epstein and Saunders MacLane Richard A. Epstein is the James Parker Hall Distinguished Service Professor of Law at the University of Chicago. Saunders MacLane is the Max Mason Distinguished Service Professor, emeritus, in the Department of Mathematics at the University of Chicago. V American universities, both public and private, are one of the great resources of this nation. It is not in the nation's long-term interest to reduce their effectiveness in meeting the intellectual and social challenges of tomorrow. In reaching our conclusions, we shall not reconsider the wisdom of the ADEA outside the university, let alone the further reach of the anti-discrimination laws. We are content to examine the mandatory retirement rule for tenured faculty of universities in its own domain and on its own merits, without making any artificial presumption for or against its continued use. Within our setting, the retirement policy for tenured faculty has served the university and the country well. Hence, it should not be reversed by legislative decree. Why Tenure?

45. A Look At Mathematics Education Fifth Edition. Keene, NH John Prentiss, 1808. Birkhoff, Garrett, maclane,saunders. Algebra (2d ed.). New York Macmillan, 1979. Colburn, Warren. http://www.math.nmsu.edu/breakingaway/works/alookatmath.html

< Return to Index Equity and Quality... Language of... A Look at Mathematics Education (written Sept. 1997) Patricia Baggett Box 30001, Dept. 3MB Department of Mathematical Sciences New Mexico State University Las Cruces, NM 88003-8001 baggett@nmsu.edu Andrzej Ehrenfeucht Computer Science Department Box 430 University of Colorado Boulder, CO 80309-0439 andrzej@cs.colorado.edu Abstract During the last 200 years, mathematics has changed radically. On the other hand, the content of mathematics taught in the elementary grades has remained virtually unchanged, causing a great discrepancy between everyday mathematics and school mathematics. 1. Mathematics education in the early years, 1800 - 2000. Many mathematics books used for educational purposes began to appear in the United States around 1800 (Sterry, 1790; Pike, 1806; Adams, 1808; Daboll, 1812; Hawney, 1813). These books contained material that was used for vocational training in arithmetic in the eighteenth century, information useful for merchants, shopkeepers, craftsmen, and artisans. The content of these books was based on several different concepts of numbers: whole numbers, common fractions taught as parts of a (fractured) whole, decimal fractions, and a variety of composite and denominate numbers. The main purposes were to teach skills in executing written algorithms, and to teach a variety of applications. The books were for teachers, and most learning took place during an apprenticeship, when a person was learning a profession.

46. ChemoInformatics Consulting, SRL -- Bookstore -- Homology Modeling Homology saunders maclane / Hardcover Our Price $35.00 (Special Order). Homologysaunders maclane / Published 1994 (Hard to Find). http://www.chemoinformatics.com/bookstore/homology.html

HOMOLOGY MODELING Interpreting the Hierarchy of Nature : From Systematic Patterns to Evolutionary Process Theories Ships in 2-3 days Lance Grande, Olivier Rieppel (Editor) / Hardcover / Published 1994 Our Price: $62.50 Read more about this title... Homology Hardcover / Published 1994 (Special Order) Read more about this title... Homology Saunders MacLane / Hardcover Our Price: $35.00 (Special Order) Homology : The Hierarchical Basis of Comparative Biology Brian K. Hall (Editor) / Hardcover / Published 1994 Our Price: $63.00 (Back Ordered) Read more about this title... Homology and Dynamical Systems John M. Franks / Paperback / Published 1982 Our Price: $17.00 (Special Order) Homology As a Tool in Neuroscience (Brain, Behavior and Evolution Journal : Vol. 38, No. 4-5) H. Baker (Editor) / Paperback / Published 1991 Our Price: $129.00 (Special Order) Homology Folding of Proteins : Application to Cytokine Engineering (Biotechnology Intelligence Unit) Subhashini Srinivasan / Hardcover / Published 1997 (Special Order) Homology Folding of Proteins: Application to Cytokine Engineering (Biotechnology Intelligence Unit) Subhashini Srinivasan / Hardcover / Published 1998 Our Price: $119.00

47. PCARACAS Alejandría BE 3.5.0.1pr3: Resultados Translate this page Botón de Red Información sobre el sistema Conexión a otros servidoresAlejandría. Autor maclane, saunders, (Comienzo). Sólo http://biblioteca.ipc.upel.edu.ve/cgi-win/be_alex.exe?Autor=MacLane, Saunders&No

48. Vergleichen, Günstiger Preis Und Kaufen. 'Arithmetik / Algebra' Bei Lycos Shopp Translate this page maclane, saunders Categories for the Working Mathematician Graduate Textsin Mathematics Vol.5 2nd ed. 1998. XII, 314 pw 10 figs. 24,5 cm Geb . http://shopping.lycos.de/shopping/ct174pg7/arithmetik_algebra7.html

Vergleichen, Günstiger Preis und Kaufen. 'Arithmetik / Algebra' bei Lycos Shopping Online Einkaufen - Sie finden bei uns Testberichte von Stiftung Warentest, Preise, Preisvergleiche und Produkt Informationen. Sie können günstige und billige Produkte und Marken Angebote vergleichen und bei unseren Shops kaufen. Lycos Startseite Lycos Shopping My Lycos Lycos A-Z Sie sind hier: Lycos Home Lycos Shopping Mathematik / Naturwissenschaften / Technik / Medizin Mathematik Arithmetik / Algebra Lidl, Rudolf; Pilz, Günter:: Applied Abstract Algebra Undergraduate Texts in Mathematics 2nd ed. 1997. 535 p. w. 112 figs. 24 cm Geb 'Buchwelt.de' Newman, Donald J.:: Analytic Number Theory Graduate Texts in Mathematics Vol.177 1998. VIII, 73 p. 24,5 cm Geb 'Buchwelt.de' Friedman, Robert:: Algebraic Surfaces and Holomorphic Vector Bundles 1998. IX, 328 p. 24,5 cm Geb 'Buchwelt.de' Maclachlan, C.; Reid, Alan W.:: The Arithmetic of Hyperbolic 3-Manifolds Graduate Texts in Mathematics Vol.219 2002. 480 p. w. 57 figs. 24,5 cm Geb 'Buchwelt.de' Bix, Robert:: Conics and Cubics

49. Vergleichen, Günstiger Preis Und Kaufen. 'Arithmetik / Algebra' Bei Lycos Shopp Translate this page Bix, Robert Conics and Cubics. maclane, saunders Categories for theWorking Mathematician. Lam Tsit-Yuen Lectures on Modules and Rings. http://shopping.lycos.de/shopping/ct174pg6/arithmetik_algebra6.html

Vergleichen, Günstiger Preis und Kaufen. 'Arithmetik / Algebra' bei Lycos Shopping Online Einkaufen - Sie finden bei uns Testberichte von Stiftung Warentest, Preise, Preisvergleiche und Produkt Informationen. Sie können günstige und billige Produkte und Marken Angebote vergleichen und bei unseren Shops kaufen. Lycos Startseite Lycos Shopping My Lycos Lycos A-Z Sie sind hier: Lycos Home Lycos Shopping Mathematik / Naturwissenschaften / Technik / Medizin Mathematik Arithmetik / Algebra Rosen, Michael:: Number Theory in Function Fields Graduate Texts in Mathematics Vol.210 2002. XII, 358 p. 24,5 cm Geb 'Buchwelt.de' Shimura, Goro:: Collected Papers 2002. 805 p. Geb 1954-1966 'Buchwelt.de' Shimura, Goro:: Collected Papers 2002. 805 p. Geb 1966-1977 'Buchwelt.de' Shimura, Goro:: Collected Papers 2002. 930 p. Geb 1978-1988 'Buchwelt.de' Goldschmidt, David M.:: Algebraic Functions and Projective Curves Graduate Texts in Mathematics Vol.215 2002. 179 p. 24,5 cm Geb 'Buchwelt.de' Deeba, Elias; Gunawardena, Ananada:: Interactive Linear Algebra with Maple V, w. CD-ROM 1998. XIII, 316 p. 23,5 cm Kt A Complete Software Package for doing Linear Algebra. (Textbooks in Mathematical Sciences) 'Buchwelt.de'

50. Infinite Lie/Kac-Moody Algebras/Groups Via Non-Category TheoryMathematics By Osh osher@ix.netcom.com Date Sat, 18 Jan 2003 180836 0500 Two prominent mathematicians,Nathan Jacobson of Yale and saunders maclane of U. Illinois Chicago http://mathforum.org/epigone/math-history-list/croyvexkherm/vq8vdo9t6rpf@legacy

Infinite Lie/Kac-Moody Algebras/Groups via Non-Category TheoryMathematics by Osher Doctorow reply to this message post a message on a new topic Back to messages on this topic Back to math-history-list Subject: Infinite Lie/Kac-Moody Algebras/Groups via Non-Category TheoryMathematics Author: osher@ix.netcom.com Date: http://education.vnsl.com/riasm/scope.html (ISKMAA 2002), and a volume by S. Kumar, "Kac-Moody Groups, their Flag Varieties and Representation Theory," Birkhauser: Boston 2002. I have been showing on www.superstringtheory.com/forum and elsewhere that the underlying Radicals are fundamentally additive-subtractive rather than multiplicative-divisive, which further exceeds what Category Theory can show since the notion of a critical distinction between addition-subtraction and multiplication-division beyond what the distributive law rather vaguely states is foreign to the philosophy of Category Theory. Osher Doctorow The Math Forum

51. MATHEMATICALLY SPEAKING: A DICTIONARY OF QUOTATIONS Browder, Felix E. maclane, saunders Quoted in Lynn Arthur Steen MathematicsToday Twelve Informal Essays The Relevance of Mathematics (p. 348). http://www.angelfire.com/tx/StatBook/math.html

Carl C. Gaither and Alma E. Cavazos-Gaither Illustrated by Andrew Slocombe Mathematically Speaking is a book of quotations (1543 quotations by 659 authors). It has, for the first time, brought together in one easily accessible form the best expressed thoughts that are especially illuminating and pertinent to the discipline of Mathematics. Some of the quotes are profound, others are wise, some are witty, but none are frivolous. Here you will find quotations from the most famous to the unknown. You may not find all the quoted `jewels' that exist, but we are sure you will find a great many of them here. The extensive author and subject indexes provide you with the perfect tool for locating quotations for practical use or pleasure, and you will soon enjoy discovering what others have said on topics ranging from addition to zero . This book will be a handy reference for the mathematician or scientific reader and the wider public interested in who has said what on mathematics. Readership: Professionals, teachers, students and general readers interested in mathematics and its impact on life. March 1998 Institute of Physics Publishing, Bristol, England

52. Catálogo De Autores maclane, saunders, 1909-(1); Maclver, RM(1);Macpherson, Crawford Brough(1); Macrae, Norman(1); Macrae, R.(1); Macsai http://biblioteca.unet.edu.ve/ALEXANDR/CATALOGOS/bcunet/Cat.Aut_14.HTM

M Ma´rin de L' Hotellerie, José Luis Maad, Margaret, 1901 Maas, Peter Mabie, Hamilton Horth, 1914 ... Myrdal, Gunnar, 1898-

53. Kleene's Bibliography 81 (1996) 37. maclane, saunders. Stephen Cole Kleene. Biographicalmemoirs. vol. 75, National Academy of Sciences of the United http://math.library.wisc.edu/biblio.htm

S.C. Kleene's Bibliography " Proof by cases in formal logic ." Annals of Mathematics, vol. 35 (1934): 529-544. " A Theory of Positive Integers in Formal Logic ." Ph.D. diss., Princeton University, September, 1933. Revised June 1934. American Journal of Mathematics, vol. 57 (1935): " The inconsistency of certain formal logics ." with J.B. Rosser, Annals of Mathematics, vol. 36 (1935), pp. 630-636. "General recursive functions of natural numbers." Mathmatische Annalen, vol. 112 (1936): 727-742. Reprinted with addendum in: Undecidable; Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. ed. by Martin Davis, Raven Press Books, 1965. "Lambda definability and recursiveness." Duke Mathematical Journal, vol. 2 (1936): 340-353. "A note on recursive functions." Bulletin of the American Mathematical Society, vol. 42 (1936): 544-546. "Formal definitions in the theory of ordinal numbers." with Alonzo Church, Fundamenta Mathematica, vol. 28 (1936): 11-21.

54. BWBCAT VIDEO 062 SEE LIBRARIAN. Algebra as a means of understanding mathematics.Mac Lane, S. (maclane, saunders) American Mathematical Society (AMS). http://library.ictp.trieste.it/VWEB/vweb.html

list of videos videos can be seen only in the library upon reservation title/author shelf A whisper from space. Jones, P. (Peter) ; Moore, R. (Ray) British Broadcasting Corporation (BBC). London, BBC, 1978. VIDEO 001 SEE LIBRARIAN The other way. Mansfield, J.M. (John M.) ; Holm, I. (Ian) British Broadcasting Corporation (BBC). London, BBC, 1974. VIDEO 002 SEE LIBRARIAN The message in the rocks. Nisbett, A. (Alec) ; Vaughan, P. (Paul) British Broadcasting Corporation (BBC). London, BBC, 1978. VIDEO 003 SEE LIBRARIAN Mars alive. Ceresole, P. (Peter) ; Pigott-Smith, T. (Tim) British Broadcasting Corporation (BBC). London, BBC, 1993. VIDEO 004 SEE LIBRARIAN 10,000 year test. Rowe, J. (John) British Broadcasting Corporation (BBC). London, BBC, 1990. VIDEO 005 SEE LIBRARIAN Prof. Hawking's universe. Jarvis, M. (Martin) British Broadcasting Corporation (BBC). London, BBC, 1983. VIDEO 006 SEE LIBRARIAN The amazing Dr. Newton. Newton, I. (Isaac) British Broadcasting Corporation (BBC). London, BBC, 1977. VIDEO 007 SEE LIBRARIAN The black holes of gravity.

55. Iterated Function System Ornstein's advisor Irving Kaplansky. Kaplansky's advisor - saunders maclane.maclane's advisor - Paul Isaac Bernays, maclane's advisor - Hermann Weyl. http://www.uwec.edu/Academic/Curric/gouletmr/tree.htm

My PhD Advisor - Robert M. Burton Bob's Advisor - Donald S. Ornstein Ornstein's advisor - Irving Kaplansky Kaplansky's advisor - Saunders MacLane MacLane's advisor - Paul Isaac Bernays MacLane's advisor - Hermann Weyl Bernays' advisor - Edmund Landau Weyl's advisor - David Hilbert Landau's advisor - Ferdinand Frobenius Hilbert's advisor - Carl Louis Ferdinand von Lindemann Frobenius's advisor - Karl Weierstrass Lindemann's advisor - Felix Klein Weierstrass' advisor - Christoph Gudermann Klein's advisor - Julius Plücker from the University of Bonn

56. Fermat's Little Theorem I believe that saunders maclane got his doctorate 1934 in G ottingen. I wouldimagine that the terminology had been long current at that time. http://www.spd.dcu.ie/johnbcos/fermat's_little_theorem.htm

Fermat's little theorem Friday 17 th August 2001 was the 400 th anniversary of the birth of Pierre de Fermat , and by way of a personal homage I decided that for the ICTMT5 meeting in Klagenfurt, Austria - held the week prior to Fermat's anniversary - I would offer a talk, using Maple, called Fermat's little theorem . It was never my intention to cover all of my prepared talk in Klagenfurt, and, in the event, I covered less than 0.1% of what I actually prepared. My Maple worksheet (129KB) may be downloaded here , and a (large) html version of it may be downloaded here large because Maple converts all outputs to gif files, and there are 447 of those in the worksheet). I dedicated my lecture to Mark Daly - a former colleague, and friend - as a token of my regard for him. Klaus Barner of Kassel university, Germany, disputes the date of Fermat's birth, and interested persons ought to read his papers: Pierre de Fermat (1601? - 1665) , European Mathematics Society Newsletter No. 42, December 2001 How old did Fermat become? 2001

57. Daniele's Casual Category Archive Logic Cambridge, 1986. MM, saunders maclane, Ieke Moerdijk Sheavesin Geometry and Logic SpringerVerlag, 1992. BW, Michael Barr http://www.daimi.au.dk/~varacca/CCT/categories.html

Daniele's Casual Category Archive Literature [SML] Saunders Mac Lane Categories for the Working Mathematician Springer-Verlag, New York, 1971 [CHW] Lecture Notes in Category Theory (Draft) [CML] Colin McLarty: Elementary Categories, Elementary Toposes Oxford, 1991 [BP] Benjamin Pierce: Basic Category Theory for the Computer Scientist MIT Press, 1991 [PT] Paul Taylor: Practical Foundation of Mathematics Cambridge, 1999 [Home page of the book] [LS] Joachim Lambek, Philip Scott: Introduction to Higher Order Categorical Logic Cambridge, 1986 [MM] Saunders MacLane, Ieke Moerdijk: Sheaves in Geometry and Logic Springer-Verlag, 1992 [BW] Michael Barr, Charles Wells: Toposes, Triples and Theories Springer-Verlag, New York, 1985 [dvi.zip] G. M. Kelly: Basic Concepts of Enriched Category Theory London Math. Soc. Lecture Notes, Cambridge University Press, 1982 Glynn Winskel, Mogens Nielsen: Models for Concurrency Chapter in Handbook of Logic and the Foundations of Computer Science, vol. 4, pages 1-148, Oxford University Press, 1995

58. This Stuff Could Blow Your Mind!! 1983. Garrett Birkhoff and saunders maclane. Algebra. New York Chelsea. 1988.TS Blyth. 1984. saunders maclane. Categories for the Working Mathematician. http://canddsmith.home.mindspring.com/FavLinks/favrefs.htm

It is only when we forget all our learning that we begin to know. Henry David Thoreau Favorite Math References Chris M. Smith M.A. Armstrong. Basic Topology . New York: Springer-Verlag. 1983. Garrett Birkhoff and Saunders MacLane. Algebra . New York: Chelsea. 1988. T.S. Blyth. Categories . New York: Longman. 1986. George L. Cain. Introduction to General Topology . Reading, Massachusetts: Addison-Wesley. 1994. Peter Freyd. Abelian Categories: An Introduction to the Theory of Functors Algebra . Menlo Park, California: Addison-Wesley. 1984. Saunders MacLane. Categories for the Working Mathematician . New York: Springer-Verlag. 1971. William S. Massey. Algebraic Topology, an Introduction . New York: Springer-Verlag. 1967. Bodo Pareigis. Categories and Functors . New York: Academic Press. 1970. Andrew H. Wallace. Algebraic Topology: Homology and Cohomology . New York: W.A. Benjamin. 1970. Andrew H. Wallace. Differential Topology, First Steps . New York: W.A. Benjamin. 1968. Andrew H. Wallace. An Introduction to Algebraic Topology . New York: Pergamon Press. 1961. BACK TO MAIN PAGE

59. ISSUES IN SCIENCE AND TECHNOLOGY: Index Volume XII XII(1)16 Krebs, Martha. XII(1)1617 Lane, Neal. XII(2)5 maclane,saunders. XII(1)17 Pings, Cornelius J., and John C. Vaughn. http://www.utdallas.edu/research/issues/xiiindex.html

ISSUES IN SCIENCE AND TECHNOLOGY Return to main page of index Return to ISSUES Homepage.

60. Das Virtuelle Bücherregal NRW Translate this page 2.905.841 3.127.124 3.371.841 3.550.173 3.555.768 3.682.496 3.724.353 4.419.0324.742.636 4.940.471 7.333.828 7.420.587 maclane, saunders 255.933 MacLaughlin http://kirke.hbz-nrw.de/dcb/Schlagwoerter/1239.html

Ein freundliches Angebot des Hochschulbibliothekszentrums des Landes Nordrhein-Westfalen Projekt 'Virtuelle Kataloge / Innovative Verfahren' Welche Ziele verfolgt das Projekt? Root-Seite Navigation: Prev Up Next MacKenzie, David N. Mackenzie, Duncan Mackenzie, Edward Montague Compton Mackenzie, Henry Mackenzie, William Mackenzie-River-Tal Mackie, John L. Mackiewicz, Józef Mackiewicz, Stanislaw MacKillip, Patricia A. Mackinder, Halford J. MacKinley, William Thomas MacKinsey and Company Mackintosh, Charles Rennie Mackintosh, Hugh R. Mackowitz, Heinz MacLachlan, Jessie MacLachlan, Laurentia MacLaine, Shirley MacLane, Saunders MacLaverty, Bernard MacLaverty, Michael MacLean Gang MacLean, Bruce MacLeish, Archibald MacLennan, Hugh MacLuhan, Marshall MacMath 9.2 MacMichael, Robert MacMillan and Co. Macmillan Company of Canada Macmillan, Harold MacMurtry, Larry MacNally, Terrence MacNamara, Robert S. MacNeice, Louis MacNeil-River-Gebiet MacNeill, Elizabeth Macoma MacOrlan, Pierre MacOS MacOS 7 MacOS 7.5 MacOs 7.6 MacOS 8 MacOS 8.5 MacOS 9 MacOS X MacOS X 10.1 MacOS X Server MacPhee, John A.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 3     41-60 of 90    Back | 1  | 2  | 3  | 4  | 5  | Next 20