41. College Mathematics Journal, The: A Generalized Chinese Remainder Theorem He received his BA from Vanderbilt and his Ph.D. from Duke University under theguidance of leonard carlitz. In 1995 he was the section lecturer of the http://www.24hourscholar.com/p/articles/mi_qa3773/is_200209/ai_n9145192

@import url(http://www.looksmartcollege.com/css/ubervert/style.css); @import url(http://www.looksmartcollege.com/css/ubervert/article.css); Home August 31, 2005 Search for in this site other sources Home College Mathematics Journal, The Content provided in partnership with Find. Top publications by title Journal of Social Issues American Enterprise AI Magazine American Mathematical Monthly ... view more titles Save. Save a copy of this page Print this page Share. Link to this page See most popular pages Magazine Cover The 29 Healthiest Foods on the Planet Ten Easy Ways to Improve Your Resume Gardening Tips - The Helpful Gardener A generalized Chinese remainder theorem College Mathematics Journal, The , Sep 2002 by Howard, Fredric T According to L. E. Dickson [1, p. 57], the Chinese Remainder Theorem can be traced back to the following problem of Sun-Tsu in the first century A.D.: "Determine a number having the remainders 2, 3, 2 when divided by 3, 5, 7 respectively." Reference 1. Leonard Eugene Dickson, History of the Theory of Numbers, Volume II, originally published in 1919 by the Carnegie Institute of Washington, reprinted by Chelsea, 1971, and the American Mathematical Society, 1999. Curve Sketching on Wall Street From a Reuters dispatch, "Stocks set to rally after steep sell-off" by Denise Duclaux, September 24, 2001:

42. Graph Theory White Pages Anthony Edward Barkauskas Ph.D. 1972 Duke; leonard carlitz Algebraic and analytic properties of Lommelpolynomials Graph Theory Publications. Efficient domination of the http://www1.cs.columbia.edu/~sanders/graphtheory/people/Barkauskas.AE.html

Use the Search Engine to get to the new data.

43. Famous Mathematicians With AC Francesco Cantelli Georg Cantor Moritz Cantor Juan Caramuel Constantin CaratheodoryPierre de Carcavi Girolamo Cardano leonard carlitz Thomas Carlyle http://www.famousmathematician.com/az/mathematician_C.htm

Mathematicians - C Renato Caccioppoli Florian Cajori Alberto Calderon Callippus John Campbell Charles Camus Doris Cannell Francesco Cantelli Georg Cantor Moritz Cantor Juan Caramuel Constantin Caratheodory Pierre de Carcavi Girolamo Cardano Leonard Carlitz Thomas Carlyle Lazare Carnot Sadi Carnot Lewis Carroll Horatio Carslaw Elie Cartan Henri Cartan Dame Mary Cartwright Felice Casorati John Cassels Giovanni Cassini Louis Castel Guido Castelnuovo Alberto Castigliano Johann Castillon Eugene Catalan Pietro Cataldi Augustin-Louis Cauchy Bonaventura Cavalieri Arthur Cayley Eduard Cech Ernesto Cesaro Ludolph van Ceulen Giovanni Ceva Tommaso Ceva Sergi Chaplygin Sydney Chapman Gabrielle du Chatelet Nikolai Chebotaryov Pafnuty Chebyshev Shiing-shen Chern Sergei Chernikov Claude Chevalley Grace Chisholm Young Sarvadaman Chowla Elwin Christoffel Chrysippus George Chrystal Graham Fan Chung Nicolas Chuquet

44. Colloquia And Seminars - UNL - Department Of Mathematics In 1960, a short paper by leonard carlitz appeared in the Proceedings of theAmerican Mathematical Society which contained the following result Theorem http://www.math.unl.edu/pi/colloquia/abstract-20050225.txt

February 25: An Introduction to the Theory of Non-Unique Factorizations in Integral Domains and Monoids Speaker: Scott Chapman (Trinity University - San Antonio, TX) Local Host: Roger Wiegand Abstract: In 1960, a short paper by Leonard Carlitz appeared in the Proceedings of the American Mathematical Society which contained the following result: Theorem: The algebraic number field Z has class number less than or equal to 2 if and only if for every nonzero integer z in Z the number of irreducible elements in every factorization z = i_1i_2 · · · i_k depends only on z. While the proof of this theorem requires only about a page, it is clearly responsible for the inception, 20 years later, of the study of non-unique factorizations into irreducible elements in integral domains and monoids. This study has many different facets, some of which reach beyond commutative algebra into combinatorics, finite abelain group theory, semigroups, monoids, and even additive number theory. This talk will briefly review the history, since Carlitz’s paper, of this subject and give an overview of the direction of current research. printable version

45. Publications Joel V. Brawley, ``In Memoriam leonard carlitz (19071999) , Finite Fields and Joel V. Brawley, ``Dedicated to leonard carlitz The Man and his Work. http://www.math.clemson.edu/~sgao/WEB/publications.html

Home Research People Courses ... Resources Applicable Algebra Lab Publications Books Alfred J. Menezes (Editor), Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone and Tomic Yaghoobian, Applications of Finite Fields Kluwer Academic Publishers, Boston/Dordrecht/Lancaster, 1993. E. F. Assmus, Jr. and J. D. Key, Designs and their Codes , Cambridge Tracts in Mathematics No. 103, Cambridge University Press, 1992. (paperback edition, 1994). J. V. Brawley and G. E. Schnibben, Infinite Algebraic Extensions of Finite Fields , Contemporary Mathematics, Vol. 95, A.M.S., Providence R.I., 1989 (reprinted, 1992). J. V. Brawley and S. M. Lukaecki, Problem Solving for High School Teachers with the Sharp EL 5200 Calculator, Clemson University Department of Mathematical Sciences, Clemson, SC 1991. Chapters in books Joel V. Brawley and Shuhong Gao, `` Mathematical Models in Classical Cryptology, Joel V. Brawley and Shuhong Gao, `` Mathematical Models in Public-key Cryptology Joel V. Brawley, `` Vector Spaces' ' in Handbook of Discrete and Combinatorial Mathematics, CRC Press, 2000, 361-369. Joel V. Brawley, ``

46. Joel V Brawley (May be viewed at http//www.strom.clemson.edu/publications/gambling/pokermath.pdf);In Memoriam leonard carlitz (19071999), Finite Fields and their http://www.math.clemson.edu/facstaff/brawley.htm

Joel V Brawley Position: Alumni Distinguished Professor of Mathematical Sciences; Professor of Curriculum and Instruction Education: PhD, Mathematics/Statistics, North Carolina State University, 1964 MS, Mathematics/Statistics, North Carolina State Unviersity, 1962 BS, Engineering Mathematics/Engineering Mechanics, North Carolina State University, 1960 Professional Interests: Algebra and discrete mathematics and their applications. Professional Activities: Mathematical Association of America, American Mathematical Society, International Linear Algebra Society Recent Publications: Video Poker in South Carolina: A Mathematical Study (with Todd D. Mateer). The SC Digest. Strom Thurmond Institute, Clemson University. 1999. (May be viewed at http://www.strom.clemson.edu/publications/gambling/pokermath.pdf) In Memoriam: Leonard Carlitz (1907-1999), Finite Fields and their Applications. 6: 203-206 (2000). Associative Rational Functions in Two Variables (with D. Mills and S. Gao). Proc. of the Fifth Internat. Conference on Finite Fields and Appl., 4356, 2001. Related Web Sites: Department of Mathematical Sciences Joel V Brawley; Professor, Mathematical Sciences; Clemson University; O-020 Martin Hall; Clemson, SC 29634-0975; 864-656-5199 (office); 864-656-5230 (fax); email:

47. Previous Issues Of The Fibonacci Quarterly 316316 In Memoriam-leonard carlitz, by FT Howard On Some Reciprocal Sumsof BrousseauAn Alternative Approach to That of carlitz, by RS Melham http://www.engineering.sdstate.edu/~fib/fibprevious.html

Back issues of The Fibonacci Quarterly are available in microfilm or hard copy from `University Microfilms International', and reprints from `UMI Clearing House', both at 300 North Zeeb Road, Dept. P.R., Ann Arbor MI 48106. Click here to go to Papers in 1996 ( any volume of 1996) Volume 34, parts A B C D ... E Papers in 1997 ( any volume of 1997) Volume 35, parts A B C D Papers in 1998 ( any volume of 1998) Volume 36, parts A B C D ... E Papers in 1999 ( any volume of 1999) Volume 37, parts A B C D Papers in 2000 ( any volume of 2000) Volume 38, parts A B C D ... E Papers in 2001 ( any volume of 2001) Volume 39, parts A B C D ... E Papers in 2002 ( any volume of 2002) Volume 40, parts A B C D ... E Papers in 2003 ( any volume of 2003) Volume 41, parts A B C D ... E Papers in 2004 ( any volume of 2004) Volume 42, parts A B C D Papers in 2005 ( any volume of 2005) Volume 43, parts A B Papers in the FEBRUARY 1996 issue ( Volume 34.1) On Some Properties of Generalized Hermite Polynomials, by Gospava Djordjevic Minmax Polynomials, by A. F. Horadam Seventh International Research Conference On the Approximation of Irrational Number with Rationals Restricted by Congruence Relations, by C. Elsner

48. O Death of leonard carlitz 9. Question on Painleve II numerics 10. Preprints inxxx Archive 11. Changes of address, WWW pages, etc. 12. http://staff.science.uva.nl/~thk/opsfnet/8.5

Subject: Nominations SIAM has accepted the report of the nominating committee for the upcoming election of officers of our Group, for the period January 1, 2002 to December 31, 2004. The candidates are as follows: Chair Daniel Lozier, National Institute for Standards oand Technology Vice Chair Charles Dunkl, University of Virginia Walter Van Assche, Katholieke Universiteit Leuven Secretary Peter Clarkson, University of Kent at Canterbury Peter McCoy, US Naval Academy Program Director Francisco (Paco) Marcellan, Universidad Carlos III de Madrid Candidates have been invited to submit biographies and statements and SIAM will shortly send ballots to the members of the Activity Group. Topic #2 - OP-SF NET 8.5 September 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor Subject: Tel Aviv Workshop on Approximation Theory [From AT-NET BULLETIN NO. 106, 25.8.2001] Workshop on Approximation Theory Celebrating Dany Leviatan's 60th Birthday February 20 - 21, 2002 Tel-Aviv Information: http://www.math.tau.ac.il/~levin/ws2002.html Organizing Committee: Nira Dyn, David Levin, Allan Pinkus Topics: Abstract and Classical Approximation Theory; Orthogonal Polynomials; Wavelets; Non-linear Approximation; Ridge Functions; Shape Preserving Approximation. Present List of International Participants: Bruce Chalmers (Riverside), Albert Cohen (Paris VII), Wolfgang Dahmen (Aachen), Ron DeVore (South Carolina), Zeev Ditzian (Edmonton), Manfred v. Golitschek (Wurzburg), Viktor Konovalov (Kiev), Giuseppe Mastroianni (Potenza), Paul Nevai (Ohio), Konstantin Oskolkov (South Carolina), Igor Shevchuk (Kiev), Jozsef Szabados (Budapest), Vladimir Temlyakov (South Carolina). Participation is by invitation only. People interested in attending should contact one of the organizers. Topic #3 - OP-SF NET 8.5 September 15, 2001 ~~~~~~~~~~~~~ From: OP-SF NET Editor

49. IngentaConnect Groups Of Permutation Polynomials Over Finite Fields induced by the linear polynomials and any power map which induces a permutationon F. This generalizes a result of leonard carlitz (1953, Proc. Amer. http://www.ingentaconnect.com/content/ap/ff/1998/00000004/00000004/art00224

Home About Ingenta Ingenta Labs Help For Publishers Why go online? Why choose IngentaConnect? Why choose CustomConnect? Access and authentication ... Contact us For Researchers About IngentaConnect Search and browse Publications available Accessing articles ... Register For Librarians Why choose IngentaConnect? Why choose IngentaConnect Premium? Activating Subscriptions Purchasing articles ... Browse Publications Groups of Permutation Polynomials over Finite Fields Author: Lidl R.R.M. Source: Finite Fields and Their Applications , Volume 4, Number 4, October 1998, pp. 450-452(3) Publisher: Academic Press View Table of Contents full text options Abstract: Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F . This generalizes a result of Leonard Carlitz (1953, Proc. Amer. Math. Soc. Language: English Document Type: Research article The full text article is available for purchase $54.10 plus tax

50. IngentaConnect Table Of Contents: Finite Fields And Their Applications leonard carlitz (19071999) pp. 203-206(4) Author Brawley JV. Decoding AlgebraicGeometry Codes by a Key Equation pp. 207-217(11) Author Farran JI http://www.ingentaconnect.com/content/els/10715797/2000/00000006/00000003

Home About Ingenta Ingenta Labs Help For Publishers Why go online? Why choose IngentaConnect? Why choose CustomConnect? Access and authentication ... Contact us For Researchers About IngentaConnect Search and browse Publications available Accessing articles ... Register For Librarians Why choose IngentaConnect? Why choose IngentaConnect Premium? Activating Subscriptions Purchasing articles ... Browse Publications Finite Fields and Their Applications ISSN 1071-5797 Publisher: Elsevier Science Volume 6, Number 3, July 2000 all issues Leonard Carlitz (1907-1999) pp. 203-206(4) Author: Brawley J.V. Decoding Algebraic Geometry Codes by a Key Equation pp. 207-217(11) Author: Farran J.I. Euler Pseudoprime Polynomials and Strong Pseudoprime Polynomials pp. 218-243(26) Author: Mauduit V. Classification of Type IV Self-Dual Z -Codes of Length 16 pp. 244-254(11) Authors: Harada M.; Munemasa A. On the Cyclicity of Goppa Codes, Parity-Check Subcodes of Goppa Codes, and Extended Goppa Codes pp. 255-281(27) Author: Berger T.P. all issues Terms and Conditions Page Help Quick Search Electronic content Fax/Ariel content Journal or book title Sign in: User name Password Remember me forgotten your password?

51. Sums Of Divisors, Perfect Numbers, And Factoring 4 leonard carlitz, The arithmetic of polynomials in a Galois field , Amer. Journ.Math.,54 (1932) 3950. 5 RD Carmichael, A table of multiply perfect http://portal.acm.org/citation.cfm?id=808680

52. Combinatorics Authors/titles Jun 2000 Title Completion of a Rational Function Sequence of carlitz Authors leonard M.Smiley Comments 8 pages Subjclass Combinatorics http://arxiv.org/list/math.co/0006

Combinatorics Authors and titles for Jun 2000 math.RT/0006004 abs ps pdf other Title: Construction of commuting difference operators for multiplicity free spaces Authors: Friedrich Knop Comments: 28 pages, plain TeX, minor changes in the exposition, slightly improved table Subj-class: Representation Theory; Combinatorics; Quantum Algebra MSC-class: Journal-ref: Selecta Math. (N.S.) 6 (2000), 443-470 math.PR/0006017 abs ps pdf other Title: The standard deviation effect (or why one should sit first base playing blackjack) Authors: E. Munoz Garcia R. Perez Marco Comments: 27 pages Subj-class: Probability; Combinatorics MSC-class: math.CO/0006036 abs ps pdf other Title: When Does the Positive Semidefiniteness Constraint Help In Lifting Procedures Authors: Levent Tuncel (University of Waterloo), Michel X. Goemans (MIT) Comments: 24 pages, 3 images Subj-class: Combinatorics; Operator Algebras math.CO/0006066 abs ps pdf other Title: Who Wins Domineering on Rectangular Boards? Authors: Michael Lachmann Cristopher Moore Ivan Rapaport Subj-class: Combinatorics Journal-ref: MSRI Workshop on Combinatorial Games 2000 math.CO/0006067

53. Publication List (Dedicated to leonard carlitz on his 90th birthday); (with J. Wetweerapong)Evaluation of some classes of binomial identities http://www.math.wvu.edu/~gould/publications.html

H. W. Gould, Articles in Professional Journals THIS IS AN ABBREVIATED LIST Note on a paper of Grosswald, Amer. Math. Monthly, 65(1954), 251-253. MR 15(1954),p.685. Some generalizations of Vandermonde's convolution, Amer. Math. Monthly, 63(1956), 84-91. MR 17(1956), p. 702. Final analysis of Vandermonde's convolution, Amer. Math. Monthly, 64(1957), 409-415. MR 19(1958), p.379. A theorem concerning the Bernstein polynomials, Math. Mag., 31(1958), 259-264. MR 20(1959), #5997. Note on a paper of Sparre Andersen, Math. Scand., 6(1958), 226-230. MR 21(1960), p.491. Dixon's series expressed as a convolution, Nordisk Mat. Tidsk., 7(1959), 73-76. Summary on p. 96. MR 22(1961), #115 Note on a paper of Steinberg, Math. Mag., 33(1959), 46-48. MR 21(1960), #4924 An iterative approximation for finding the n-th root of a number, Math. Mag., 33(1959), 61-69. MR 23(1962) #B556. Generalizations of a theorem of Jensen concerning convolutions, Duke Math. J., 27(1960), 71-76. MR 22(1961), #5585. Stirling number representation problems, Proc. Amer. Math. Soc.

54. The Arithmetic Of Polynomials In A Galois Field leonard carlitz*. Department of Mathematics, California Institute of Technology.*National Research Fellow. Full text. Full text is available as a scanned http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1076006

55. HLAVATY MSS. II Ranier Burghardt, Herbert Busemann, Elmore Everest Butterfield, Stewart ScottCairns, Nigel Calder, leonard carlitz, Robert Daniel Carmichael, http://www.indiana.edu/~liblilly/lilly/mss/html/hlavaty2.html

HLAVATY MSS. II Correspondence with friends in Czechoslovakia and different parts of the world deals almost exclusively with personal and family matters. About thirty percent of all of the correspondence is in Czech and some in Slovak. Collection size: 8,012 items For more information about this collection and any related materials contact the Manuscripts Department, Lilly Library, Indiana University, Bloomington, IN 47405 Telephone: (812) 855-2452.

56. AUTHOR INDEX, GHI G Gabai, Hyman Generalized Fibonacci K-Sequences Proc VIII (1999) 201 In Memoriam leonard carlitz 38.4 (2000) 316 IntegersRelated to the Bessel Function J1(z), 23.3 (1985) 249 Lacunary Recurrences http://www.mscs.dal.ca/Fibonacci/auth-ghi.txt

57. Some Fibonacci Personalities Home MacTutor History Of Brother Alfred Brousseau, FSC, 1907 1988. leonard carlitz, 1907 - 1999.Herta Freitag, 1908 - 2000. Verner Emil Hoggatt, Jr., 1921 - 1981. http://www.mscs.dal.ca/Fibonacci/biographies.html

Some "Fibonacci Personalities" Home MacTutor History of Mathematics ... Studies Click on the small pictures to see one or two larger ones, and click on the names to see a biographical sketch. Leonardo of Pisa (Fibonacci), 1170 - 1250. Samuel Beatty, 1881 - 1970. Jacques Binet, 1786 - 1856. Brother Alfred Brousseau, F.S.C., 1907 - 1988. ... Willem Abraham Wythoff, 1865 - 1939.

58. PNAS -- Index By Author (Feb 15 1931, 17 (2)) carlitz, leonard. K. Keeler, Clyde E. M. Michal, AD Murnaghan, Francis D. R.Ramsperger, HC Rutzler, JE. T. Thomas, Tracy Yerkes. W http://www.pnas.org/content/vol17/issue2/aindex.shtml

Index by Author: Feb 15 1931; 17 (2) [Table of Contents] 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 B Bancroft, Wilder D. [PDF] Borsook, Henry [PDF] Byerly, Perry [PDF] C Carlitz, Leonard [PDF] K Keeler, Clyde E. [PDF] M Michal, A. D. [PDF] Murnaghan, Francis D. [PDF] R Ramsperger, H. C. [PDF] Rutzler, J. E. [PDF] T Thomas, Tracy Yerkes [PDF] W Waddington, G. [PDF] Whitney, Hassler [PDF] Whitney, Hassler [PDF] Winegarden, Howard M. [PDF] Current Issue Archives Online Submission ... Site Map

59. PNAS -- Table Of Contents (Feb 15 1931, 17 (2)) leonard carlitz The Arithmetic of Polynomials in a Galois Field PNAS 1931 17120122. Access through JSTOR. Hassler Whitney The Coloring of Graphs http://www.pnas.org/content/vol17/issue2/

Table of Contents February 15, 1931; 17 (2) [Index By Author] Henry Borsook and Howard M. Winegarden On the Specific Dynamic Action of Protein PNAS 1931 17: 75-91. [PDF] Perry Byerly The California Earthquakes of Nov. 28, 1929. And the Surface Layers of the Earth in California PNAS 1931 17: 91-100. [PDF] Clyde E. Keeler The Independence of Dominant Spotting and Recessive Spotting ("Piebald") in the House Mouse PNAS 1931 17: 101-102. [PDF] H. C. Ramsperger and G. Waddington The Interpretation of the Thermal Decomposition of Nitrous oxide PNAS 1931 17: 103-105. [PDF] Wilder D. Bancroft and J. E. Rutzler Reversible Coagulation in Living Tissue. I PNAS 1931 17: 105-111. [PDF] Tracy Yerkes Thomas On the Unified Field Theory. IV PNAS 1931 17: 111-119. [PDF] Leonard Carlitz The Arithmetic of Polynomials in a Galois Field PNAS 1931 17: 120-122. [PDF] Hassler Whitney The Coloring of Graphs PNAS 1931 17: 122-125. [PDF] Hassler Whitney Non-Separable and Planar Graphs PNAS 1931 17: 125-127. [PDF] Francis D. Murnaghan The Principle of Maupertuis PNAS 1931 17: 128-132.

60. Here Are The Names Currently [April 1999] In The Index At Http Torsten Carleson, Lennart carlitz, leonard Carlotto, MArk J. Carlson, D.Carlson, Walter M. Carlsson, Bengt Carnap, Rudolf Carnot, Sadi Carpinelli, http://www.math.niu.edu/~rusin/known-math/99/photos

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

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