1. Seki Biography of takakazu Seki (16421708) takakazu Seki was born into a samuraiwarrior family. However at an early age he was adopted by a noble family http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Seki.html

Takakazu Seki Kowa Born: March 1642 in Fujioka, Kozuke, Japan Died: 24 Oct 1708 in Edo (now Tokyo), Japan Click the picture above to see three larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Takakazu Seki was born into a samurai warrior family. However at an early age he was adopted by a noble family named Seki Gorozayemon. The name by which he is now known, Seki, derives from the family who adopted him rather than from his natural parents. Seki was an infant prodigy in mathematics. He was self-educated in mathematics having been introduced to the topic by a servant in the household who, when Seki was nine years old, realised the talent of the young boy. Seki soon built up a library of Japanese and Chinese books on mathematics and became acknowledged as an expert. He was known as 'The Arithmetical Sage', a term which is carved on his tombstone, and soon had many pupils. His position in life is described in [18] as follows:- In due time he, as a descendant of the samurai class, served in public capacity, his office being that of examiner of accounts to the Lord of Koshu, just as

2. Yumoto, Takakazu Tropical ecology. Profile. http://www.ecology.kyoto-u.ac.jp/member/yumoto.html

3. Seki Biography of takakazu Seki (16421708) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

4. References For Seki References for the biography of takakazu Seki. A Hirayama, The year in whichtakakazu Seki copied the Yang Hui Suanfa (Japanese), Sugakushi Kenkyu 68 http://www-groups.dcs.st-and.ac.uk/~history/Printref/Seki.html

References for Takakazu Seki Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: Y Mikami, The Development of Mathematics in China and Japan (Leipzig-New York, 1913). Articles: M Fujiwara, Miscellaneous notes on the history of Wazan. VII. (The works of Takakazu Seki) (Japanese), T Hamada, Y Michiwaki and M Oyama, On the influence of the 'Seki's School versus the Saijo School controversy' in the provinces (Japanese), Sugakushi Kenkyu A Hirayama, On the 'Ketsugisho Tojutsu' of Takakazu Seki (Japanese), Sugakushi Kenkyu A Hirayama, The year in which Takakazu Seki copied the 'Yang Hui Suanfa' (Japanese), Sugakushi Kenkyu H Hirose, Takakazu Seki on astonomy and the calendar (Japanese), Sugakushi Kenkyu S Hosoi, The history of mathematics of Takakazu Seki (Japanese), Sugaku H Kato, On the work of Takakazu Seki (Japanese), Sugaku Y Michiwaki, T Hamada, O Toshio and M Oyama, On a mathematical problem for an anniversary of Takakazu Seki's death (Japanese), Sugakushi Kenkyu T Ogawa, Takakazu Seki - another type of mathematics? (Japanese), Sugaku 45 (1) (1993), 86-90.

5. Girls’ Horror Comics Includes a magazine list and bibliographies for takakazu Nagakubo, Chie Watari, and other artists. http://www.thirteens.net/~ghc/

In any case, as long as Narumi Kakinouchi Vampire series and Takakazu Nagakubo Karura Mau! are still running in the Susperia Mystery Featured Authors ÔÎ˜H‘ã Michiyo Akaishi Chie Watari ‰i‹v•Û‹Mˆê ... Takakazu Nagakubo One of the true masters of the genre. Other Artists A B C E ... Links Search the Site AND OR Case Insensitive Sensitive Please send comments or corrections here ‚²ˆÓŒ©E‚²Žw“E‚Í ‚Öƒ[ƒ‹‰º‚³‚¢B

6. Lawrence University Scarff Visiting Professors takakazu Kuriyama. takakazu Kuriyama, LL.D. '93, who attended Lawrence University in the mid1950s and went on to become Japan's ambassador to the http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Takakazu Satoh takakazu Satoh Associate Professor. Department of Mathematics Tokyo Institute ofTechnology, Ohokayama 2-12-1, Meguro-ku, Tokyo, 152-8551 http://mathpc-satoh.math.titech.ac.jp/en/TkkzSatoh.html

Takakazu Satoh Associate Professor Department of Mathematics Tokyo Institute of Technology, Oh-okayama 2-12-1, Meguro-ku, Tokyo, 152-8551 JAPAN e-mail: satopug2cm mathpc-satoh.math.titech.ac.jp Research area: Number theory, especially: Modular forms and differential operators acting on them Properties of elliptic curves over finite or non Archimedean local fields my c.v. List of Papers Unpublished Preprint(s) Research announcement On degrees of polynomial interpolations related to ECC. Tanja Lange and Arne Winterhof gave many results on degrees of polynomial interpolations of functions related to DL based cryptosystems including ECC in their series of papers. We gave two more results on the topic: The one concerns about ECDL on curves with an endomorphism of degree 2 or 3. The other concerns about embeddings of a subgroup of the multiplicative group of a finite field to an elliptic curve. I gave a seminar talk Generalized division polynomials A generalization of division polynomials to non rational integer endomorphisms of elliptic curves with complex multiplications and an algorithm for computing them are given. The time complexity of this algorithm (with respect to a number of bit operations) for a given imaginary quadratic integer (identified with the endomorphism of the elliptic curve) is evaluated. The results are announced at Conference in Number Theory in Honour of Professor H.C. Williams

8. Counting Points On Elliptic Curves Robert Harley, Pierrick Gaudry, Fran§ois Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to takakazu Satoh. http://www.math.jussieu.fr/~fouquet/elliptic.html

Counting points on elliptic curves One of the topics of my PhD research is point counting on elliptic curves using the new algorithm due to Takakazu Satoh. My colleagues Robert Harley, Pierrick Gaudry and François Morain and I have recently established new records for point counting in characteristic 2. A copy of the announcement of our 3001-bit record can be found here A copy of the announcement of our 5003-bit record can be found here A copy of the announcement of our 8009-bit record can be found here You can also find a copy of the paper we wrote about this algorithm and its implementation here Let E be the curve: over GF(2^n) . We represent the field as GF(2)[x]/(f(x)) where f is an irreducible polynomial of degree n . The coefficient we chose is: which comes from the ASCII encoding (ISO-8859-1) of the following line by Charles Baudelaire: N'es-tu pas l'oasis où je rêve? The results we obtained are 2^n + 1 - t where: n = 503 t = -31238564670483795450312817872056405257868594699 n = 1009 t = 807681026366028357085789135197617870605796659019 n = 1511 t = -28400768556934958867743240430395694772857313718 n = 2003 t = -54257716382449163322217965867619130414983986889 n = 2503 t = 375456780359377839428248525231477119570486033306 n = 3001 t = -14403755582543872125177435497927178175213015805 n = 3511 t = 414328759607065317343606376361429657475308002212 n = 4001 t = 801772519193752131932619560339947365971034799872 The polynomials f(x) and the run-times were: f(x) CPU Time Memory used

9. Takakazu Satoh takakazu Satoh Associate Professor http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

10. Takakazu Satoh S Home Page takakazu Satoh s Home Page. Japanese English Norwegian. http://mathpc-satoh.math.titech.ac.jp/

Takakazu Satoh's Home Page

11. Seki, Kowa (Takakazu) Seki, Kowa (takakazu) (c. 16421708) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

12. International Canopy Network-CV-Takakazu Yumoto takakazu Yumoto Secretary (for Field Biology Course) Research Institute for Biology and Nature 335 Takashimacho - Kamigyo-ku Kyoto 602-0878, Japan http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Edo takakazu Seki Kowa St Andrews. Chokuyen Naonobu Ajima - St Andrews Aida Yasuaki - St Andrews. takakazu Seki Kowa - Brazil General History http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

14. Seki, Kowa (Takakazu) Seki, Kowa (takakazu) (c. 16421708). Japanese mathematician who created a newmathematical notation system and used it to discover many of the theorems and http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/S/Seki/1.html

Seki, Kowa (Takakazu) (c. 1642-1708) Japanese mathematician who created a new mathematical notation system and used it to discover many of the theorems and theories that were being - or were shortly to be - discovered in the West. Seki was born in Fujioka in Gunma prefecture. Much of his reputation stems from the social reform he introduced in order to develop the study of mathematics in Japan and make it widely accessible. He introduced Chinese ideograms to represent unknowns and variables in equations, and although he was obliged to confine his work to equations up to the fifth degree - his algebraic alphabet (endan-jutsu) was not suitable for general equations of the nth degree - he was able to create equations with literal coefficients of any degree and with several variables, and to solve simultaneous equations. In this way he was able to derive the equivalent of f(x), and thereby to arrive at the notion of a discriminant - a special function of the root of an equation expressible in terms of the coefficients. Another of Seki's contributions was the rectification of the circle; he obtained a value for that was correct to the 18th decimal place.

15. Takazazu YAMAMOTO Inorganic Resources Division takakazu YAMAMOTO, Ph.D. Professor http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. DBLP Takakazu Kawamata takakazu Kawamata. List of publications from the DBLP Bibliography Server FAQ http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Seki Takakazu Kowa - Yosida, K. A Brief Biography of takakazu Seki (1642? O Connor, JJ andRobertson, EF takakazu Seki Kowa. Includes portrait. http://famous.adoption.com/famous/seki-takakazu-kowa.html

@import url(/uni/adoption.com/rev6/styles/common.css); @import url(/uni/adoption.com/rev6/styles/screen.css); @import url(/uni/adoption.com/rev6/styles/tabs.css); @import url(/uni/adoption.com/rev6/styles/nav.css); Seki Takakazu Kowa Seki was born into a samurai warrior family, the second son of Nagaakira Utiyama, but was adopted as a young boy by another noble family, the Seki Gorozayemon. He was a self-educated child prodigy in mathematics from the age of nine. He studied determinants and Bernoulli numbers, and was the first in Japan to write on magic squares. He also studied Diophantine equations and the calculus. In some areas his work predates that of Europeans now credited with priority (e.g., Bernoulli numbers). He was also a renowned teacher and the examiner of accounts to the Lord of Koshu. Texas Looking to adopt? Pregnant? References Microsoft Encarta 98 Encyclopedia, 1993-97 Dictionary of Scientific Biography Mikami, Yoshio. The Development of Mathematics in China and Japan. (New York: Chelsea Pub. Co., 1961) Yosida, K. "A Brief Biography of Takakazu Seki (1642?-1708)," The Mathematical Intelligencer 3 (1981), pp. 121-22

18. Takakazu Mori - US Patent Inventor - Patent Storm takakazu Mori Patented inventions by inventor takakazu Mori. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. MSN Encarta - Takakazu Seki takakazu Seki (1640?1708), Japanese government official and pioneering mathematicianof Other Features from Encarta. Search Encarta for takakazu Seki http://encarta.msn.com/encyclopedia_761582885/Takakazu_Seki.html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Subscription Article MSN Encarta Premium: Get this article, plus 60,000 other articles, an interactive atlas, dictionaries, thesaurus, articles from 100 leading magazines, homework tools, daily math help and more for $4.95/month or $29.95/year (plus applicable taxes.) Learn more. This article is exclusively available for MSN Encarta Premium Subscribers. Already a subscriber? Sign in above. Takakazu Seki Takakazu Seki (1640?-1708), Japanese government official and pioneering mathematician of the Edo period (1603-1867), when Japan was ruled by shoguns,... Want more Encarta? Become a subscriber today and gain access to: Daily Math Help Literature Guides Researcher Tools Paper-Writing Guides 60,000 + articles Interactive Atlas Magazine Center Find more about Takakazu Seki from Other Features from Encarta Search Encarta for Takakazu Seki © 2005 Microsoft MSN Privacy Legal Advertise Feedback ... Help

20. Art Culos Analizados Autores Mukae, Naomi; Yokoyama, Hideki; Yokokura, takakazu; Sakoyama, Yasuhiko; Sakahira, Hideki; Nagata, Shigekazu http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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