Experimental math
The Experimental Mathematics is a discipline of mathematics , which is located between classical mathematics and calculations with the computer. In contrast to scientific computing , which serves to solve practical problems, experimental mathematics supports mathematical research itself. The computer is a tool for applying methods of numerical mathematics and computer algebra . Prominent application examples are the four-color problem and Kepler's conjecture . By using the LLL algorithm published since 1982, Andrew Odlyzko and Herman te Riele were able to refute Mertens' conjecture in 1985 .
The journal Experimental Mathematics was founded in 1992 to promote the subject and its methodology . The Journal of Experimental Algorithmics was first published in 1996 as a paperless publication by the Association for Computing Machinery .
In February 2002 the British numeric specialist Lloyd Nicholas Trefethen called a competition under the title 100-Digit Challenge to solve ten extremely difficult calculation problems in the field of scientific computing. Their solution with the greatest possible accuracy required both mathematical ingenuity and mastery of the most advanced numerical methods. After a large number of participants, the varied solutions with the solutions achieved were published and showed the unexpected efficiency of the combined efforts.
literature
- RF Churchhouse, J.-C. Herz (Ed.): Computers in mathematical research. North Holland, Amsterdam 1968.
- Jürg Nievergelt, Joel Craig Farrar and Edward M. Reingold: Computer Approaches to Mathematical Problems. Prentice Hall, Englewood Cliffs 1974.
- D. Chudnovsky , RD Jenks (Ed.): Computer algebra. Courant Institute NY, 1984. (Lecture Notes Pure Appl. Math. Vol. 113) Marcel Dekker NY, 1989.
- NM Stephens, MP Thorne (Ed.): Computers in mathematical research. Cardiff 1986. (Inst. Of Math. And its Appl. Conf. Series, New Series 14) Clarendon Press, Oxford 1988.
- D. Chudnovsky, RD Jenks (Ed.): Computers in mathematics. Stanford University 1986. (Lecture Notes Pure Appl. Math. Vol. 125) Marcel Dekker NY, 1990.
- E. Kaltofen, SM Watts (Ed.): Computers and mathematics. MIT 1989. Springer, 1989.
- Richard S. Varga: Scientific computation on mathematical problems and conjectures. Society for Industrial and Applied Mathematics (SIAM), Philadelphia 1990, ISBN 0898712572 .
- Peter Borwein : Computational Excursions in Analysis and Number Theory. (CMS Books in Mathematics 10) Springer, 2002, ISBN 0387954449 .
- Stephen Wolfram : A New Kind of Science . Wolfram Media, Inc., 2002, ISBN 1-57955-008-8 .
- Jonathan Borwein , David Bailey : Mathematics by Experiment: Plausible Reasoning in the 21st Century. AK Peters 2003, ISBN 1568812116 .
- Shangzhi Li, Falai Chen, Yaohua Wu, Yunhua Zhang: Mathematics experiments. World Scientific 2003, ISBN 9812380507 .
- Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing. SIAM 2004, ISBN 089871561X .
- Bornemann, Laurie, Wagon, Waldvogel: Solving numerical problems: A foray along the "SIAM 10x10-Digit Challenge". Springer, 2006, ISBN 3540341145 .
- DH Bailey, JM Borwein, NJ Calkin, R. Girgensohn, DR Luke, VH Moll: Experimental Mathematics in Action. AK Peters, 2007, ISBN 156881271X .
- Tewodros Amdeberhan, Victor H. Moll (Ed.): Tapas in Experimental Mathematics. Contemporary Mathematics Volume 457, AMS 2008, ISBN 0821843176 .
- Christoph Pöppe: The computer as a formula discoverer . Spectrum of Science Publishing Company, Heidelberg January 2009, p. 76-78 .
- Tewodros Amdeberhan, Luis A. Medina, Victor H. Moll (Eds.): Gems in Experimental Mathematics. Contemporary Mathematics Volume 517, AMS 2010, ISBN 0821848690 .
Web links
- Website of the journal Experimental Mathematics
- Website for Experimental Mathematics (English)
- Website for the German edition of the book by Bornemann et al.
- Institute for Experimental Mathematics
- David H. Bailey, Jonathan M. Borwein: Exploratory experimentation and computation , Notices AMS 58 (2011) No. 10, pp. 1410–1419 (pdf, 464 kB)