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Making Computers Do Math

Join Prof. Richard Fateman in this lecture as he discusses the integration of mathematics and artificial intelligence, exploring the potential of building math experts, GUI problems, and the capabilities of the worldwide web. Discover the tools and funding available to advance the field.

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Making Computers Do Math

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  1. Making Computers Do Math Prof. Richard Fateman Fall, 2001 University of California, Berkeley Oct 30, 2001 Richard Fateman

  2. What could we possibly mean? • Solve applied mathematics problems • Convert math statements to effective algorithms (programs) • Follow specific commands to perform algebraic transformations • Prove theorems • or Search for counter-examples • Prove programs correct (combine previous ideas!) • Read (and write!) texts and handbooks to produce indexed re-usable math knowledge Oct 30, 2001 Richard Fateman

  3. Brute force algebra... Oct 30, 2001 Richard Fateman

  4. Is Math an AI problem? Oct 30, 2001 Richard Fateman

  5. Is Math an AI problem? • Can we build a math expert? • Must we build an artificial intelligence? • Can we teach math with or without other interactions? • Obvious success in limited domains. • All of math? Not so easy! Oct 30, 2001 Richard Fateman

  6. Complex domains, representation problems? Oct 30, 2001 Richard Fateman

  7. Is doing Math a GUI Problem? • Plot3D[Sin[x*y],{x,0,4},{y,0,4}] Oct 30, 2001 Richard Fateman

  8. Can the world-wide web do what a single computer cannot do? Oct 30, 2001 Richard Fateman

  9. Yes, in some ways • Access the library to get printed or on-line data about a topic • Answer specific questions using education-level appropriate approaches on topics from elementary school arithmetic through calculus to advanced math (Distributed Expert) • Search in on-line databases for relevant articles, programs, formulas to help solve problems. • Fix, update central repository of know-how Oct 30, 2001 Richard Fateman

  10. What else ? • Communicate among active servers: can we have networked solvers cooperating or competing to solve problems? • Encode math formulas so that multiple programs (CAS, TeX, Editor, numeric compiler) can communicate with a common channel • MathML/XML ? Oct 30, 2001 Richard Fateman

  11. Tools • Computer algebra systems, general or special purpose • Mathematica, Maple, Macsyma, GAP, PARI, • Interactive computer systems for scientific calculation • Matlab, Octave, MathCad • Library research systems • NEC ResearchIndex • California Digital Library Oct 30, 2001 Richard Fateman

  12. Very specific topics Oct 30, 2001 Richard Fateman

  13. TILU, Table of Integrals LookUp • Building the world's most expert (human or non-human) symbolic indefinite and definite integration program, on-line. • Algorithms • Tables • Generation of new solutions • Archiving newly found information Oct 30, 2001 Richard Fateman

  14. Code generation • The generation of highly specific and maximally efficient programs for certain numerical computations, e.g. approximate solution of differential equations tuned to specific equations or specific computers or specific memory configurations. Numerical routines based on difficult-to-program symbolic approximations such as Taylor series. Oct 30, 2001 Richard Fateman

  15. “Expert” shells / Search • The building of expert shells for stating and solving problems. • Assisting NEC's ResearchIndex project to decode postscript specifications of journal article pages tofind math, and encode the math in (say) TeX. Allowing it to be indexed. Oct 30, 2001 Richard Fateman

  16. Graphical User Interfaces • Building universal front ends that understand math typing and even handwriting (Biscotti, Texmacs, Livemath, Graphing Calculator) ...and that talk to everyone else. • Naive vs. skilled humans: • Who knows thatxsinx is the same as x sin(x)? Oct 30, 2001 Richard Fateman

  17. Macsyma / open source • Re-building the Macsyma computer algebra system as open-source: • an opportunity to re-engineer in current technology; • convert to a tool-based orientation; • combine with other programs Octave, Texmacs, Pari, • advanced algorithms Oct 30, 2001 Richard Fateman

  18. Current Funding • 1+ funded new research assistantships (NSF) for projects related to computer algebra/ scientific environments • (possible) additional funding for digital library related activity. • fateman@cs.berkeley.edu Oct 30, 2001 Richard Fateman

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