A Proof Environment for Teaching Mathematics

Abstract

The EPGY Theorem Proving Environment is a computer program used by students to write mathematical proofs in a selection of computer-based, proof-intensive mathematics courses at the high-school and university level. The system allows easy input of mathematical expressions, application of standard proof strategies and logical inference rules, application of mathematical rules, and verification of logical inference. Each course has its own language, database of theorems, and mathematical rules. The system uses a combination of automated reasoning and symbolic computation to verify individual proof steps. The proof environment has been used by over 170 students who have taken the EPGY high-school geometry course. In addition to providing a general overview of the system, we describe what we have learned from student use of the Theorem Proving Environment in the EPGY geometry course.

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References

  1. 1.

    Chuaqui, R. and Suppes, P.: An equational deductive system for the differential and integral calculus, in P. Martin-Lof and G. Mints (eds.), Proceedings of COLOG-88 International Conference on Computer Logic (Tallin, USSR), Springer-Verlag, Berlin, 1990, pp. 25–49.

    Google Scholar 

  2. 2.

    Chou, S., Gao, X. and Zhang, J.: Machine Proofs in Geometry: Automated Production of Readable Proofs for Geometry Theorems, World Scientific, Singapore, 1994.

    Google Scholar 

  3. 3.

    Education Program for Gifted Youth (EPGY): Theorem Proving Environment Overview, http://epgy.stanford.edu/TPE.

  4. 4.

    Fitch, F. B.: Symbolic Logic: An Introduction, The Ronald Press Company, New York, 1952.

    Google Scholar 

  5. 5.

    McCune, W.: OTTER 3.0 reference manual and guide, Technical Report ANL-94/6, Argonne National Laboratory, January 1994.

  6. 6.

    McCune, W.: MACE 2.0 reference manual and guide, Technical Memorandum 249, Argonne National Laboratory, May 2001.

  7. 7.

    McMath, D., Rozenfeld, M. and Sommer, R.: A computer environment for writing ordinary mathematical proofs, in R. Nieuwenhuis and A. Voronkov (eds.), Proc. 8th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Lecture Notes in Artificial Intelligence 2250, Springer-Verlag, Berlin, 2001.

    Google Scholar 

  8. 8.

    Ravaglia, R.: User's Guide for the Equational Derivation System, Education Programfor Gifted Youth, Palo Alto, California, 1990.

    Google Scholar 

  9. 9.

    Ravaglia R., Alper, T. M., Rozenfeld, M. and Suppes, P.: Successful applications of symbolic computation, in N. Kajler (ed.), Human Interaction with Symbolic Computation, Springer-Verlag, New York, 1998, pp. 61–87.

    Google Scholar 

  10. 10.

    Suppes, P. (ed.): University-Level Computer-Assisted Instruction at Stanford: 1968-1980, Institute for Mathematical Studies of the Social Sciences, Stanford University, Stanford, California, 1981.

    Google Scholar 

  11. 11.

    Suppes, P. and Takahashi, S.: An interactive calculus theorem-prover for continuity properties, J. Symbolic Comput. 7 (1989), 573–590.

    MATH  MathSciNet  Article  Google Scholar 

  12. 12.

    Velleman, D.: How to Prove It: A Structured Approach, Cambridge University Press, Cam-bridge, UK, 1994.

    Google Scholar 

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Sommer, R., Nuckols, G. A Proof Environment for Teaching Mathematics. Journal of Automated Reasoning 32, 227–258 (2004). https://doi.org/10.1023/B:JARS.0000044825.55318.95

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  • EPGY Theorem Proving Environment
  • computer-based learning
  • automated reasoning