![]() Melis, E., Andres, E., Budenbender, J., Frischauf, A., Goduadze, G., Libbrecht, P., et al.: Active-Math: A generic and adaptive web-based learning environment. The Semantic Web: Research and Applications, 370–375 (2010) 25–32 (2004)ĭavid, C., Kohlhase, M., Lange, C., Rabe, F., Zhiltsov, N., Zholudev, V.: Publishing math lecture notes as linked data. In: Proceedings of the 42nd Annual Meeting on Association for Computational Linguistics, pp. Wolska, M., Kruijff-Korbayová, I.: Analysis of mixed natural and symbolic language input in mathematical dialogs. Mathematical Knowledge Management, 346–360 (2006) Urban, J.: XML-izing Mizar: making semantic processing and presentation of MML easy. In most cases, the most simple, elegant and beautiful proof of a given theorem will be the one presented. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs, pp. How to Do it Step 1 is usually easy, we just have to prove it is true for n1 Step 2 is best done this way: Assume it is true for nk Prove it is true for nk+1 (we can use the nk case as a fact. Rudnicki, P.: An overview of the Mizar project. Gentzen, G.: Untersuchungen über das logische Schlie βen. For instance, the proof that root 2 is irrational, or that there are infinitely many primes. I'm talking proofs that A level (11th or 12th grade) students could understand. British Journal of Educational Technology 34(5), 625–638 (2003) What are your favourite simple mathematical proofs I was wondering what people's favourite simple proofs are. 173–204 (2006)Īczel, J., Fung, P., Bornat, R., Oliver, M., O’Shea, T., Sufrin, B.: Software that assists learning within a complex abstract domain: the use of constraint and consequentiality as learning mechanisms. Handbook of Research on the Psychology of Mathematics Education: Past, Present, and Future, pp. Mariotti, M.A.: Proof and proving in mathematics education. Hanna, G.: Some pedagogical aspects of proof.
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