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Seminar at Universidade Federal Rio de Janiero, February 20, 2002
How do we think about axioms and proof in mathematics?
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Based on recent publications on the way that mathematicians use thought experiments and formal deductions to build up mathematical theories and how axiomatic theories are conceived by different students. In particular I refer to work from recent PhD theses at Warwick University.
Useful references for the talk are:
David Tall & Shlomo Vinner (1981). Concept Image and Concept Definition: with special reference to limits and continuity, Educational Studies in Mathematics, 12 151–169. (Historical: an oldie but goodie!)
Liz Bills & David Tall (1998). Operable Definitions in Advanced Mathematics: The case of the Least Upper Bound, Proceedings of PME 22, Stellenbosch, South Africa, 2, 104–111.
Marcia Pinto & David Tall (2001). Following students’ development in a traditional university classroom, Proceedings of PME 25, (4), 57-64.
Erh-Tsung Chin & David Tall (2001), Developing Formal Mathematical Concepts over Time. Proceedings of PME 25, (2), 241-248.
Erh-Tsung Chin & David Tall (in draft), University Students Embodiment of Quantifiers.
David Tall (2001), Natural and Formal Infinities, Educational Studies in Mathematics.
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