Demostración matemática

Compartimos recursos directos (y contextuales) para iniciarse en el aprendizaje y enseñanza de la demostración matemática.

[rev. 2021.04.25]

“One metaphor of proof is a route, which might be a desert track boring and unimpressive until one finally reaches the oasis of one’s destination, or a foot path in green hills, exciting and energizing, opening great vistas to unexplored lands and seductive offshoots leading far away, even after the initial destination point has been reached.” —Yuri I. Manin [Foundations as superstructure, p. 14]
Observación: Los libros indicados con Π (π mayúscula) requieren para su visualización y descarga, ser accesados desde una dirección web (IP) dentro del campus ITT (Tomás Aquino, Otay), CONRICyT o su equivalente.

Referencias iniciales:

  1. ΠAigner, Martin; Günter M. Ziegler (2014) Proofs from THE BOOK, 5/e. Springer {⇒Link a PDF 299pp.} [vía CONRICyT] {2018.01.16}
  2. ΠEberdein, Andrew; Ian J. Dove (2013) The Argument of Mathematics. Springer {⇒Link a PDF 391pp.} [vía CONRICyT] {2018.01.16}
  3. Badger, M. S., et al. (c. 2012) Teaching Problem-Solving in Undergraduate Mathematics. [Obs. include proof problems] {PDF, 138pp., 2018.01.16}
  4. Calude, Christian S., et al. (2004) Passages of Proof. {2019.12.24}
  5. Cheng, Eugenia (2004) How to write proofs: a quick guide. Department of Mathematics, Univ. of Chicago {2020.08.03}
  6. ΠDawson, John W., Jr. (2015) Why Prove it Again? Alternative Proofs in Mathematical Practice. Springer {⇒Link a PDF 211pp.} [vía CONRICyT] {2018.01.24}
  7. Feen, Ethan A. (2018) The Uses of Spurious Proofs in Teaching Mathematics. Thesis. Harvard University. {2020.06.25}
  8. Mason, John et al. (2010) Everyone can start (Chap. 1 of Thinking Mathematically). {ver adaptación en Univ. Alberta}
  9. Neunhäuserer, Jörg (s/f) 12² Beautiful Mathematical theorems with short proofs.   @2021.0425
  10. Oshiro, Erika (2019) A Historical Approach to Understanding Explanatory Proofs Based on Mathematical Practices. Univ. of South Florida. {2021.04.05}
  11. Ottesen, S. T. (2009). Relating university mathematics teaching practices and students’ solution processes. Roskilde: Roskilde Universitet. {2018.01.16}
  12. Ramírez Ortegón, Marte Alejandro (2005) La libreta pingüino. {2018.08.15}
  13. Rodin, Andrei V. (2020) Axiomatic Architecture of Scientific Theories. Saint-Petersburg State University. {2021.04.05}
  14. Tanswell, Fenner Stanley (1017) Proof, Rigour & Informality: A Virtue Account of Mathematical Knowledge. Disertación Doctoral. Univ. of St. Andrews. {2021.04.06}
  15. Wolf, Robert S. (2008) Proof, logic and conjecture: the mathematician’s toolbox. {2018.08.15}

Consejos selectos: