44 research outputs found
M茅s sobre conjectures i demostracions
Get PDFEl professor George P贸lya, professor em猫rit de matem脿tiques a la Universitat de Stanford, 茅s un
reconegut matem脿tic de recerca, autor d'aproximadament dos-cents cinquanta articles en matem脿tiques
i en educaci贸matem脿tica, aix铆 com d'uns quants llibres 脿mpliament llegits. Entre d'altres:
Com plantejar i resoldre problemes, Matem脿tiques i raonament plausible i El descobriment en matem脿tiques,
entre d'altres. Les seves confer猫ncies, v铆deos i escrits han estimulat extraordin脿riament
l'inter猫s en la resoluci贸 de problemes i han influ茂t en ensenyants de totes les etapes educatives
M茅s sobre conjectures i demostracions
Get PDFEl professor George P贸lya, professor em猫rit de matem脿tiques a la Universitat de Stanford, 茅s un
reconegut matem脿tic de recerca, autor d'aproximadament dos-cents cinquanta articles en matem脿tiques
i en educaci贸matem脿tica, aix铆 com d'uns quants llibres 脿mpliament llegits. Entre d'altres:
Com plantejar i resoldre problemes, Matem脿tiques i raonament plausible i El descobriment en matem脿tiques,
entre d'altres. Les seves confer猫ncies, v铆deos i escrits han estimulat extraordin脿riament
l'inter猫s en la resoluci贸 de problemes i han influ茂t en ensenyants de totes les etapes educatives
The Uses of Argument in Mathematics
Get PDFStephen Toulmin once observed that `it has never been customary for
philosophers to pay much attention to the rhetoric of mathematical debate'.
Might the application of Toulmin's layout of arguments to mathematics remedy
this oversight?
Toulmin's critics fault the layout as requiring so much abstraction as to
permit incompatible reconstructions. Mathematical proofs may indeed be
represented by fundamentally distinct layouts. However, cases of genuine
conflict characteristically reflect an underlying disagreement about the nature
of the proof in question.Comment: 10 pages, 5 figures. To be presented at the Ontario Society for the
Study of Argumentation Conference, McMaster University, May 2005 and LOGICA
2005, Hejnice, Czech Republic, June 200
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Full text linkOptimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
