Results 1 to 10 of about 1,003,903 (269)

Mathematical proof: from mathematics to school mathematics. [PDF]

Philos Trans A Math Phys Eng Sci, 2019
Proof plays a central role in developing, establishing and communicating mathematical knowledge. Nevertheless, it is not such a central element in school mathematics. This article discusses some issues involving mathematical proof in school, intending to characterize the understanding of mathematical proof in school, its function and the meaning and ...
Rocha H.
europepmc   +5 more sources

Practical Theory Extension in Event-B [PDF]

, 2013
. The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas ...
Butler, Michael, Maamria, Issam
core   +1 more source

Proof phenomenon as a function of the phenomenology of proving [PDF]

, 2015
Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of ...
Hipólito, Inês
core   +1 more source

Matching concepts across HOL libraries [PDF]

, 2014
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same.
C So, C. Kaliszyk, C. Kaliszyk, C. Keller, F. Haftmann, F. Rabe, J. Harrison, J. Harrison, J. Hurd, J. Urban, John Harrison, Konrad Slind, M. Bortin, Makarius Wenzel, Steven Obua   +14 more
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On the nonlinear stability of mKdV breathers [PDF]

, 2012
A mathematical proof for the stability of mKdV breathers is announced. This proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and ...
Akhmediev N, Alejo M A Gorria C Vega L, Alejo M A Muñoz C, Alejo M A Muñoz C Vega L, Claudio Muñoz, Dysthe K, Holmer J Perelman G Zworski M, Kapitula T, Kevrekidis P G, Lamb G L, Maddocks J H, Miguel A Alejo, Schuur P C   +12 more
core   +2 more sources

Mathematical Proofs

Synthese, 2003
The aim I am pursuing here is to describe some general aspects of mathematical proofs. In my view, a mathematical proof is a warrant to assert a non-tautological statement which claims that certain objects (possibly a certain object) enjoy a certain property. Because it is proved, such a statement is a mathematical theorem.
openaire   +2 more sources

The Informal Logic of Mathematical Proof

, 2003
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form.
Brockriede Wayne, Churchill Winston, Doron, Eemeren Frans van, Eemeren Frans van, Hamblin Charles, Hoffman Paul, Jaffe Arthur, Kempe Alfred, MacKenzie Donald, Rav Yehuda, Rota Gian-Carlo, Swart Edward, Thurston William, Toulmin Stephen, Toulmin Stephen, Tymoczko Thomas, Walton Douglas, Walton Douglas, Walton Douglas, Willard Charles, Wilson Robin, Wittgenstein Ludwig   +22 more
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Premise Selection for Mathematics by Corpus Analysis and Kernel Methods [PDF]

, 2012
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of ...
A Grabowski, A Riazanov, A Tarski, A Trybulec, B Scholkopf, CM Bishop, Daniel Kühlwein, E Tsivtsivadze, Evgeni Tsivtsivadze, J Meng, J Shawe-Taylor, J Urban, J Urban, J Urban, Jesse Alama, Josef Urban, MD Richard, P Rudnicki, R Rifkin, S Schulz, S Shalev-Shwartz, Tom Heskes   +21 more
core   +4 more sources

Evidence, Proofs, and Derivations [PDF]

, 2019
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice ...
Aberdein, Andrew
core   +2 more sources

Twisted duality of the CAR-Algebra [PDF]

, 2002
We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed ...
Araki H., Avron J., Baumgärtel H., Borac S., Davis C., Dell’Antonio G. F., Dixmier J., Doplicher S., Fernando Lledó, Foit J. J., Halmos P. R., Hellmut Baumgärtel, Hislop P. D., Lledó F., Matthias Jurke, Rieffel M. A., Summers S. J., Wassermann A.   +17 more
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