Related papers: Constructive mathematics
The testimony and practice of notable mathematicians indicate that there is an important phenomenological and epistemological difference between superficial and deep analogies in mathematics. In this paper, we offer a descriptive theory of…
Review of: Brigitte Le Roux and Henry Rouanet, Geometric Data Analysis, From Correspondence Analysis to Structured Data Analysis, Kluwer, Dordrecht, 2004, xi+475 pp.
We investigate different set-theoretic constructions in Residuated Logic based on Fitting's work on Intuitionistic Set Theory. We start by stating some results concerning constructible sets within valued models of Set Theory. We present two…
A plausible future mathematical claim must satisfy two constraints: it should follow the direction of prior work and respect the formal dependencies that constrain what can validly follow. Existing approaches typically model only one of…
We present some new sharp constructions for the Szemer\'{e}di-Trotter theorem. These constructions generalize previous work of Erd\H{o}s, Elekes, Sheffer and Silier, Guth and Silier, and the author. In the past, arguments showing the…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…
We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…
Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
Constructive-deductive method for plane Euclidean geometry is proposed and formalized within Coq Proof Assistant. This method includes both postulates that describe elementary constructions by idealized geometric tools (pencil, straightedge…
Analysing several characteristic mathematical models: natural and real numbers, Euclidean geometry, group theory, and set theory, I argue that a mathematical model in its final form is a junction of a set of axioms and an internal partial…
We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a…
These few pages briefly present the way in which Activity Theory has been adopted for several years now by French researchers in didactics of mathematics and has been adapted to study the learning of school mathematics in relation with the…
Structural approaches to myth and narrative are compelling in close reading but hard to compare across traditions, media, and scale. We propose a formal framework that renders L\'evi-Straussian transformation as mathematics while remaining…
We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra…
It is well known that most constructive and predicative foundations aiming to develop Bishop's constructive analysis are incompatible with a classical predicative development of analysis as put forward by Weyl in his $\textit{Das…
The first part of the present article consists in a survey about the dynamical constructive method designed using dynamical theories and dynamical algebraic structures. Dynamical methods uncovers a hidden computational content for numerous…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…