Related papers: Galois Got his Gun
Pre-college mathematics modeling instruction often frames mathematics as being separated from reasoning about the real world -- and commonly treats reasoning mathematically and reasoning about the real-world context as separate stages of a…
In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the…
We develop a Galois theory for difference ring extensions, inspired by Magid's separable Galois theory for ring extensions and by Janelidze's categorical Galois theory. Our difference Galois theorem states that the category of difference…
This text is addressed to mathematicians who are interested in generalized functions and unbounded operators on a Hilbert space. We expose in detail (in a "formal way" - as done by Heisenberg and Pauli - i.e. without mathematical…
The arithmetic of Hilbert modular forms has been extensively studied under the assumption that the forms concerned are "paritious" -- all the components of the weight are congruent modulo 2. In contrast, non-paritious Hilbert modular forms…
The topic of this paper is, on the one hand to introduce algebraic analysis results of \'Etienne B\'ezout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints.…
The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and…
This lecture recalls the memory of Baron Roland Eotvos, an outstanding figure of the experimental exploration of the gravitational interaction.
Differential equations have arithmetic analogues in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations and the present paper is concerned with the "linear" ones. The equations…
The paradoxical aspect of integration of a social group has been highlighted by Peter Blau (Exchange and Power in Social Life, Wiley and Sons, 1964). During the integration process, the group members simultaneously compete for social status…
We introduce the new notion of the "quasi-Galois point" in Algebraic geometry, which is a generalization of the Galois point. A point $P$ in projective plane is said to be quasi-Galois for a plane curve if the curve admits a non-trivial…
Developing expertise in physics entails learning to use mathematics effectively and efficiently as applied to the context of physical situations. Doing so involves coordinating a variety of concepts and skills including mathematical…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
What is the role of algebra in classical mathematics education? How does it relate to the four quadrivial arts? These questions have troubled the mathematical community since the introduction of algebra into the Renaissance academy by men…
The concept of number and its generalization has played a central role in the development of mathematics over many centuries and many civilizations. Noteworthy milestones in this long and arduous process were the developments of the real…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
There is a lack of consensus within the literature as to how `fairness' of algorithmic systems can be measured, and different metrics can often be at odds. In this paper, we approach this task by drawing on the ethical frameworks of…
We study the relation between the Galois group $G$ of a linear difference-differential system and two classes $\mathcal{C}_1$ and $\mathcal{C}_2$ of groups that are the Galois groups of the specializations of the linear difference equation…
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. The central claim of this paper is…