Related papers: Arithmetic, Geometry, and Coding Theory: Homage to…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
In three articles published in CNJ in 2012 and 2016 , we discussed some links between mathematical sciences, coin minting and numismatics. This article is a continuation of this cycle. It tells the story of selected important developments…
The purpose of this survey article is to introduce the reader to a connection between Logic, Geometry, and Algebra which has recently come to light in the form of an interpretation of the constructive type theory of Martin-L\"of into…
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…
A homage to the life and mathematics of John K. S. McKay. Obituary for the Bulletin of the London Mathematical Society.
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
A portrait of Kurt Goedel with emphasis on his work on relativity theory and idealistic philosophy.
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
This paper is a criticism on "A Mathematician's Apology" by G. H. Hardy.
This article introduces, informally, the substance and the spirit of Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger historical record.
We consider the Geometria Practica of Christopher Clavius, S.J., a suprisingly eclectic and comprehensive textbook of practical geometry, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI…
This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
The paper describes the contributions of Alain Colmerauer to the areas of logic programs (LP) and constraint logic programs (CLP).
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
This chapter surveys the advances of the past decade arising from the contributions of Indian mathematicians in the broad areas of operator algebras and operator theory. It brings together the work of twenty mathematicians and their…
This is a compilation of some well known propositions of Alain Connes concerning the use of noncommutative geometry in mathematical physics.
We introduce and study the notion of a logarithmic vertex algebra, which is a vertex algebra with logarithmic singularities in the operator product expansion of quantum fields; thus providing a rigorous formulation of the algebraic…