Related papers: Aryabhata's Mathematics
We investigate the mathematics behind 1500 year old root extraction methods presented by Aryabhata in his famous mathematical treatise "Aryabhatiya". Also, we look at their computational complexity.
I present examples of mathematical objects that are of interest for public key cryptography. Text for the Journ\'ee Annuelle 2007 of the SMF.
This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent…
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
It is noted that an efficient algorithm for calculating a $p$-adic height could have cryptanalytic applications.
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
This paper offers a glimpse of the major contributions made by Arabs to mathematics in middle ages history period. Its purpose is to stimulate interest in an object based on mutual respect and understanding. We give a short list of the most…
Recent analyses of Brahmagupta's discourse on the cyclic quadrilateral, and of Baudh\=ayana's approximate quadrature of the circle, have shown that it is useful to submit mathematical texts to a form of literary analysis. Several passages…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
We review results of papers written on the topic of polynomial amoebas with an emphasis on computational aspects of the topic. The polynomial amoebas have a lot of applications in various domains of science. Computation of the amoeba for a…
We give a brief overview of the area of Banach algebras, intended for a general mathematical audience.
Few among us would know that the first mention of the sine and the enumeration of the first sine table are to be credited to Aryabhata. The method to generate this relies on the sine difference formula which is derived using ingenious…
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…
These lectures notes were written for a summer school on Mathematics for post-quantum cryptography in Thi\`es, Senegal. They try to provide a guide for Masters' students to get through the vast literature on elliptic curves, without getting…
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
Recently, additive combinatorics has blossomed into a vibrant area in mathematical sciences. But it seems to be a difficult area to define - perhaps because of a blend of ideas and techniques from several seemingly unrelated contexts which…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and…