New Results on Triangulation, Polynomial Equation Solving and Their Application in Global Localization

This thesis addresses the problem of global localization from images. The overall goal is to find the location and the direction of a camera given an image taken with the camera relative a 3D world model. In order to solve the problem several subproblems have to be handled. The two main steps for constructing a system for global localization consist of model building and localization. For the model construction phase we give a new method for triangulation that guarantees that the globally optimal position is attained under the assumption of Gaussian noise in the image measurements. A common framework for the triangulation of points, lines and conics is presented. The second contribution of the thesis is in the field of solving systems of polynomial equations. Many problems in geometrical computer vision lead to computing the real roots of a system of polynomial equations, and several such geometry problems appear in the localization problem. The method presented in the thesis gives a significant improvement in the numerics when Gröbner basis methods are applied. Such methods are often plagued by numerical problems, but by using the fact that the complete Gröbner basis is not needed, the numerics can be improved. In the final part of the thesis we present several new minimal, geometric problems that have not been solved previously. These minimal cases make use of both two and three dimensional correspondences at the same time. The solutions to these minimal problems form the basis of a localization system which aims at improving robustness compared to the state of the art

Schubert calculus and Intersection theory of Flag manifolds

Hilbert's 15th problem called for a rigorous foundation of Schubert's calculus, in which a long standing and challenging part is Schubert's problem of characteristics. In the course of securing the foundation of algebraic geometry, Van der Waerden and Andr\'{e} Weil attributed the problem to the determination of the intersection theory of flag manifolds. This article surveys the background, content, and resolution of the problem of characteristics. Our main results are a unified formula for the characteristics, and a system description for the intersection rings of flag manifolds. We illustrate the effectiveness of the formula and the algorithm via explicit examples.Comment: 24 pages, 1 figur

MALI'S EDUCATIONAL SYSTEM: AN OVERVIEW OF MATHEMATICS CURRICULUM IN MALI, FROM KINDERGARTEN TO SECONDARY SCHOOL

Mali as an undeveloped country, education is still placed in an important role. To make more people know its education, this article presents the structure of the education system in Mali and especially for mathematics education. Mathematics play a key role in people's lives. Whether one is intellectual or illiterate mathematics are useful for everybody, Mathematics education and the cure for mathematics education is a great concern in the Malian education system. Our goal in this paper is to formulate recommendations for improvement and development of mathematics education in Mali. It gives an overview of the mathematics education programs such as the purpose and objectives of mathematics education from kindergarten to high school. It also concerns the method of mathematics teaching or the pedagogy used. In addition, there is a reflection of the content of mathematics curriculum of the first and second cycle of basic and secondary education. Our concern here is teaching and learning approaches of mathematics in Mali. The article also measures about the Master Training Institutes (IFM) and teacher training schools of secondary education; it clearly lists the problems of mathematics education besides and finally.  Article visualizations

The Impact of Alan Turing: Formal Methods and Beyond

© 2019, Springer Nature Switzerland AG. In this paper, we discuss the influence and reputation of Alan Turing since his death in 1954, specifically in the field of formal methods, especially for program proving, but also in a much wider context. Although he received some recognition during his lifetime, this image was tarnished by the controversy at the time of his death. While he was known and appreciated in scientific circles, he did not enter the public’s consciousness for several decades. A turning point was the definitive biography produced by Andrew Hodges in 1983 but, even then, the tide did not turn very rapidly. More recent events, such as the celebrations of his birth centenary in 2012 and the official British royal pardon in 2013, have raised Turing’s fame and popularity among the informed general public in the United Kingdom and elsewhere. Cultural works in the arts featuring Turing have enhanced his profile still further. Thus, the paper discusses not only Turing’s scientific impact, especially for formal methods, but in addition his historical, cultural, and even political significance. Turing’s academic ‘family tree’ in terms of heritage and legacy is also covered

Enacting Inquiry Learning in Mathematics through History

International audienceWe explain how history of mathematics can function as a means for enacting inquiry learning activities in mathematics as a scientific subject. It will be discussed how students develop informed conception about i) the epistemology of mathematics, ii) of how mathematicians produce mathematical knowledge, and iii) what kind of questions that drive mathematical research. We give examples from the mathematics education at Roskilde University and we show how (teacher) students from this program are themselves capable of using history to establish inquiry learning environments in mathematics in high school. The realization is argued for in the context of an explicit-reflective framework in the sense of Abd-El-Khalick (2013) and his work in science education