Some aspects of history of Indian mathematics in 18th and early 19th century

This thesis is an attempt to throw light on the works of some Indian Mathematicians who wrote in Arabic or persian In the Introductory Chapter on outline of general history of Mathematics during the eighteenth Bnd nineteenth century has been sketched. During that period there were two streams of Mathematical activity. On one side many eminent scholers, who wrote in Sanskrit, .he l d the field as before without being much influenced by other sources. On the other side there were scholars whose writings were based on Arabic and Persian text but who occasionally drew upon other sources also.

ICT Tools for Teaching & Learning

Page 1. ICT Tools for Teaching & Learning G Santhosh Kumar Cochin University Page 2. Agenda • What is ICT? • Why integrate ICT in Education? • What are the Challenges? • What are the good resources? Page 3. Questions # “Despite the increasing use of ICT, the need for teachers is as great as ever” # “Placing ICT in schools will automatically improve the quality of education that children receive” #”The Internet is unsafe for children to use because there is so much dangerous material available on it” Page 4. What is ICT? • ICT is short for ..

Econometrics as an Academic Discipline in Higher Education: An Exploratory Study of the Need, Relevance and Significance

Econometrics is a young science. It developed during the twentieth century in the mid-1930’s, primarily after the World War II. Econometrics is the unification of statistical analysis, economic theory and mathematics. The history of econometrics can be traced to the use of statistical and mathematics analysis in economics. The most prominent contributions during the initial period can be seen in the works of Tinbergen and Frisch, and also that of Haavelmo in the 1940's through the mid 1950's. Right from the rudimentary application of statistics to economic data, like the use of laws of error through the development of least squares by Legendre, Laplace, and Gauss, the discipline of econometrics has later on witnessed the applied works done by Edge worth and Mitchell. A very significant mile stone in its evolution has been the work of Tinbergen, Frisch, and Haavelmo in their development of multiple regression and correlation analysis. They used these techniques to test different economic theories using time series data. In spite of the fact that some predictions based on econometric methodology might have gone wrong, the sound scientific nature of the discipline cannot be ignored by anyone. This is reflected in the economic rationale underlying any econometric model, statistical and mathematical reasoning for the various inferences drawn etc. The relevance of econometrics as an academic discipline assumes high significance in the above context. Because of the inter-disciplinary nature of econometrics (which is a unification of Economics, Statistics and Mathematics), the subject can be taught at all these broad areas, not-withstanding the fact that most often Economics students alone are offered this subject as those of other disciplines might not have adequate Economics background to understand the subject. In fact, even for technical courses (like Engineering), business management courses (like MBA), professional accountancy courses etc. econometrics is quite relevant. More relevant is the case of research students of various social sciences, commerce and management. In the ongoing scenario of globalization and economic deregulation, there is the need to give added thrust to the academic discipline of econometrics in higher education, across various social science streams, commerce, management, professional accountancy etc. Accordingly, the analytical ability of the students can be sharpened and their ability to look into the socio-economic problems with a mathematical approach can be improved, and enabling them to derive scientific inferences and solutions to such problems. The utmost significance of hands-own practical training on the use of computer-based econometric packages, especially at the post-graduate and research levels need to be pointed out here. Mere learning of the econometric methodology or the underlying theories alone would not have much practical utility for the students in their future career, whether in academics, industry, or in practice This paper seeks to trace the historical development of econometrics and study the current status of econometrics as an academic discipline in higher education. Besides, the paper looks into the problems faced by the teachers in teaching econometrics, and those of students in learning the subject including effective application of the methodology in real life situations. Accordingly, the paper offers some meaningful suggestions for effective teaching of econometrics in higher education

A CRITICAL STUDY OF THE I/W-'ll/EA/6'1.-' OF GANDHIJI AND HIS TEACHING ON MODERN HINDI POETRY

Hindi

Einige Ergebnisse von vergleichenden Untersuchungen in England und Deutschland zum Lehren und Lernen von Mathematik in Realitätsbezügen

In der Arbeit werden einige Resultate von vergleichenden empirischen Untersuchungen zu unterschiedlichen Konzeptionen eines realitätsbezogenen Mathematikunterrichts, wie sie in England und Deutschland häufig vertreten werden, dargestellt. Bei diesen Untersuchungen werden in verschiedenen Fallstudien, die u.a. auch strukturelle Unterschiede zwischen den Bildungssystemen in England und Deutschland und den zugrundeliegenden Erziehungsphilosophien berücksichtigen, Auswirkungen dieser Konzeptionen auf die Einstellung der Lernenden zum Mathematikunterricht, ihr Bild von Mathematik, ihr Verständnis mathematischer Begriffe und Methoden sowie ihre Fähigkeiten zur Anwendung mathematischer Methoden zum Lösen realer Problemaufgaben untersucht. Die hier dargestellten Erhebungen sind Teil eines längerdauernden Kollaborationsprojekts zwischen den Universitäten Exeter und Kassel.

The problem of the graphic artist

'The problem of the graphic artist' is a small example of applying elementary mathematics (divisibility of natural numbers) to a real problem which we ourselves have actually experienced. It deals with the possibilities for partitioning a sheet of paper into strips. In this contribution we report on a teaching unit in grade 6 as well as on informal tests with students in school and university. Finally we analyse this example methodologically, summarise our observations with pupils and students, and draw some didactical conclusions.

ONTIC: A Knowledge Representation System for Mathematics

Ontic is an interactive system for developing and verifying mathematics. Ontic's verification mechanism is capable of automatically finding and applying information from a library containing hundreds of mathematical facts. Starting with only the axioms of Zermelo-Fraenkel set theory, the Ontic system has been used to build a data base of definitions and lemmas leading to a proof of the Stone representation theorem for Boolean lattices. The Ontic system has been used to explore issues in knowledge representation, automated deduction, and the automatic use of large data bases.

Teaching an Old Robot New Tricks: Learning Novel Tasks via Interaction with People and Things

As AI has begun to reach out beyond its symbolic, objectivist roots into the embodied, experientialist realm, many projects are exploring different aspects of creating machines which interact with and respond to the world as humans do. Techniques for visual processing, object recognition, emotional response, gesture production and recognition, etc., are necessary components of a complete humanoid robot. However, most projects invariably concentrate on developing a few of these individual components, neglecting the issue of how all of these pieces would eventually fit together. The focus of the work in this dissertation is on creating a framework into which such specific competencies can be embedded, in a way that they can interact with each other and build layers of new functionality. To be of any practical value, such a framework must satisfy the real-world constraints of functioning in real-time with noisy sensors and actuators. The humanoid robot Cog provides an unapologetically adequate platform from which to take on such a challenge. This work makes three contributions to embodied AI. First, it offers a general-purpose architecture for developing behavior-based systems distributed over networks of PC's. Second, it provides a motor-control system that simulates several biological features which impact the development of motor behavior. Third, it develops a framework for a system which enables a robot to learn new behaviors via interacting with itself and the outside world. A few basic functional modules are built into this framework, enough to demonstrate the robot learning some very simple behaviors taught by a human trainer. A primary motivation for this project is the notion that it is practically impossible to build an "intelligent" machine unless it is designed partly to build itself. This work is a proof-of-concept of such an approach to integrating multiple perceptual and motor systems into a complete learning agent.

An Application of Augmented Reality (AR) in the Teaching of an Arc Welding Robot

Augmented Reality (AR) is an emerging technology that utilizes computer vision methods to overlay virtual objects onto the real world scene so as to make them appear to co-exist with the real objects. Its main objective is to enhance the user’s interaction with the real world by providing the right information needed to perform a certain task. Applications of this technology in manufacturing include maintenance, assembly and telerobotics. In this paper, we explore the potential of teaching a robot to perform an arc welding task in an AR environment. We present the motivation, features of a system using the popular ARToolkit package, and a discussion on the issues and implications of our research.

The Personal tutorial guidance sessions in the framework of the teaching-learning field of the Bologna process: University of Minho (first cycle) courses students’ perceptions

The Bologna Process defends the adoption of a higher education in teaching-learning methodologies that – in contraposition to the previous model based on the transmission of knowledge, which for being essentially theoretical, gives the student a passive role in the knowledge construction process – allows a (pro) active, autonomous and practical learning, where the student acquires and develops his competences. The personal tutorial guidance sessions are included in the teaching contact hours. This abstract presents a study about the University of Minho (first cycle) Courses Students’ perceptions of the personal tutorial guidance sessions’ relevance in the scope of the learning-teaching process, so as to confirm if the implementation/implantation of the commonly called tutorial (type) education, as an approach to an active, autonomous and practical learning, is sensed by the learners themselves