18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathemati
Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.
Pi Mathematical Pi Song (Full Version)
This Is The Full Version Of The Pi Pi Mathematical Pi Song! Written by Antoni Chan and Ken Ferrier. Note, this is not mine.
7 Babylonian mathematical style
This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.
6 The social context of Babylonian mathematical activity
This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.
5.3 Mathematical graphs: What could they mean?
Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.
5.2 Mathematical graphs: How do you read them?
Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.
5.1 Mathematical graphs: special terms
Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.
4.5.1 Mathematical models
Engineering is about extending the horizons of society by solving technical problems, ranging from the meeting of basic human needs for food and shelter to the generation of wealth by trade. Engineers see the problems more as challenges and opportunities than as difficulties. What they appear to be doing is solving problems, but in fact they are busy creating solutions, an altogether more imaginative activity.
Experiències matemàtiques. Reglets de Maria Antònia Canals
Durada: 8 min. Vídeo. CREAMAT.
En aquest capítol d'"Experiències Matemàtiques" produït des del CREAMAT, centre de recursos per ensenyar i aprendre matemàtiques del Departament d'Educació, es presenta una innovadora proposta per a l'aprenentatge de les matemàtiques.
Els reglets Author(s):
Virtual Learning Environments as a Supplement to Traditional Teaching
Many factors influence teaching nowadays. Numbers of students are increasing, some students pay for studies and require more flexible teaching, more students have access to Internet, the learning material is changing rapidly (especially of subjects, related to information technologies), publishing industry is slow and expensive. All that stimulates usage of modern technologies in education. Virtual Learning Environments (VLEs) is one of the forms of e-learning. They open new ways of teaching and
Information Technologies for Biology Education: Computerized Electrophysiology of Plant Cells
Biology has moved from a bench-based discipline to a bioinformational science in modern times but application of computational and analytical methods of informatics in it is still a problem for many researchers and students of biology. We suggest to integrate cost effective and practical combination of the real and the virtual laboratories into the undergraduate biological science curriculum. This laboratory work illustrates passive and active electrical properties of plant cell membranes while
Patchworking as a Metaphor for Learning
Understanding youth, learning and technology
On basis of a close empirical examination of a Danish team of 'Power Users' and their work on a self-chosen learning challenge this thesis argues how we can theoretically understand, analyse and methodologically approach learning processes through the metaphorical lens of patchworking.
The metaphor of patchworking highlights how
learning processes can be seen as processes of stitching and weaving together different patches and pieces into something new. The patches and pieces may not
Remote Training via WEB for Operation and Maintenance of a
Rain Monitoring Equipment using PHP and G
The aim of this paper is to present the development and implementation of an interactive environment via WEB for the training of non-centralized technician teams that work with the maintenance of ambient monitoring equipment. The case presented here is concerned to the network of Pluviologgers installed in the State of Santa Catarina, Brazil. The tools used for the construction of the WEB environment and, also, the requirements are detailed. The methodology and the techniques presented in this c
Using visualizations to teach problem-solving skills in mathematics: Which kind of visualization wor
In the experiment described in this paper we investigated the effects of different kinds of computer-based visualizations on the acquisition of problem-solving skills in the domain of probability theory. Learners received either purely text-based worked examples, text plus an instruction to mentally imagine the examples contents, or they could retrieve either static pictures or concrete animations that depicted the problem statement and the problem states achieved by applying a specific solut
Apport de lingénierie ontologique aux environnements de formation à distance
Cet article explore le potentiel de lontologie et de lingénierie ontologique pour augmenter lintelligence dans les environnements de formation à distance, ainsi que dans la conception de ces environnements. Il contient une introduction à lontologie avec ses origines dans la philosophie occidentale, une discussion des relations entre lintelligence artificielle et lingénierie ontologique, suivie dune description des méthodologies et des outils dingénierie ontologique. Plusieu
Analyse de fichiers de traces d'étudiants : aspects didactiques
Users of a learning platforms are usually required to log in, that provides a great deal of data. The general question studied here is: how to exploit this data to help the different actors involved? At first let us introduce the platform and the experiments we conducted. Then we use a didactic model to produce a qualitative analysis from the quantitative data collected. A simple exercise classification emerges from the construction of two indicators. It is consistent with the different experim
Sustaining Interaction in a Mathematical Community of Practice
This paper focuses on an activity in which students explore sequences through a game, using ToonTalk programming and a web-based collaboration system. Our analytical framework combines theory of communities of practice with
domain epistemology. We note three factors which influence the length and quality of interactions: facilitation, reciprocation and audience-awareness.
The Aplusix-Editor: A New Kind of Software for the Learning of Algebra
The first part of the paper presents our conception of a new kind of software for helping students to learn algebra. Such software has three main characteristics. First it includes an advanced editor that allows the student to build easily algebraic expressions. Second it reifies the student's reasoning as a tree. Third it verifies the student's calculations. In the second part, we present the Aplusix-Editor, a system of that kind that we have realised, and we describe the first tests of this sy
User Interfaces for a Virtual Learning Environment: Two Study Cases
A recent powerful idea in the design of Web-based learning environments is the usage of virtual places. The employment of interface metaphors is one of the approaches enabling inexperienced users to feel comfortable in such virtual environments. We have designed a Virtual Environment for Distance Education and Training (VEDET), which provides basic virtual spaces, resources, and services. In this paper we discuss the user interface of two Web-based distance learning courses Business on the Inter
Designer integration in training cycles : IEEE LTSA model adaptation
This paper describes an architecture centered on a component model for the course cycle. This
model guides a re-engineering process based on the observed use scenarii. It is applied in an
institutional framework and uses learning devices provided by the open source community. The
architecture integrates the latest works on learning technology standards.
