Also in the book Calculus For Dummies by Mark Ryan, here comes a nice trick for using a quadratic formula for factoring trinomials.
Saturday, February 19, 2011
Different Methods for Solving Quadratic Equations
Thursday, February 17, 2011
DEFINITION: Axioms
A statement or proposition that is regarded as being established, accepted, or self-evidently true
It seems that even Mathematics considers certain things beyond discussion or with definition out of question, and most surprisingly, takes them as the basis for everything else to derive and build upon. Is that not any hazardous?
Well, after all, we are humans, and thus unable to capture the essence of origin, of the core, of the seed, thoroughly and precisely through our reasoning, and in not doing so, we can say that there is no other way around when it comes to reasoning.
Shall we reach a level of knowledge beyond current, more effectively than just ordinary reasoning, in order to go further?
There must be a path, and if you know it, share it with us :)
Physics: Kinematics Terms
Terms
Kinematics - Kinematics is concerned with describing the way in which objects move.
Displacement - An objects total change in position. If a man runs around an oval 400 meter track, stopping at the precise location he began, though he ran a distance of 400 meters, his total displacement was 0.
Dynamics - Dynamics focuses on understanding why objects move the way they do.
Reference frame - The coordinate system with respect to which motion is being described.
Speed - A measure of how fast an object is moving.
Average velocity - The time-average of the velocity function over a specified time-interval. (See formula below.)
Instantaneous velocity - The value of the velocity function at a particular instant in time. (See formula below.)
Gravitational acceleration - The gravitational acceleration of objects near the earth's surface is the same for all objects regardless of mass and is given by the number g = 9.8m/s2 .
Scalar-valued function - A function that outputs scalars (regular numbers). Most common functions that you are probably familiar with are scalar-valued functions.
Vector-valued function - A function that outputs vectors. This means that while the domain of the function may consist of scalars, the values in the range are all vectors.
Position function - A position function can be either scalar-valued (for motion in one dimension) or vector-valued (for motion in two or three dimensions). At each point in time its value represents the position of an object at that time.
Velocity function - This function is the time-derivative of the position function, and gives the velocity of an object at each point in time.
Acceleration function - This function is the time-derivative of the velocity function, and the second time-derivative of the position function. It gives the value of the acceleration of an object at each point in time.
Time-derivative - The time-derivative of a function is a new function whose value at each point represents the rate of change of the original function with respect to time.
Simple harmonic motion - Periodic motion that can be described by special types of position functions. Examples of simple harmonic motion include an object moving in a circle and a ball bouncing up and down on a spring.
Formulae
| The average velocity for an object with position function x(t) over the time interval (t 0, t 1) . | v avg = |
| The instantaneous velocity at time t for an object with position function x(t) . | v(t) =  |
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Source: http://www.sparknotes.com/physics/kinematics/intro/terms.html
Saturday, February 12, 2011
Robots to get their own internet
Robots could soon have an equivalent of the internet and Wikipedia.
European scientists have embarked on a project to let robots share and store what they discover about the world.
Called RoboEarth it will be a place that robots can upload data to when they master a task, and ask for help in carrying out new ones.
Researchers behind it hope it will allow robots to come into service more quickly, armed with a growing library of knowledge about their human masters.
Share plan
The idea behind RoboEarth is to develop methods that help robots encode, exchange and re-use knowledge, said RoboEarth researcher Dr Markus Waibel from the Swiss Federal Institute of Technology in Zurich.
"Most current robots see the world their own way and there's very little standardisation going on," he said. Most researchers using robots typically develop their own way for that machine to build up a corpus of data about the world.
This, said Dr Waibel, made it very difficult for roboticists to share knowledge or for the field to advance rapidly because everyone started off solving the same problems.
By contrast, RoboEarth hopes to start showing how the information that robots discover about the world can be defined so any other robot can find it and use it.
RoboEarth will be a communication system and a database, he said.
In the database will be maps of places that robots work, descriptions of objects they encounter and instructions for how to complete distinct actions.
The human equivalent would be Wikipedia, said Dr Waibel.
"Wikipedia is something that humans use to share knowledge, that everyone can edit, contribute knowledge to and access," he said. "Something like that does not exist for robots."
It would be great, he said, if a robot could enter a location that it had never visited before, consult RoboEarth to learn about that place and the objects and tasks in it and then quickly get to work.
While other projects are working on standardising the way robots sense the world and encode the information they find, RoboEarth tries to go further.
"The key is allowing robots to share knowledge," said Dr Waibel. "That's really new."
RoboEarth is likely to become a tool for the growing number of service and domestic robots that many expect to become a feature in homes in coming decades.
Dr Waibel said it would be a place that would teach robots about the objects that fill the human world and their relationships to each other.
For instance, he said, RoboEarth could help a robot understand what is meant when it is asked to set the table and what objects are required for that task to be completed.
The EU-funded project has about 35 researchers working on it and hopes to demonstrate how the system might work by the end of its four-year duration.
Early work has resulted in a way to download descriptions of tasks that are then executed by a robot. Improved maps of locations can also be uploaded.
A system such as RoboEarth was going to be essential, said Dr Waibel, if robots were going to become truly useful to humans.
===============================
Source: News Technology at BBC (http://www.bbc.co.uk/news/technology-12400647)
European scientists have embarked on a project to let robots share and store what they discover about the world.
Called RoboEarth it will be a place that robots can upload data to when they master a task, and ask for help in carrying out new ones.
Researchers behind it hope it will allow robots to come into service more quickly, armed with a growing library of knowledge about their human masters.
Share plan
The idea behind RoboEarth is to develop methods that help robots encode, exchange and re-use knowledge, said RoboEarth researcher Dr Markus Waibel from the Swiss Federal Institute of Technology in Zurich.
"Most current robots see the world their own way and there's very little standardisation going on," he said. Most researchers using robots typically develop their own way for that machine to build up a corpus of data about the world.
This, said Dr Waibel, made it very difficult for roboticists to share knowledge or for the field to advance rapidly because everyone started off solving the same problems.
By contrast, RoboEarth hopes to start showing how the information that robots discover about the world can be defined so any other robot can find it and use it.
RoboEarth will be a communication system and a database, he said.
In the database will be maps of places that robots work, descriptions of objects they encounter and instructions for how to complete distinct actions.
The human equivalent would be Wikipedia, said Dr Waibel.
"Wikipedia is something that humans use to share knowledge, that everyone can edit, contribute knowledge to and access," he said. "Something like that does not exist for robots."
It would be great, he said, if a robot could enter a location that it had never visited before, consult RoboEarth to learn about that place and the objects and tasks in it and then quickly get to work.
While other projects are working on standardising the way robots sense the world and encode the information they find, RoboEarth tries to go further.
"The key is allowing robots to share knowledge," said Dr Waibel. "That's really new."
RoboEarth is likely to become a tool for the growing number of service and domestic robots that many expect to become a feature in homes in coming decades.
Dr Waibel said it would be a place that would teach robots about the objects that fill the human world and their relationships to each other.
For instance, he said, RoboEarth could help a robot understand what is meant when it is asked to set the table and what objects are required for that task to be completed.
The EU-funded project has about 35 researchers working on it and hopes to demonstrate how the system might work by the end of its four-year duration.
Early work has resulted in a way to download descriptions of tasks that are then executed by a robot. Improved maps of locations can also be uploaded.
A system such as RoboEarth was going to be essential, said Dr Waibel, if robots were going to become truly useful to humans.
===============================
Source: News Technology at BBC (http://www.bbc.co.uk/news/technology-12400647)
Skynet? Cientistas europeus desenvolvem internet para robôs compartilharem conhecimento
Cientistas europeus estão desenvolvendo uma grande rede para robôs compartilharem o conhecimendo que adquirem sobre o mundo e aprenderem como realizar as tarefas para as quais forem designados. O projeto se chama RoboEarth e seria uma espécie de Wikipedia robótica - ou nas piores visões da ficção científica, a Skynet do filme "Exterminador do Futuro"
A RoboEarth será uma mistura de sistema de comunicação e banco de dados, disse o professor Markus Waibel, do Instituto Suíço de Tecnologia, em Zurique. Ele afirma que hoje os pesquisadores desenvolvem máquinas com maneiras diferentes de compreender o mundo.
"A chave é dar aos robôs a possibilidade de compartilhar conhecimento. A maioria dos robôs atuais vê o mundo de sua própria maneira e quase não há padrões a serem seguidos" explica Waibel, em entrevista à BBC.
O banco de dados trará mapas sobre os locais de trabalho dos robôs, descrições de objetos que eles encontram e instruções sobre como cumprir ações distintas. Quando um robô dominar uma técnica, poderá publicar a informação na rede e ela estará disponível para todas as outras máquinas conectadas.
Os pesquisadores esperam que a ferramenta aumente a utilidade das máquinas e permita que eles se adaptem com mais facilidade. Ao chegar a um ambiente novo, por exemplo, um robô poderá baixar informações sobre o lugar, objetos presentes e tarefas a serem executadas.
Como exemplo, Waibel citou um robô com funções domésticas. Com as informações apropriadas disponíveis no RoboEarth, a máquina saberia o que fazer e quais objetos pegar se o dono mandar que ela arrume a mesa.
O projeto é financiado pela União Europeia e envolve 35 pesquisadores. Os primeiros resultados devem estar disponíveis em cerca de quatro anos.
As comparações com a Skynet são inevitáveis. No filme, a rede é construída pela empresa Cyberdyne Systems e controla todos os sistemas militares dos EUA. Após ganhar auto-consciência, o sistema decide que todos os seres humanos são inimigos e precisam ser exterminados. Mas tudo isso é apenas ficção, claro.
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Fonte: O Globo (http://oglobo.globo.com/tecnologia/mat/2011/02/09/skynet-cientistas-europeus-desenvolvem-internet-para-robos-compartilharem-conhecimento-923759578.asp)
Concrete first, abstract later
"From a pedagogical point of view, there is no doubt that for most students, concrete examples should precede abstraction"
That is a simple but yet meaningful phrase that I liked and took out of David Poole's book named Linear Algebra, A Modern Introduction.
I wish most teachers and professors would adopt that approach in class, what truly connects students with conceivable day-to-day sense, than move on to abstract areas of understanding.
A first word on Linear Algebra
Linear algebra is a branch of mathematics that studies vectors. Working according to certain rules, it mainly uses families of vectors called vector spaces or linear spaces, along with functions that input one vector and output another. Such functions that are well-behaved are called linear maps (or linear transformations or linear operators) and can always be represented by matrices.
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I quite enjoyed it, it put it simple and it was straightforward.
By Wikipedia
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