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Good math videos
Posted: 18 November 2010 06:05 PM   [ Ignore ]   [ # 16 ]
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http://www.youtube.com/watch?v=BipvGD-LCjU

Finite Simple Group of Order Two.

(well known in “math circles”)

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Posted: 19 November 2010 10:49 AM   [ Ignore ]   [ # 17 ]
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Good one! smile

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Posted: 08 December 2010 11:49 AM   [ Ignore ]   [ # 18 ]
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So, if we want to change the path that the country is on, then how ‘bout raising the public appreciation for how important mathematics is, realize that it is the queen of all sciences giving a great amount of credibility to the other sciences.

‘Wake-up call’: U.S. students trail global leaders

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Posted: 16 December 2010 06:38 AM   [ Ignore ]   [ # 19 ]
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Although I didn’t have much of a problem compared to others in my early years learning math, I remember there were a lot of confusing things that didn’t make sense at the time. For instance, when they were teaching us the rules of algebra, the teacher would lead off the course with, “For all Real numbers, ...” At the time I was confused but afraid to say anything as others likely were, but I was thinking, duh, what do expect, fake numbers? We didn’t learn imaginary numbers until the end of the year. So I thought the teacher was being strangely awkward and redundant.

Once I finished school, I bought myself textbooks and retaught myself from scratch. When teachers teach, they tend to skip chapters and material and probably presume the students understand more than they really do. But if kids get confused (or people in general), they are not going to speak up if they think their thoughts are too stupid to ask. I surely didn’t want to be the one to ask, “Is there such thing as imaginary numbers in math?”, and be ridiculed for such stupidity for thinking I was serious.

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Posted: 23 December 2010 05:32 PM   [ Ignore ]   [ # 20 ]
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Good points Scott Mayers.  Imaginary numbers is one of those annoying problematic terms in Mathematics, it and “real” are misnomers.

Everyone else, in school the only bad question is the question that you don’t ask.  I wish this thread to be the same way.  Students need that sort of re-assurance that the classroom is the place for questions, that’s really the best place to ask them.  Without an answer to your question, you’ll be confused about the rest of the semester and beyond.  downer  Reviewing and teaching yourself the math that you missed, for whatever reason you missed it, is a great idea.  Why waste an education?  Math texts have changed, you can find one written in a style that YOU like, now-a-days.  When a student asks a question, they should expect that the teacher try to answer it for them in a way that the student understands.  grin 

Mathematically speaking, imaginary numbers become real when multiplied together, real becomes imaginary when multiplied by an imaginary.

definition: i = sqrt(-1)

3i * 5i = 15i^2 = 15(-1) = -15

, or in other words

3*sqrt(-1) * 5*sqrt(-1) = (3*5) * (sqrt(-1))^2 = (15) * (-1) = -15

, and

3 * 5i = 15i

Electrical voltage, amperage, and power are calculated with complex numbers.  In physics, the complex numbers really exist, they are how the physical world behaves, they are measurable, that is their importance, their application, their practicality.  The imaginary number seems like a mathematical impossibility, a number that can become real or imaginary (not real) in mathematics, but in physics they both really exist.  Once again, reality is more fascinating than fiction!  smile  Some people think that if you know how to count, then you know all the numbers, but there is more to number theory than just counting the naturals.  smile

This video is good, I like when the narrator Derek Owens says that “In that sense, I like to think of the complex numbers as the real numbers, unfortunately the term ‘real’ is already taken.  But these are real in the sense that, ‘they are the numbers that really do the job’.” [9:18]  That Derek Owens shows some good insight, which makes his a pretty good math video.  smile

Complex Numbers, Part 7 - Why We Need Them, Continued

Drexel Math forum -  Imaginary Numbers (text)

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Posted: 08 January 2011 09:57 PM   [ Ignore ]   [ # 21 ]
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The Cassiopeia Project has got some videos on quantum mechanics that are very accessible and a bit mathematical, pleasantly so.  Other videos too.  Click if you’d like.

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Posted: 09 January 2011 07:36 AM   [ Ignore ]   [ # 22 ]
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Thanks for the link to the Cassiopeia Project. The videos are also available from iTunes. I’m downloading the lot of them right now.

edit:fixed a typo

[ Edited: 08 August 2011 06:49 AM by DarronS ]
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Posted: 08 August 2011 06:43 AM   [ Ignore ]   [ # 23 ]
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This video series was good because they included the math.  They include it as animations, which really makes the math clear.  I originally saw this on PBS TV in high school, at a time when I was struggling with math and loosing my enthusiasm for school.  This show really picked up my spirits.  It’s as compelling as it is instructive.  smile  The math should be included, not left out, for the sake of popularity.

They introduce calculus in the second episode.

“Mechanical Universe” was done well by Caltech Professor David Goodstein and Dr. James F. Blinn did the computer animations.

Caltech: The Mechanical Universe – 01 – Introduction
Caltech: The Mechanical Universe – 02 – The Law of Falling Bodies
Caltech: The Mechanical Universe – 03 – Derivatives
Caltech: The Mechanical Universe – 04 – Inertia
Caltech: The Mechanical Universe – 05 – Vectors
Caltech: The Mechanical Universe – 06 – Newton’s Laws
Caltech: The Mechanical Universe – 07 – Integration
Caltech: The Mechanical Universe – 08 – The Apple and The Moon
Caltech: The Mechanical Universe – 09 – Moving in Circles
Caltech: The Mechanical Universe – 10 – Fundamental Forces
Caltech: The Mechanical Universe – 11 – Gravity, Electricity, Magnetism
Caltech: The Mechanical Universe – 12 – The Millikan Experiment
Caltech: The Mechanical Universe – 13 – Conservation of Energy
Caltech: The Mechanical Universe – 14 – Potential Energy
Caltech: The Mechanical Universe – 15 – Conservation of Momentum
Caltech: The Mechanical Universe – 16 – Harmonic Motion
Caltech: The Mechanical Universe – 17 – Resonance
Caltech: The Mechanical Universe – 18 – Waves (This one’s not on Google Video for some reason)
Caltech: The Mechanical Universe – 19 – Angular Momentum
Caltech: The Mechanical Universe – 20 – Torques and Gyroscopes
Caltech: The Mechanical Universe – 21 – Kepler’s Three Laws (also not on Google Video)
Caltech: The Mechanical Universe – 22 – The Kepler Problem
Caltech: The Mechanical Universe – 23 – Energy and Eccentricity (also not on Google Video)
Caltech: The Mechanical Universe – 24 – Navigating in Space
Caltech: The Mechanical Universe – 25 – Kepler to Einstein
Caltech: The Mechanical Universe – 26 – Harmony of the Spheres
Caltech: The Mechanical Universe – 27 – Beyond the Mechanical Universe
Caltech: The Mechanical Universe – 28 – Static Electricity
Caltech: The Mechanical Universe – 29 – The Electric Field
Caltech: The Mechanical Universe – 30 – Potential and Capacitance
Caltech: The Mechanical Universe – 31 – Voltage, Energy and Force
Caltech: The Mechanical Universe – 32 – The Electric Battery
Caltech: The Mechanical Universe – 33 – Electric Circuits
Caltech: The Mechanical Universe – 34 – Magnetism
Caltech: The Mechanical Universe – 35 – The Magnetic Field
Caltech: The Mechanical Universe – 36 – Vector Fields and Hydrodynamics
Caltech: The Mechanical Universe – 37 – Electromagnetic Induction
Caltech: The Mechanical Universe – 38 – Alternating Current
Caltech: The Mechanical Universe – 39 – Maxwell’s Equation
Caltech: The Mechanical Universe – 40 – Optics and Beyond (watching this while I do all this copy-pasting)
Caltech: The Mechanical Universe – 41 – The Michelson-Morley Experiment
Caltech: The Mechanical Universe – 42 – The Lorentz Transformation
Caltech: The Mechanical Universe – 43 – Velocity and Time
Caltech: The Mechanical Universe – 44 – Mass, Momentum and Energy
Caltech: The Mechanical Universe – 45 – Temperature and Gas Laws
Caltech: The Mechanical Universe – 46 – Engine of Nature
Caltech: The Mechanical Universe – 47 – Entropy
Caltech: The Mechanical Universe – 48 – Low Temperatures
Caltech: The Mechanical Universe – 49 – The Atom
Caltech: The Mechanical Universe – 50 – Particles and Waves
Caltech: The Mechanical Universe – 51 – From Atoms to Quarks
Caltech: The Mechanical Universe – 52 – The Quantum Mechanical Universe

[ Edited: 08 August 2011 06:49 AM by jump_in_the_pit ]
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Posted: 25 August 2011 01:35 PM   [ Ignore ]   [ # 24 ]
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NOVA did a good job exploring the history and potential of fractals.  I loved how they stressed the connection fractals have to natural complex shapes such as branching trees/blood vessels, the dynamic shapes of clouds, the patterns of noise in telephone lines, the flow of water.  Shapes with amazing properties of being complex, but stemming from simple rules. 

The complex fractal shapes having strange properties like an infinite perimeter but within a finite area, a property that prevented mathematicians of the past from plotting them by hand.  Computers overcoming that limitation.  Or the property of self-similarity, where zooming in closer to the shape the fractal looks the same as you get closer to it.  The property of roughness too.

And then there is the artistic connection where artists, using some math tools, found new abilities that they never had thought possible before.  When generating virtual landscapes with drama, grandeur, and detail in Hollywood movies, fractals do it, and more artistry.

Fractals are opening up biological, artistic, and other fields, fields that used to be considered off-limits, now open to a new possibility… mathematics.  smile


Hunting the hidden dimension

[ Edited: 26 August 2011 08:15 AM by jump_in_the_pit ]
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Posted: 01 November 2011 09:00 PM   [ Ignore ]   [ # 25 ]
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School is broken.  How do we fix it?

Salman Khan talk at TED 2011 (from ted.com)

Salman Khan meets Bill Gates

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Posted: 01 November 2011 11:42 PM   [ Ignore ]   [ # 26 ]
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A member of our monthly evening CFI discussion group often brought his ten year old daughter there, and she was working on a simple mathematical puzzle.  I dug out one of my earliest math puzzle books and brought it for her at the next meeting.  However, it got me to thinking.  I saw my first math puzzle book when I was about ten and in the youth section of the local library, and I got hooked.  I must have gone through every puzzle book they had there, then got my parents to buy me others.  While I couldn’t do quite a few of them, I read the well spelled out solutions in the back of the books.  It had never occurred to me, but that was probably the reason that I loved algebra from the first moment, and it made complete sense to me.  Little did I know that those books were teaching me the concepts necessary while I thought I was just playing.

Occam

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Posted: 02 November 2011 07:45 PM   [ Ignore ]   [ # 27 ]
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Good story Occam, and yes I think that playing and discovery are the natural ways to learn and school should have more of that, bring out the natural scientist in everyone.  grin 

That’s why Good Math Videos are merely good and not excellent.  Television is an old technology that shows videos, but videos are one-way there is no interaction its just the obsolete couch potato idea again.  Instead, now-a-days, we have computers, these are the modern technology that allows interactive discovery and play, even if that potential has not been well utilized by commercial software.  I do see some who agree with me who are offering to step forward with some good interactive “physics java applet” (just Google search that phrase to see many examples).  Here’s some examples:

http://www.falstad.com/mathphysics.html
http://pdukes.phys.utb.edu/PhysApplets/appmenu.htm

That’s shows that the free software movement can do some things that the commercial software won’t really do.  Java is just the language of choice in achedemia and science it seems, rather than Flash.  So you’ll need the proper java plugins to use those.

Once the video becomes interactive then it could be called many things, like interactive animation, simulation, video game, virtual laboratory, etc.  Video games are made with good physics simulations, the math really is in there, and if they’d show the audience some of the math then they could become educational, but no that hasn’t happened.

And to step from excellent interactive discovery up to great, one needs a customizable, self documenting, programmable interface to the interactive video.  They need to offer a good interpreter so that the audience can recreate, customize, experiment, and expand the interactive video that they’re using.  Books are good, as you said, but they just aren’t as dynamic and exciting as a computer can be, one can play a video game not just read it.  smile

Interactive tests where the test tells you when your answer is wrong, giving you some constructive or encouraging feedback immediately, and then giving you a chance to look-up and double-check your answers, this may sound like a very simple idea, but I’ve tried it and it is a very good learning technique.  It can be scored as 95% or higher is passing.  Astropitch is close to what I’m talking about, but has no feedback and unlimited retrys.

If Kahn has Gates’ money behind him, I hope he learns that video is the old has-been technology, and dynamic interaction that is customizable is the modern way.  With Gates’ money, there is no reason that modern learning tools can’t be made into a Flash, Java Applet, Javascript, widget for a web browser, desktop application, or cell phone app.  I hope that Kahn gets that idea and stops putting so much energy into the one-way videos.  But did you hear him say that he wants to use his video to free up the teacher’s time for more face-to-face interaction?  Isn’t that ironic, computers providing more time for in-person human interaction!  smile  Its ironic, but no surprise that bringing automation home can do that.  smile

Long term memory is another big issue that needs better techniques for proper learning.

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Posted: 06 November 2011 11:57 PM   [ Ignore ]   [ # 28 ]
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Richard Feynman asks why math, but can’t answer the question with anything but, math is needed.  At the end of part four he explains that as people argue that they prefer one philosophy or another as the best description of nature, that technique never works only the tests will work.  Huh, funny the way he puts it.

Richard Feynman: Relation of Mathematics and Physics (Part 1/6)

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Posted: 07 November 2011 07:55 AM   [ Ignore ]   [ # 29 ]
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jump_in_the_pit - 06 November 2011 11:57 PM

Richard Feynman asks why math, but can’t answer the question with anything but, math is needed.  At the end of part four he explains that as people argue that they prefer one philosophy or another as the best description of nature, that technique never works only the tests will work.  Huh, funny the way he puts it.

Richard Feynman: Relation of Mathematics and Physics (Part 1/6)

It’s all “tricks and gimmicks.” LINK

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Posted: 07 November 2011 10:29 PM   [ Ignore ]   [ # 30 ]
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Wow!  Feynman criticizes ARISTA, the National Academy of Science, and the Nobel Price all in one video!  big surprise  smile  Do the math, do the science, don’t publicize yourself… good one.

Richard Feynman, the Nobel, ‘It’s a pain in the neck.’

Social science gets a little tongue lashing too.

R. P. Feynman on social sciences

And the great scientist Sheldon demonstrates what’s wrong with the hard sciences!!  LOL

Sheldon Cooper On Social Sciences


Richard Feynman - Manhattan Project

[ Edited: 08 November 2011 12:07 AM by jump_in_the_pit ]
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