Category: College Algebra

Logarithm Graphs in Wolfram Alpha

At the Wolfram Alpha Workshop at ICTCM, there was universal disappointment about the fact that you cannot get a graph of a logarithm that is only over the real numbers.  We tried everything we could think of to remove the complex part of the graph. Personally, I have tried and tried and tried and tried to explain the problem with this in the feedback window for Wolfram Alpha, but been universally unsuccessful.   Every time I suggest a change, I am told that the “After review, our internal development group believes the plots for input “log(x)” are correct.” … yes, I know that … that doesn’t mean it’s the answer that most people will be looking for. I find it ironic that “inverse of e^x” produces the graph we’d like to see, and even gives log(x) as an equivalent. But then ask for a graph of  log(x) or ln(x) and the graph will always include the solution over the complex numbers. What’s worse is that W|A inconsistently decides when to use reals only and when to use both complex and real numbers.  For example, the output for y=ln(x), y=x includes the complex numbered plot, while the output for y=ln(x), y=2x-3 includes only the Reals.  What!?!  Actually, I have some idea why this is … it seems that in some cases, if the extra graph intersects the real part of...

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Math Videos at the Sputnik Observatory

The Sputnik Observatory, is dedicated to providing a venue for viewing and sharing ideas and philosophies of contemporary culture.  Jonathan Harris, who worked on the mindblowing sociological website We Feel Fine, is the site director and blog creator for Sputnik Observatory.  Sputnik also has a host of codirectors with diverse backgrounds in journalism, architecture, and ballet.  Members of Sputnik have spent the last ten years interviewing scientists, philosophers, academics, and the like.  They have over 200 videos of conversations on themes such as coherence, interspecies communication, and urban metabolism. “Sputnik Observatory is a New York not-for-profit educational organization dedicated to the study of contemporary culture. We fulfill this mission by documenting, archiving, and disseminating ideas that are shaping modern thought by interviewing leading thinkers in the arts, sciences and technology from around the world. Our philosophy is that ideas are NOT selfish, ideas are NOT viruses. Ideas survive because they fit in with the rest of life. Our position is that ideas are energy, and should interconnect and re-connect continuously because by linking ideas together we learn, and new ideas emerge.” Here are some of the short interviews that involve mathematics (and all really COOL mathematics).  All of these can be embedded into course shells. Will Wright – Possibility Space Ian Stewart – Alien Mathematics Ian Stewart – Pattern-Seeking Minds Lord Martin Rees – Simple Recipe Trevor Paglen –...

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Intriguing Inverses

Finally, I’ve made a sequel to Funky Function Notation. Here is Intriguing Inverses. Feel free to use it in online courses or use in the classroom. Enjoy.   Possibly Related Posts: Group Exploration in Math Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in...

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Modern War follows a Linear Regression

Just watched an amazing 7-minute TED talk on The Mathematics of War where an interdisciplinary team of researchers (physics, mathematics, economist, intelligence, computers) figured out how to mine data from public streams of information to collect and analyze modern warfare. It turns out that when they began plotting the number killed in an attack with the frequency of those attacks, they found the data was linear. Not only was this relationship linear, but the same linear relationship then appeared in every modern war they looked at (with slopes that varied slightly). So, next they modeled the probability of an event where x people are killed. Finally, they went back to each conflict to try to understand the meaning the slope of the line.  It turns out that the alpha value (which hovers around 2.5) has to do with the organizational structure of the resistance.  If the resistance becomes more fragmented, it is pushed closer to 3.  If the resistance becomes more organized, it is pushed closer to 2. Anyways, it’s only seven minutes.  You should definitely watch it! Possibly Related Posts: Group Exploration in Math Learning at Scale Slides from ICTCM Elaborations for Creative Thinking in STEM Learning Math is Not a Spectator Sport Recorded Webinar: Teaching Math in...

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Mathematics of Coercion

Bruce Bueno de Mesquita, a consultant to the CIA and DOD, uses mathematical analysis to predict the outcome of “messy” human events in this 2009 TED Talk: Three predictions on the future of Iran, and the math to back it up.  He claims that we can use mathematics to predict the outcomes of complex negotiations or situations involving coercion (everything that has to do with politics and business). His modeling is based in Game Theory, which (he says) is based on three assumptions that (1) people are rationally self-interested, (2) that people have values and beliefs, and (3) people face limitations.  The CIA verifies the predictive ability of the model, claiming it is correct 90% of the time even when the experts are wrong. To build a model of the outcomes, he says he need to know (1) Who has a stake in the decision? (2) What do they say they want? (3) How focused are they on one issue compared to other issues? (4) How much persuasive influence could they exert?  Using this, we can predict behavior by assuming that everybody cares about two things: the outcome (effect on their career) and the credit (ego).  In the model, you must be able to estimate people’s choices, chances they are willing to take, values, and beliefs about other people.  Believe it or not, history is not necessary for the...

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