I would have liked to post this in mathematical symbols, but I haven’t figured out if they even exist on my Mac. Please bear with me as I put these two problems in words.
Starting with n=2 at what point will summing 1/n be greater than 2?
Starting with n=1 at what point will summing 1/2n be greater than 2?
Hint on the second: see http://magree.blogspot.com/2013/08/unlimited-has-its-limits.html and the links in that entry.
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Tuesday, April 15, 2014
Monday, October 26, 2009
The End of Ignorance
I've long thought that all of us, myself included, don't learn all that we could as well as we could. Today I did have the importance of one learning tool reinforced - serendipity!
I was wandering around the web and decided to visit The Huffington Post, and I stumbled on a sidebar item, "Math is not hard: A Simple Method…" whose full title is "Math Is Not Hard: A Simple Method That is Changing The World", by Julia Moulden.
It is about John Mighton, a man who had his own struggles with learning. Mighton was a playwright who supplemented his income as a tutor. That led to his deciding to be a mathematician. But his struggles with the subject almost made him give up. Remembering some of his tutoring experiences, he broke things down into small increments and went on to get a Ph.D.
He started a not-for-profit organization to promote a different way of teaching math - http://jumpmath.org.
He has written two books whose title alone should lead us to rethink teaching and our own learning - "The End of Ignorance" and "The Myth of Ability".
If you read Julia Moulden's article, be sure to follow as many links as you can, including the one to Thomas Friedman's article, "The New Untouchables", New York Times, 2009-10-21. I was going to write a blog about Friedman's article but as usual didn't find a round tuit. Ah, that's the secret of learning, finding round tuits:)
I was wandering around the web and decided to visit The Huffington Post, and I stumbled on a sidebar item, "Math is not hard: A Simple Method…" whose full title is "Math Is Not Hard: A Simple Method That is Changing The World", by Julia Moulden.
It is about John Mighton, a man who had his own struggles with learning. Mighton was a playwright who supplemented his income as a tutor. That led to his deciding to be a mathematician. But his struggles with the subject almost made him give up. Remembering some of his tutoring experiences, he broke things down into small increments and went on to get a Ph.D.
He started a not-for-profit organization to promote a different way of teaching math - http://jumpmath.org.
He has written two books whose title alone should lead us to rethink teaching and our own learning - "The End of Ignorance" and "The Myth of Ability".
If you read Julia Moulden's article, be sure to follow as many links as you can, including the one to Thomas Friedman's article, "The New Untouchables", New York Times, 2009-10-21. I was going to write a blog about Friedman's article but as usual didn't find a round tuit. Ah, that's the secret of learning, finding round tuits:)
Math Is Not Hard: A Simple Method That Is Changing The World
The following is my comment to Julia Moulden's column of the same title. The above picture was added by the Huffington Post when I checked that I wanted my comment posted on my blog.
I've long thought that most of us can learn more than we do. Years ago I heard a radio interview where the speaker had a boy tell him, "I'm dumb" and the man replied, "Who told you that." Most of us have had people tell us that they were never any good in math, foreign languages, music, or whatever. The true answer is that they didn't have enough interest to invest some time in the subject.
I have proven it with my own increased singing ability. I once was told that I was hopeless. After years of my taking voice lessons, that same person is delighted with my ability. No, nobody is going to pay me to sing, but I have been asked back to sing solos.
I wrote about some of this experience in "Men Can Sing", http://www.cpinternet.com/~mdmagree/men_can_sing_2005-02-03.html
If you are interested in a subject, start somewhere. Read about it, get lessons on it, just do something. And be willing to change and correct yourself.
Read the Article at HuffingtonPost
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