Wednesday, June 30, 2010
Mathematics in the Newtonian Era
We will now move on to the last and exciting phase of the early modern mathematics which is the Newtonian era (17th century). Some of the highlights of this period are: analytic geometry of Descartes (a blend of Greek geometry and Indian algebra), Probability theory by Pascal and Fermat, Number theory by Fermat, and last but not the least, the inception of Calculus by Newton and Leibniz which has eventually shaped the modern world in which we live. As you can see this is a huge treasure of knowledge on which modern mathematics is based upon. Please read the relevant chapters from the book and post your comments. I look forward to reading them.
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I have some suggestions for what we should do for our presentations. I have "crunched the numbers" for presenting for 2 or 3 days. Feedback will allow Dr. Chebolu to accurately make his final decision. Excluding 10 minutes for breaks per day and I estimated 14 groups. We are left with 280 and 420 total minutes for presenting. 280/14=20 per group (14 minutes required+ 6 minutes for que/overtime) 420/14= 30 per group (15 required + 15 que/overtime)
ReplyDeleteMore suggestions and feedback would be appreciated.
In response to the above comment I would say that I prefer to spread the talks in 3 days because it would hard to squeeze all the presentations in 2 days. At this moment I am expecting 13 presentations. So that should give us about 420/13 = ~ 32 minutes per presentation. In that case, I would think it would be most reasonable to give 25 minutes for presentation and the remaining 5-7 minutes for questions/overtime. We can talk more about this in class today.
ReplyDeleteOne of the fascinating things in Chapter 15 is the origin of probability theory. We also saw this explained in "The Math Life" video explained by Diaconis at Stanford University. Probability theory began when a french Gambler who was trying to analyse some dice bets on order to maximise his profits. He was confused about something and he wrote to Pascal for help. Pascal and Fermat corresponded with each other on this problem and that marks the beginning of probability theory. Isn't that interesting how a gambler on the street can be the cause of a vital branch of mathematics?
ReplyDeleteThis is a comment from Justin Walega:
ReplyDeleteWhile a few days delayed, I remember us discussing how evolution gave us paired organs for a reason - 2 eyes, 2 ears, etc. During the topic, I quickly thought of an animal which was quite different than most - the whale. While we have our eyes on the front of our face so that we can define distances accurately, a whale has its eyes on it sides (comparable to where our ears lie). Therefore a whale can see 2 objects, while losing a great deal of areas of vision ahead and behind it.
To quote, "Man may, in effect, be said to look out on the world from a sentry-box with two joined sashes for his window. But with the whale, these two sashes are separately inserted, making two distinct windows, but sadly impairing the view." http://www.aimeee.com/whale.html
I found this fascinating as again the world throws in an exception and how the concept of distance would be greatly affected. How exactly can a whale see how far away an object is? Does it need to use other senses? Is the inability to see close objects in front an issue?
-Justin Walega
For the homework problem #34,
ReplyDeletethe problem tells us to add 2bx+2b^2
but in order for the left hand side to be a perfect square i think they meant for us to add 2bx^2+2b^2
in case anyone else was having problems with that question
In today's lecture, Kevin has asked me for the time frame when this old method (shaving head and tottoing) of secret communication happened. I did a google search and this is what I found. Apparently, this was the practice from the time of the Greeks.
ReplyDeleteSteganography:
From Greek and translating as covered writing or hidden writing, and dating to 440 B.C., steganography is the art or science, or system, of hiding the existence of a message. In The Histories of Herodotus, the Greek historian Herodotus mentions several examples. Into the wood backing of a wax tablet, Demeratus carved a message warning his countrymen of an impending attack. He then applied the wax, which hid the message from view until it was removed by the intended recipient. Another method involved shaving the head of a slave and tattooing a message on his scalp. After the hair grew back enough to cover the message, the slave could be sent through enemy lines, and his head could be shaved again to read the message.
working on problem 12.34 and am getting some strange fractions for my depessed cubic. anyone else getting p = -16 1/3 and q = 19 11/27?
ReplyDeleteto get those fractions I had added 2bx + b^2 to both sides instead of the suggested -2bx + b^2...frustrating.
ReplyDeleteIn comment to the evolution of animals. I believe most herbivores evolve to see "two fronts" as a means of protection. Carnivorous eyes need to judge distance and stalk their prey ahead of them (one concentrated front). Most herbivorous live in packs allowing for numerous front views. I know that when archeologist look at bones of extinct animals they see where the eyes are situated and the shape of teeth to judge what kind of animal this was. Yeah, we use other senses to judge where objects are. (ears are obvious and was covered in class) If an object hits us with out us seeing it, our brains still can estimate where the object should be. This uses the sense of touch it accurately judge where we see the object. The study concluded that if an object can hit and any additional bounce would just aid our senses in pin pointing exactly where the object was. I saw this reenacted in an episode of Sports Science because they wanted to understand how Chris Moore caught a football.You can watch the catch here at http://www.youtube.com/watch?v=J25FVrP-MdA
ReplyDelete