Group items tagged mathematics - NYU Probability Summer 2009

Probability theory - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...Probability_theory

shared by bouchra alami on 20 Jul 09 - Cached

Probability theory is the branch of mathematics concerned with analysis of random phenomena.[1] The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
- bouchra alami on 20 Jul 09
  
  This is my first try with taging in Diigo. Important to know anyway :)
  
  <div class="cArrow"> </div><div class="cContentInner">This is my first try with taging in Diigo. Important to know anyway :)</div>
  
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Set theory - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/Set_theory

v63.0233.2009Su set theory mathematics wikipedia

shared by Matthew Leingang on 01 Jul 09 - Cached

Matthew Leingang on 01 Jul 09

Overview of the history, philosophy, and basic operations in set theory. Fortunately, sets are an extremely flexible way to describe mathematical objects, such as the sample space of some experiment. To our disappointment, it turns out to not be the be-all, end-all of mathematics, but that's a subject for a logic course.

<div class="cArrow"> </div><div class="cContentInner">Overview of the history, philosophy, and basic operations in set theory. Fortunately, sets are an extremely flexible way to describe mathematical objects, such as the sample space of some experiment. To our disappointment, it turns out to not be the be-all, end-all of mathematics, but that's a subject for a logic course.</div>

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Behind Monty Hall's Doors: Puzzle, Debate and Answer? - The New York Times - 0 views

www.nytimes.com/...-puzzle-debate-and-answer.html

v63.0233.2009Su puzzle conditional probability Monty Hall problem

shared by John Muccini on 14 Jul 09 - Cached

Matthew Leingang on 14 Jul 09

Although I did not enter the debate, I remember the Marilyn vos Savant vs. the mathematicians episode. I was in high school at the time. Marilyn's solution is sound, and her tactics are indeed wise: to people who disagreed with her explanation, she suggested they simply experiment and see what they find. So both the Bayesian and frequency models of probability are brought into play here. Persi Diaconis, the carnival card shark turned Harvard mathematics professor who I mentioned in class, is also quoted in this article. The Marilyn vs. the Mathematicians rematch did not turn out so well for her. When Wiles and Taylor finally proved Fermat's Last Theorem, she pronounced it phony because she didn't understand it. The mathematical consensus remains that the proof is good.

<div class="cArrow"> </div><div class="cContentInner">Although I did not enter the debate, I remember the Marilyn vos Savant vs. the mathematicians episode. I was in high school at the time. Marilyn's solution is sound, and her tactics are indeed wise: to people who disagreed with her explanation, she suggested they simply experiment and see what they find. So both the Bayesian and frequency models of probability are brought into play here. Persi Diaconis, the carnival card shark turned Harvard mathematics professor who I mentioned in class, is also quoted in this article. The Marilyn vs. the Mathematicians rematch did not turn out so well for her. When Wiles and Taylor finally proved Fermat's Last Theorem, she pronounced it phony because she didn't understand it. The mathematical consensus remains that the proof is good.</div>

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Math and the City - Olivia Judson Blog - NYTimes.com - 0 views

judson.blogs.nytimes.com/...math-and-the-city

probability V63.0233.2009SU zipf zeta nature sociology

shared by Sam V on 31 Jul 09 - Cached

Sam V on 31 Jul 09

Evidence of a surprising mathematical pattern (Zipf Distribution) in both the relative populations of cities and the calories burned by mice.

<div class="cArrow"> </div><div class="cContentInner">Evidence of a surprising mathematical pattern (Zipf Distribution) in both the relative populations of cities and the calories burned by mice.</div>

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Matthew Leingang on 03 Aug 09

That's very cool. I hadn't known anything about the Zipf Distribution before.

<div class="cArrow"> </div><div class="cContentInner">That's very cool. I hadn't known anything about the Zipf Distribution before.</div>

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Flora Kwong on 03 Aug 09

Whoa. I guess humans are more in tune with their surroundings than we think.

<div class="cArrow"> </div><div class="cContentInner">Whoa. I guess humans are more in tune with their surroundings than we think.</div>

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Some Really Hard Probability Problems - 0 views

ocw.mit.edu/...prob.pdf

shared by Matthew Leingang on 21 Jul 09 - No Cached

Marc Tourangeau on 21 Jul 09

I pulled this up from the MIT Open CourseWare page under their Problem Solving class. I think they use problems of this caliber to prepare for the Putnam exam.

<div class="cArrow"> </div><div class="cContentInner">I pulled this up from the MIT Open CourseWare page under their Problem Solving class. I think they use problems of this caliber to prepare for the Putnam exam.</div>

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...2 more comments...
Sam V on 21 Jul 09

I wonder if we as a class could take on this one... 3. An unfair coin (probability p of showing heads) is tossed n times. What is the probability that the number of heads will be even?

<div class="cArrow"> </div><div class="cContentInner">I wonder if we as a class could take on this one... 3. An unfair coin (probability p of showing heads) is tossed n times. What is the probability that the number of heads will be even?</div>

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Matthew Leingang on 21 Jul 09

That's a great idea. First, try it for specific values of n. If n=1, then the number of heads is even if it's 0, so P(even) = 1-p. If n=2, you could have 0 or 2 heads, so P(even) = (1-p)^2 +p^2 = 1-2p. Obviously there's going to be some kind of binomial identity, but what?

<div class="cArrow"> </div><div class="cContentInner">That's a great idea. First, try it for specific values of n. If n=1, then the number of heads is even if it's 0, so P(even) = 1-p. If n=2, you could have 0 or 2 heads, so P(even) = (1-p)^2 +p^2 = 1-2p. Obviously there's going to be some kind of binomial identity, but what?</div>

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Matthew Leingang on 22 Jul 09

OK, I now know two ways to solve this. The first way was along the lines you described in the break to me, Sam. It makes more sense than I originally thought, and with your Discrete Math knowhow you might be able to solve it. There's also a clever way, which I admit I didn't figure out until I solved it the other way.

<div class="cArrow"> </div><div class="cContentInner">OK, I now know two ways to solve this. The first way was along the lines you described in the break to me, Sam. It makes more sense than I originally thought, and with your Discrete Math knowhow you might be able to solve it. There's also a clever way, which I admit I didn't figure out until I solved it the other way.</div>

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Matthew Leingang on 22 Jul 09

That's a great list of problems btw!

<div class="cArrow"> </div><div class="cContentInner">That's a great list of problems btw!</div>

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The New Nostradamus | GOOD - 0 views

www.good.is/...the-new-nostradamus

v63.0233.2009su politics prediction mathematics

shared by hannar lee on 16 Jul 09 - Cached

hannar lee on 16 Jul 09

Michael A. M. Lerner talks with the man who is putting the "science" back in political science.

<div class="cArrow"> </div><div class="cContentInner">Michael A. M. Lerner talks with the man who is putting the "science" back in political science.</div>

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BRIDGE; BETTING WITH THE ODDS - The New York Times - 0 views

www.nytimes.com/...dge-betting-with-the-odds.html

v63.0233.2009Su probability cards bridge yarborough

shared by Matthew Leingang on 08 Jul 09 - Cached

the second Earl of Yarborough offered an interesting bet to his whist-playing friends: a thousand to one against them picking up a hand with no card above a nine. Mathematics was on his side since the odds are 1,827 to 1. There is no record that he ever paid off.
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Matthew Leingang on 08 Jul 09

NY Times article about bridge and probability

<div class="cArrow"> </div><div class="cContentInner">NY Times article about bridge and probability</div>

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Matthew Leingang on 08 Jul 09

Unfortunately, the rest of the column is full of bridge jargon and I don't play. This is like NASCAR for nerds.

<div class="cArrow"> </div><div class="cContentInner">Unfortunately, the rest of the column is full of bridge jargon and I don't play. This is like NASCAR for nerds.</div>

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The Mathematics of Magic: The Gathering - 0 views

www.kibble.net/magic01.php

shared by Matthew Leingang on 04 Jul 09 - Cached

- Matthew Leingang on 06 Jul 09
  
  Interesting point. I think there's a lot of math behind designing any popular game involving chance. For instance, legend has it the game High-Ho Cherry-O! was engineered to make the expected game length about equal to the attention span of the children playing it. Here you have a case of designers not understanding the game they were developing. Casino games seem simple enough to attract interest (and pay often enough to keep it) but still manage to benefit the house.
  
  <div class="cArrow"> </div><div class="cContentInner">Interesting point. I think there's a lot of math behind designing any popular game involving chance. For instance, legend has it the game High-Ho Cherry-O! was engineered to make the expected game length about equal to the attention span of the children playing it. Here you have a case of designers not understanding the game they were developing. Casino games seem simple enough to attract interest (and pay often enough to keep it) but still manage to benefit the house.</div>
  
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Parimutuel betting - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...Parimutuel_betting

v63.0233.2009Su parimutuel gambling example informative probability mathematics

shared by Matthew Leingang on 02 Jul 09 - Cached

Matthew Leingang on 02 Jul 09

Describing the system by which money is won and odds are calculated in horse racing and large-prize lottery games.

<div class="cArrow"> </div><div class="cContentInner">Describing the system by which money is won and odds are calculated in horse racing and large-prize lottery games.</div>

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Vehicle registration plates of Indiana - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...registration_plates_of_Indiana

combinatorics indiana v63.0233.2009Su

shared by Matthew Leingang on 16 Jun 09 - Cached

Matthew Leingang on 16 Jun 09

Unless you're really interested in all the pictures of license plates, scroll down to "County coding" to see the mathematically relevant part. Ask yourself: how many license plates can be generating in the scheme used from 1963 to 2008? How many can be generated in the new scheme?

<div class="cArrow"> </div><div class="cContentInner">Unless you're really interested in all the pictures of license plates, scroll down to "County coding" to see the mathematically relevant part. Ask yourself: how many license plates can be generating in the scheme used from 1963 to 2008? How many can be generated in the new scheme?</div>

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Matthew Leingang on 16 Jun 09

A gallery of Indiana license plates and description of the various coding schemes used.

<div class="cArrow"> </div><div class="cContentInner">A gallery of Indiana license plates and description of the various coding schemes used.</div>

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Stable marriage problem - Wikipedia, the free encyclopedia - 0 views

en.wikipedia.org/...Stable_marriage_problem

v63.0233.2009Su

shared by Samantha Spilkin on 13 Jul 09 - Cached

Matthew Leingang on 14 Jul 09

Interesting...although the solution algorithm seems more suited to prom than marriage...

<div class="cArrow"> </div><div class="cContentInner">Interesting...although the solution algorithm seems more suited to prom than marriage...</div>

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Truman Deeb on 20 Jul 09

Mathematical marriage counseling? Sounds interesting.

<div class="cArrow"> </div><div class="cContentInner">Mathematical marriage counseling? Sounds interesting.</div>

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Glen Whitney's quest for a math museum : The New Yorker - 0 views

www.newyorker.com/...090803ta_talk_paumgarten

v63.0233.2009Su mathematics interesting

shared by Matthew Leingang on 05 Aug 09 - Cached

Matthew Leingang on 05 Aug 09

Not so much relevant to probability but a nice story and it mentions an NYU professor.

<div class="cArrow"> </div><div class="cContentInner">Not so much relevant to probability but a nice story and it mentions an NYU professor.</div>

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