Comments for Math-Blog

Comment on Faster, Better, Cheaper Search Engines by Adam

2009-10-29T17:33:13Z

Antonio: Excellent, thank you very much!

Comment on Faster, Better, Cheaper Search Engines by Antonio Cangiano

2009-10-28T17:33:16Z

Adam, I added a PDF version for you to download.

Comment on Faster, Better, Cheaper Search Engines by Adam

2009-10-28T17:19:00Z

Why do people put their PDFs on websites where you can’t download them without Flash and without signing up?

*sigh*

Comment on The Cost of Not Understanding Probability Theory by Calcatraz

2009-10-27T07:27:54Z

Thanks for an interesting read. I knew about most of these, but not the specifics of the Italian Lotto. Another source of misunderstanding probability occurs when humans try to do mental calculations involving very large numbers. A million is about the same as a billion, right?

Comment on On the Importance of Mathematics by OJO OMOTAYO JESUJOBA

2009-10-26T19:30:19Z

Well, I love mathematics with Passion and i am almost through with my Masters Degree in Mathematics and i will love to do my PHD(Doctorate) in Mathematics.May God help me.Once again, keep it up.

Comment on Faster, Better, Cheaper Search Engines by Ian Parker

2009-10-26T11:27:02Z

It is easy to say these thing. In fact the modern search engine is extremely sophisticated in what it is trying to do.

Most search engines these days use LSI (Latent Semantic Indexing). This presents each web page as being a vector. Some remarkable associations between websites that have got similar vectors.

http://chris.ikit.org/ksv2.pdf

is very impressive. It should be pointed out that LSI scanning is CPU intensive. OK once a page has been done it has been done.

One thing I would like Google to do is to use vectors when searching from within a document you are writing. It does not appear to do this.

Comment on The Cost of Not Understanding Probability Theory by Antonio Cangiano

2009-10-18T22:27:28Z

> Say that 5 bets are made and then the 6th one is a win.

#1: spends 1, wins 0
#2: spends 2, wins 0
#3: spends 4, wins 0
#4: spends 8, wins 0
#5: spends 16, wins 0
#6: spends 32, wins 32*11.232

So the net is:

won = 32*11.232 = 359.392
spent = 63 (1 + 2 + 4 + …)

net = won – spent = last_wager * 11.232 – (2*last_wager -1) = last_wager * 9.232 + 1

Sudeep’s formula is the correct one. I updated my post.

Comment on The Cost of Not Understanding Probability Theory by David Friedman

2009-10-18T21:38:14Z

Sandeep wrote:

>
>For your calculation of the additional
>payout for martingale, i think the correct
>formula should have been
>(last wager * 9.232 ) + (initial wager)
>
>

Antonio wrote:

>Sudeep, the 11.232x payout includes your >last bet, and the initial wager is assumed >to be 1 Euro here. The general formula is: >(last wager * 8.232) + initial wager.

Say that 5 bets are made and then the 6th one is a win.

First bet: bets 1 loses 1
Second bet: bets 2 loses 2
Third bet: bets 4 loses 4
Fourth bet: bets 8 loses 8
Fifth bet: bets 16 loses 16

he loses a total of 31 before he wins.

When he wins, he wins 32*11.232 .

So the net is:

won = 32*11.232
lost = 31

net = won – lost
net = 32*11.232 – 31

net = last_wager*11.232 – (last_wager-1)
= last_wager*10.232 + 1

This seems very confusing to me since it isn’t either of the two other answers.

I originally thought I might have the same answer as Sudeep. My understanding is that by 11.232 what is meant is that if the bettor has only 5 euros in his pocket and he bets all 5 euros then if he wins he can put 11.232*5 = 51.16 euros in his pocket.

I see though that your answer to Sudeep and your formula in the blog post is consistent:

answer to Sudeep:

(last wager * 8.232) + initial wager

blog post:

(last wager x 8.232 + 1)

given that initial wager=1

Comment on Blogging in Math Class by Amy Bowser

2009-10-17T15:21:23Z

I am going to incorporate this idea in my art class. They will be assigned days to post and comments to make. I am leaving it up to the students on the art topic. It should be fun to see their ideas. Thanks.

Here is my blog:
http://abowser555.wordpress.com/2009/10/17/blogging-in-math-class/

Comment on A 10 minute tutorial for solving Math problems with Maxima by David Friedman

2009-10-16T20:22:44Z

I’m trying Maxima now, after closing my sage session. I ran into trouble using sage to define a symbolic sum e.g. you want to define a function like:

f(x) = sum(i, i, 1, x);

apparently sage cannot do that at this point in the development. It was disappointing that sage couldn’t do this (or if it is possible to do this I couldn’t figure it out after an hour of trying).

sage is actually the first hit after a google search for “sage”, so it is still popular, and maybe it’ll improve by leaps and bounds, but at least after the first ten minutes I have a better feeling about Maxima.

when I was searching for a way to solve my problem I found this thread, which indicates
that this functionality is on the way for the sage:

http://groups.google.com/group/sage-support/browse_thread/thread/cf9cb4e92ce3bc04/f5e41d8aa31294e4?lnk=gst&q=sum#f5e41d8aa31294e4

it seems to me that sage is more of an interface to or a concatenation of a lot of other programs (latex, r, maxima, python etc., and also commercial programs like mathematica, matlab). I guess one has to ask whether when doing a task it is better to use sage as a single command center, or to just use that program directly.