Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts

Thursday, 9 December 2010

Graph theory in 4 min.

Monday, 19 November 2007

The Unique Effects of Including History in College Algebra

via Scout Report:

A team of mathematicians at Black Hills State University {...} decided to investigate what the effects of including historical modules in college algebra might be in regards to students' understanding and mathematical communication.


The result - 'Over the last three years at BHSU, great strides have been made in improving student outcomes in College Algebra with the inclusion of history in the course.':
1. increase in following enrolling (triagonometry) - 5 students in 2003 and 2004 to 20 students in 2007
2. significant improvement on test problems where mathematical vocabulary and notation have created difficulty for students in the past.
3. 10% increase in the College Algebra passing rate since 2005 has come since the addition of the historical modules

The faculty feels that including historical development of mathematics is of key importance and believe that the full benefits of history inclusion have yet to be reached.

Sunday, 20 May 2007

Why Axiomatize Set Theory?

I like mathematics because I like the intellectual challenges it can offer.

Here is a good one:

Russell's paradox concerns the set R={ s | s ∉ s}. Is R∈R? If R∈R, then by the definition of R∉R. But by definition, if R∉R, then R∈R. So R is clearly not a well-defined set.


Answer? Read the rest of the original post.

Friday, 23 February 2007

What's Special About This Number?

via BoingBoing

BoingBoing listed the first 11 numbers. Here is the next 10.

11 is the largest known multiplicative persistence.
12 is the smallest abundant number.
13 is the number of Archimedian solids.
14 is the smallest number n with the property that there are no numbers relatively prime to n smaller numbers.
15 is the smallest composite number n with the property that there is only one group of order n.
16 is the only number of the form xy = yx with x and y different integers.
17 is the number of wallpaper groups.
18 is the only number that is twice the sum of its digits.
19 is the maximum number of 4th powers needed to sum to any number.
20 is the number of rooted trees with 6 vertices.


Frankly, I don't a lot of the special properties, e.g.

Abundant Number [http://mathworld.wolfram.com/AbundantNumber.html] is a positive integer n for which
s(n)=sigma(n)-n>n,

where sigma(n) is the divisor function and s(n) is the restricted divisor function. The quantity sigma(n)-2n is sometimes called the abundance. The first few abundant numbers are 12, 18, 20, 24, 30, 36, ... (Sloane's A005101). Abundant numbers are sometimes called excessive numbers.

There are only 21 abundant numbers less than 100, and they are all even. The first odd abundant number is
945==3^3.7.5.


That 945 is abundant can be seen by computing
s(945)==975>945.


Any multiple of a perfect number or an abundant number is also abundant. Every number greater than 20161 can be expressed as a sum of two abundant numbers.


Mathematically oriented people surely will be interested in the whole list (from 0 to 9999) which only a few numbers without some significance.