A Microblog by Gaurav Tiwari

Thoughts, discoveries and administrative updates from Gaurav Tiwari. All opinions are personal and are not endorsed by any brand or person.

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Gowers’ blog is Blog of the Month for October 2011

Reader’s brain is variable. It changes according to what it read. 🙂 I have changed the pattern of selection and style of writing about BLOG OF THE MONTH. At the beginning of August, I planned that I will select some blogs from the education blog-o-sphere and will award to appreciate them for their excellent work. I know these awards will probably never make a difference but hope too that they’ll keep their good works on. So, here is the list of my 10 most favorite blogs, one of which, Gowers’ Weblog, is my Blog of The Month, for October 2011.

Previous Month’s Results:

Disclaimer: Please note that this selection is personal and I have no affiliation with any organization. Your views are invited in form of comments. I have a huge list of other blogs at My Blogs Page. Have a look. If you have a very good blog which I’ve not noticed yet ; or want to provide feedback about this selection, please feel free to comment below.

Cameron Counts – Blog of the Month for August 2011

I announced to choose a blog from the education blogosphere as Blog of the Month. To complete this task, I googled for days, read them, analyzed them and now I have the winner of ‘Blog of the Month’.
This is the first month of this series and discussing article is made in hurry, so one can feel an emptiness and lack of interest in it. But believe, Blog of the month was not selected in hurry. I took quick looks on about 500 blogs and thousands of posts. I created a list of all blogs I read and rated them on behalf of their qualities, visitors, content, language etc. From the list of 513 blogs, the shortlisted blogs were:

  1. What’s New (math)
  2. Gödel’s Lost Letter and P=NP(Math and Computer Science)
  3. Peter Cameron’s Blog(math)
  4. Let’s Play Math(math)
  5. Unapologetic Mathematician(math)
  6. Cock Tail Party Physics(Physics)
  7. WordPress Tips(Blogging)
  8. Honglang Wang’s Blog (Math and Programming)
  9. The GeomBlog(CS)
  10. Republic Of Mathematics (Math and Media)

I count a lot of things that there’s no need to count. Just because that’s the way I am. But I count all the things that need to be counted.

And Yes! The blog of the month is Peter Cameron’s Blog with useful content, interactive language and multidimensional approach to mathematics.
count1.jpg

About Peter Cameron’s Blog

Peter Cameron is a professor of mathematics in London and he writes about math, media and education at http://cameroncounts.wordpress.com. He mingles everything with math, like poetry – media – fun and internet. His blog is full of expositories, problems and results, Posts about doing – playing and learning mathematics, Poetry, Events Talks and Conferences, typesetting and Mathematics in Media. A list of categorized posts can be found here.

Chess Problems

  1. In how many ways can two queens, two rooks, one white bishop, one black bishop, and a knight be placed on a standard $ 8 \times 8$ chessboard so that every position on the board is under attack by at least one piece?
    Note: The color of a bishop refers to the color of the square on which it sits, not to the color of the piece.
  2. Can you attack every position on the board with fewer than seven pieces?

Solution

  1. Two ways as follow:
    chess1chess2
  2. No. (…and I’m not pretty sure about this No)

Improved chessboard images via this website using Creative Commons.

What is Real Analysis?

Real analysis is the branch of Mathematics in which we study the development on the set of real numbers. We reach on real numbers through a series of successive extensions and generalizations starting from the natural numbers. In fact, starting from the set of natural numbers we pass on successively to the set of integers, the set of rational numbers and that of real numbers.
Let $ \mathbf {Q}$ be the set of rational numbers. It is well known that $\mathbf {Q}$ is an ordered field, i.e., $ \mathbf {Q}$ is an Algebraic Structure on which the operations of addition, subtraction, multiplication and division by a non-zero number can be carried out. Also the set $\mathbf {Q}$ is equipped with a relation called “less than” which is an order relation. Between two rational numbers there exist infinite number of elements of $\mathbf {Q}$. Thus the system of rational numbers seems to be dense and so apparently complete. But it is quite easy to show that there exist some numbers which are not rational. Such numbers are called irrational numbers. The set/collection of rational and irrational numbers combined is called the set of real numbers. Study of these numbers is Real Analysis.

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