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Welcome 2012 – The National Mathematical Year in India

Wednesday, December 28th, 2011 08:23 / 18 Comments

Srinivasa Ramanujan (Photo credit: Wikipedia)

I was very pleased on reading this news that Government of India has decided to celebrate the upcoming year 2012 as the National Mathematical Year. This is 125th birth anniversary of math-wizard Srinivasa Ramanujan (1887-1920). He is one of the greatest mathematicians India ever produced. Well this is ‘not’ the main reason for appointing 2012 as National Mathematical Year as it is only a tribute to him. Main reason is the emptiness of mathematical awareness in Indian Students. First of all there are only a few graduating with Mathematics and second, many not choosing mathematics as a primary subject at primary levels. As mathematics is not a very earning stream, most students want to go for professional courses such as Engineering, Medicine, Business and Management. Remaining graduates who enjoy science, skip through either physical or chemical sciences. Engineering craze has developed the field of Computer Science but not so much in theoretical Computer Science, which is one of the most recommended branches in mathematics. Statistics and Combinatorics are almost ‘died’ in many of Indian Universities and Colleges. No one wants to deal with those brain cracking math-problems: neither students nor professors. Institutes where mathematics is being taught are struggling with the lack of talented lecturers. Talented mathematicians don’t want to teach here since they aren’t getting much money and ordinary lecturers can’t do much more. India is almost ‘zero’ in Mathematics and some people including critics still roar that we discovered ‘zero’, ‘pi’ and we had Ramanujan.

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$Chalkboard with Math Problem$

Interesting and Must Read Papers and Articles in Mathematics

Tuesday, December 27th, 2011 09:10 / 2 Comments

Mathematics is beautiful and there is no place of ugly mathematics in this world. Mathematics is originated from creativity and it develops with research papers. Research Papers aren’t only very detailed and tough to understand for general student, but also interesting. Here, I have collected the list of some excellent articles and research papers (belong mainly to Math) which I have read and are easily available online. The main source of this list is ArXiv.org and you may find several research papers on ArXiv by visiting http://arxiv.org/.
If you know any other paper/article which you find extremely interesting and that is not listed here, then please do comment mentioning the article name and URL. Papers/articles are cited as paper-title first, then http url and at last author-name.

[It is better adviced to open these links to a new tab/window for smooth reading. ]

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Newton’s Trinity College Notebook is Online!

Sunday, December 18th, 2011 10:53 / 2 Comments

Cambridge Digital Library had made Newton’s exceptionally great works online.
Some times ago they added the Trinity College Notebook by Isaac Newton, which he used to teach in the college in 17th century.

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GauravTiwari.org

Wednesday, November 30th, 2011 19:46 / 9 Comments

If you are doing good, go for great! And if great - chase the best.

This is a statement which I follow the most. Time is changing rapidly for me and I am more rapidly. At MY DIGITAL NOTEBOOK —I devoted my heart and brain to mathematical and recreational writing. But, wpgaurav.wordpress.com looked ugly in the sense of cuteness of my blog. gauravtiwari lying on
A custom-domain is not very important in the process of getting readers —your blogging does so, but it is very important if you are serious to your name. I love my name and that’s why I opted for my own domain than traditional *.wordpress.com URL. I was looking for an excellent domain name for my blog and what on the earth could be better than my full name? I didn’t look for gauravtiwari.com, whether that was available or not and directly went to register gauravtiwari.org. This made a sense because I treat myself as an organisation and I successfully got it registered. The process was extremely easy and effective, however I failed purchasing the domain twice. Reason —both of my cards weren’t international. I used my friend’s VISA card and finally in third attempt —I had it (well, I paid him back in cash).
Some people might think that I was inspired by declaration of WordAds on WordPress.com but that is not true. When I reached at 40000 hits, I dreamt for my domain –which will have no range–Full of recreations—full of knowledge. I don’t have more to write on this topic since I am completing my book ‘A Trip To Mathematics‘. If you are a regular reader of this blog please update you bookmarks. wpgaurav.wordpress.com is now gauravtiwari.org Thanks for your support my friends and WordPress.com guys! I love math. I love WordPress. I love you.

WordPress URL Shortening: An Interesting Consequence

Thursday, November 24th, 2011 01:43 / 15 Comments

Long post and page URLs can be annoying. There are times when you may want to edit WordPress slugs for long titled posts or pages, so you can share a shorter link with friends. Here’s an example: http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/ (one of the most popular posts from my blog). Would you like to write these (about) hundred characters? Or would you like to use WP.ME link shortener, which for this post was http://wp.me/p14tlY-hv ? Well, second idea sounds better than first one. But you’ll never get the same satisfaction from it because blog URL http://wpgaurav.wordpress.com is not visible, and also looks odd when typed in address bar. What then? This post is on some choices you might want to try. But before we go, let me explain what slug is?
A slug is a few words that describe a post or a page. Slugs are usually an URL friendly version of the post title (which has been automatically generated by WordPress), but a slug can be anything you like. Slugs are meant to be used with permalinks as they help describe what the content at the URL is. The post slug is the part of the URL after the date in a post’s URL. When the default post slug is created, all letters will be converted to lowercase, spaces will be exchanged with dashes, and any special characters will be removed. You can modify the post slug by clicking the Edit button next to it in visual editor. When you’re finished editing, click Save and then Update Post/Page. »via WordPress Codex

How to shorten a WordPress post or page slug with a more efficient way?

Here are some interesting ways to define a personalised, very short and share-friendly version of URL for your post.

Eliminate the ‘time-stamp’ from the slug and
http://wpgaurav.wordpress.com/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
redirects to the same post at
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
So it got a little shorter.
Want it to be even shorter? Then cut one or more characters from the URL: For example:
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is/
http://wpgaurav.wordpress.com/derivative-of-x-squared-is-2x-or-x/ etc. are equivalent and redirect to the same post.
Want it be shorter still? Then eliminate everything but single word. e.g., http://wpgaurav.wordpress.com/derivative/
Looks cool, no? Yes, Just like a Page URL on WordPress.com! And it redirects to the same post as all other links above.
Is the word too long for you? Then abbreviate it to
http://wpgaurav.wordpress.com/der/
Want it be still shorter? Try the shortest, a single letter: http://wpgaurav.wordpress.com/d/ ! Well, it does not redirect to http://wpgaurav.wordpress.com/2011/02/06/derivative-of-x-squared-is-2x-or-x-where-is-the-fallacy/
Where does it go? It goes to d’ Alembert’s Test of Convergence . Reason is specified below at point 2.

Here are some points, which follow and guide you on shortening URLs:

Hyphens are not important when considering shortened-urls.
Any URL of the type http://wpgaurav.wordpress.com/d redirects to a post/page which slug starts with ‘d’. If there are two posts having slugs starting with the same letter of the alphabet (here d),then it will, in alpahabetical order, redirect to that post which first word (if same then second word) comes first in English Dictionary. For example http://wpgaurav.wordpress.com/d will redirect to http://wpgaurav.wordpress.com/d-alembert/ rather than to http://wpgaurav.wordpress.com/derivative/
If two/more posts have the same slugs and you are using an identical shortener that it might go to any of them, then that will (should) redirect to the post which was published earlier.
Some slugs are not allowedin posts or pages on WordPress.com and they are:
- Periods(.) are not allowed in slugs.
- /activate/
- /category/
- /comments/
- /feed/
- /i/
- /next/
- /signup/
- /tag/
- /wp-admin/
- /wp-content/
You can not shorten your post URLs /page URLs (this way) until published.
This trick also works for self hosted WordPress.org blogs.

So, are you going to experiment with your WordPress.com Post URLs?

Disclaimer: There is no technical basis for these shortening tricks. They are soley based on experiments with WordPress.com slugs. This post was made under supervision of timethief, I am grateful to her. I would also like to say thanks to Ganesh Dhamodkar, who was the guy I tested all these with.
Feel free to comment if you are getting any problem in shortening URLs or if just want to say ‘Hi’.

Long URL for this Post: http://wpgaurav.wordpress.com/2011/11/24/wordpress-url-shortening/

Short URL for this post: http://wpgaurav.wordpress.com/wor/

Blog of the Month Awards – October 2011

Thursday, October 6th, 2011 11:56 / 11 Comments

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’s Weblog, is my Blog of The Month, for October 2011.

Gower’s Weblog:
Blog of the Month for October 2011.

Prof. Timothy Gowers (a.k.a. Tim Gowers) is a field medalist and an eminent mathematician. He is a member of the Department of Pure Mathematics and Mathematical Statistics at Cambridge University . He is ideal of many student and math majors including me. I was not a huge fan of his writing as he has written only a few articles after I joined the web. But as he started his series on ‘CAMBRIDGE TEACHING‘, I have become a regular reader of his weblog. One math student must read his posts on Cambridge Teaching.
Most Recent Post: Basic logic — relationships between statements — converses and contrapositives
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Study Notes Announcements and more…

Thursday, September 22nd, 2011 19:12 / 2 Comments

Announcement

Hi all!
I know some friends, who don’t know what mathematics in real is, always blame me for the language of the blog. It is very complicated and detailed. I understand that it is. But MY DIGITAL NOTEBOOK is mainly prepared for my study and research on mathematical sciences. So, I don’t care about what people say (SAID) about the

A Torus

content and how many hits did my posts get. I feel happy in such a way that MY DIGITAL NOTEBOOK has satisfied me at its peak-est level. I would like to thank WordPress.com for their brilliant blogging tools and to my those friends, teachers and classmates who always encourage me about my passion. For me the most important thing is my study. More I learn, more I will go ahead. So, today (I mean tonight) I have decided to write some lecture-notes (say them study-notes, since I am not a lecturer) on MY DIGITAL NOTEBOOK. I have planned to write on Group Theory at first and then on Real Analysis. And this post is just to introduce you with some fundamental notations which will be used in those study-notes.

Notations

Conditionals and Operators
$r /; c$ : Relation $r$ holds under the condition $c$ .
$a=b$ : The expression $a$ is mathematically identical to $b$ .
$a \ne b$ : The expression a is mathematically different from $b$ .
$x > y$ : The quantity $x$ is greater than quantity $y$ .
$x \ge y$ : The quantity $x$ is greater than or equal to the quantity $y$ .
$x < y$ : The quantity $x$ is less than quantity $y$ .
$x \le y$ : The quantity $x$ is less than or equal to quantity $y$ .
$P := Q$ : Statement $P$ defines statement $Q$ .
$a \wedge b$ : a and b.
$a \vee b$ : a or b.
$\forall a$ : for all $a$ .
$\exists$ : [there] exists.
$\iff$ : If and only if.
Sets & Domains
$\{ a_1, a_2, \ldots, a_n \}$ : A finite set with some elements $a_1, a_2, \ldots, a_n$ .
$\{ a_1, a_2, \ldots, a_n \ldots \}$ : An infinite set with elements $a_1, a_2, \ldots$
$\mathrm{\{ listElement /; domainSpecification\}}$ : A sequence of elements `listElement` with some `domainSpecifications` in the set. For example, $\{ x : x=\frac{p}{q} /; p \in \mathbb{Z}, q \in \mathbb{N^+}\}$ $a \in A$ : $a$ is an element of the set A.
$a \notin A$ : a is not an element of the set A.
$x \in (a,b)$ : The number x lies within the specified interval $(a,b)$ .
$x \notin (a,b)$ : The number x does not belong to the specified interval $(a,b)$ . Standard Set Notations
$\mathbb{N}$ : the set of natural numbers $\{0, 1, 2, \ldots \}$
$\mathbb{N}^+$ : The set of positive natural numbers: $\{1, 2, 3, \ldots \}$
$\mathbb{Z}$ : The set of integers $\{ 0, \pm 1, \pm 2, \ldots\}$
$\mathbb{Q}$ : The set of rational numbers
$\mathbb{R}$ : The set of real numbers
$\mathbb{C}$ : The set of complex numbers
$\mathbb{P}$ : The set of prime numbers.
$\{ \}$ : The empty set.
$\{ A \otimes B \}$ : The ordered set of sets $A$ and $B$ .
$n!$ : Factorial of n: $n!=1\cdot 2 \cdot 3 \ldots (n-1) n /; n \in \mathbb{N}$