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Why only mathematics?

Tuesday, February 5th, 2013 10:52 / Leave a Comment

This is the question, I asked myself.

Why only mathematics? Why so serious stuffs?

Why not have something new? New like adding more creativity and engaging more topics.

MY DIGITAL NOTEBOOK was aimed to be a notebook type blog, in which thoughts and useful class-notes were to be written. What happened? I quit writing here.

(more…)

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.

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: $n!=1\cdot 2 \cdot 3 \ldots (n-1) n /; n \in \mathbb{N}$