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

Other mathematical notations, constants and terms will be introduced as their need.

For Non-Mathematicians:
Don’t worry I have planned to post more fun. Let’s see how the time proceeds!

## The Way To Prime

This animation image illustrates how to find prime numbers between 2 to 120. Not too mathematical this time, but sticky one. Hope you will enjoy it.

Finding Primes

Source: Unknown

## 381654729 : An Interesting Number Happened To Me Today

Image via Wikipedia

You might be thinking why am I writing about an individual number? Actually, in previous year annual exams, my registration number was 381654729. Which is just an ‘ordinary’ 9-digit long number. I never cared about it- and forgot it after exam results were announced. But today morning, when I opened “Mathematics Today” magazine’s October 2010, page 8; I was brilliantly shocked. 381654729 is a nine digit number with each of the digits from 1 to 9 appearing once. The whole number is divisible by 9. If you remove the right-most digit, the remaining eight-digit number is divisible by 8. Again removing the next-right-most digit leaves a seven-digit number that is divisible by 7. Similarly, removing next-rightmost digit leaves a six-digit number that is divisible by 6. This property continues all the way down to one digit.
Further research on this number provided a term for this number as Poly-divisible Number.
And I also noticed that a similar problem has been asked in U S A Mathematical Talent Search  competition. See the first question in the doc below:

To view this document in appropriate size click on View tab of the doc.

After this beautiful incident, I would like to quote a statement here:

Mathematical Wonders happen with Mathematicians.

Numbers always chase me.

## Social Networks for Math Majors

Math or Mathematics is not as difficult as it is thought to be. Mathematical Patterns, Structures, Geometry and its use in everyday life make it beautiful. ‘Math majors’ term generally include Math students, Math professors and researchers or Mathematicians. Internet has always been a tonic for learners and whole internet is supposed to be a social network, in which one shares and others read, one asks & others answer. There are thousands of social networks (and growing) where you enjoy your days, share fun etc. However there are only a few social (mathematical) networks which are completely focused on math and related sciences. But these are brilliantly good enough to demonstrate the wisdom of mathematicians. I have tried to list my favorite social networking websites on mathematics. Please have a read and give feedback in form of comments
Click On Images To Visit Corresponding Websites.

# Math.Stack Exchange

Mathematics StackExchange Website

Mathematics Stack exchange is a website dedicated to all types of mathematical discussions. You can ask questions, give answers, comment on questions and vote for it. Registration is very easy and takes seconds. Depending on your work, you are given ‘reputations’. Depending upon some special works, you are also given some privileges.

This is a free, community driven Q&A for people studying math at any level and professionals in related fields. It is a part of the Stack Exchange network of Q&A websites, and it was created through the open democratic process defined at Stack Exchange Area 51. (more…)

A comic via SpikedMath.com

## Blog Of The Month – September 2011

Last month, in August 2011, I awarded (actually I devoted my Love to) Peter Cameron’s blog as  Blog of the month. In this month too, I had created a list of approx. 140 blogs all across the web for the blog of the month,
Here is a list of 10 blogs which are  my personal favorites at this time and I love reading them regularly:

Richard's Blog

Richard Wiseman

And Blog Of The Month for September is Richard Wiseman’s  Blog located at http://richardwiseman.wordpress.com. He is an absolute puzzler, great author  and his blog involves everything that one, who is not a math major,  may also think and care about.

Psychologist and author Professor Richard Wiseman carries out research into luck, the science of self-help, perception, belief and deception.

He has some vieos on Youtube!

Richard Wiseman's Books

His Latest Post is  Five funny signs which he published just today.

Review:

Total: 10/10
Design: 10/10
Content: 10/10
Periodicity Of Content:10/10
Language: 10/10 [easiest]
Content Management: 9/10
Interaction: 9.5/10
View: 9/10

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.

Last Updated: Sep. 6, 2011

14:24 India Standard Time

## Credit Card Mathematics

What do you know about your credit card? Have you ever checked whether your Credit Card is valid or not?
See what Jess says about Credit Card Codes. It is a real fun.

I checked. And thanked god that my card was valid. Try it at your own!