CS 6101: Mathematical Foundations of Computer Science lecturenotes

Syllabus:

Divisibility, prime numbers, Congruences, Fermat's theorem, Chinese remainder theorem,
Groups and subgroups, Lagrange’s theorem, rings, finite fields, polynomial arithmetic, quadratic residues,
discrete logarithms, elliptic curve arithmetic. Fundamental principles of counting, derangements, partitions,
partial order, lattices and Boolean algebra, generating functions, solution of recurrences. Graphs, Euler's
formula, applications of Kuratowski's theorem, graph colouring, chromatic polynomials, weighted trees,
spanning trees, max-flow.


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True Friendship :) :)

I Wanted A Friend

Who Could Stay Beside Me,

Who Could Inspire, Motivate Me

At The Time of Sorrow.....

My Heart Was In Immense Pain

I Wanted A Heart, Which Can Heal My Pain

The Very Moment I Heard Door Bell.

To My Surprise It Was You...

You Wrapped Me In Your Arms,

I Tried To Hide My Tears Behind Your Shoulders...

But, Was Inconsolable....

You Felt My Pain...You Felt My Fear....

You Felt My Grief Stricken Heart..

You Felt That, My Heart Is In Immense Pain.....

You Just Stayed Quiet.

You Tried To Understand The Up Rooted

Cause of My Pain..

I Felt Relieved After You Took Me

To Sea Shore...Waves Were Splashing My

Foot  And Pain Washed Away Through Those Waves :) :)

Such Is Our True Friendship

You Came To Me, When I Needed You The Most.....

You Supported Me, When I Needed Supporting Arms,

You Washed Away My Pain Taking Me To Sea Shore

Even At The Late Night :) :)

Tomorrow Is A New Day

If today you feel very sad
For reasons beyond your control
Think about tomorrow
And reset all of your goals.



You cannot be everything to everyone
No matter how hard you try
Just do the very best you can
As each day passes you by.



You deserve the very best
For the kindness that you give
The love you share with other's
And the Christian way you live.



So please do not worry if
People are not what they seem to be
As long as we have each other
Special friends, you and me.

One Day At A Time

One Day At A Time

Our lives are made up of a million moments,
spent in a million different ways.
Some are spent searching for
love, peace, and harmony.
Others are spent surviving day by day.



But there is no greater moment
than when we find that life,
with all it's joys and sorrows,
is meant to be lived one day at a time.
It's in this knowledge that we discover
the most wonderful truth of all.

Whether we live in a forty-room mansion,
surrounded by servants and wealth,
or find it a struggle to manage
the rent month to month,
we have it within our power to be fully
satisfied and live a life with true meaning.



One day at a time - we have that ability,
through cherishing each moment
and rejoicing in each dream.
We can experience each day anew,
and with this fresh start we have
what it takes to make all our dreams come true.
Each day is new, and living one day at a time
enables us to truly enjoy life and live it to the fullest.

Dream Big Differently

Different ~~





How are we so "different"?
If "different" is just a thing.
If we all have certain features,
What does "different" bring?



People filled with hatred,
Can't possibly see,
That there's not really "differences"
Between you and me.



Looks can't show "difference" ,
If they're just there to be seen.
If you don't look like someone else,
Why are they so mean?



If being "different" is what is wrong,
I'd rather not be right.
And I'd want to finish living,
Doing the "different" fight.

Be The Special Someone

Be someone



Be someone who listens, and you will be heard.

Be someone who cares, and you will be loved.

Be someone who gives, and you will be blessed.

Be someone who comforts, and you will know peace.

Be someone who genuinely seeks to understand, and you will be wise.

Be someone kind, someone considerate, and you will be admired.

Be someone who values truth, and you will be respected.

Be someone who takes action, and you will move life forward.

Be someone who lifts others higher, and your life will be rich.

Be someone filled with gratitude, and there will be no end to the things for which you'll be thankful.

Be someone who lives with joy, with purpose, as your own light brightly shines.

Be, in every moment, the special someone you are truly meant to

Life is beautifull without changes

20 years back - School bag.
Today - Office bag.

20 years back - Lekhak Note book.
Today - HP Note book.



20 years back - Hero Ranger.
Today - Hero Honda.

20 years back - Half pants.
Today - Full pants.



20 years back - Playing with plastic car running on battery and remote.
Today - Playing with metal car running on petrol and gear.

20 years back - Scared of Teachers and exams.
Today - Scared of Bosses and targets.



20 years back - Wanting to be class topper.
Today - Wanting to be 'Employee of the month'.

20 years back - Quarterly exams.
Today - Quarterly results.



20 years back - Annual School Magazine.
Today - Company Annual Report.

20 years back - Annual exams.
Today - Annual appraisals.



20 years back - Pocket money.
Today - Salary.

20 years back - Waiting for Diwali crackers.
Today - Waiting for Diwali bonus.



20 years back - Running after grades and prize cups.
Today - Running after incentives and promotions.

20 years back - Craving for the latest toy in the market.
Today - Craving for the latest gadget in the market.



20 years back - Eager to watch the latest cartoon show.
Today - Eager to watch the latest blockbuster.

20 years back - Crush on class mate.
Today - Crush on colleague.



So essentially nothing has changed!!