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I like them very much. However, I am asking whether the book would help me to solve them

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Agnishom;

The best way to learn anything is to solve problems. Dry lectures you will forget within a week, but a solved problem shows you how.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Hmm...

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

It is how gAr, anonimnystefy and I work.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

You can take a look at the "Oh, oh, oh, merry analsis", "Expectation", " Generating functions!", and many more. Many of them started because I (but not only I) wanted to learn about knew topics. You will find that all of those threads consist only of problems and nothing but problems.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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What are these?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

Various threads here on the forum.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Oh! I forgot

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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What does the big O notation signify?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

**Online**

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi Agnishom;

There are many of these threads filled with good problems.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Hmm..

But what is the meaning of the big O?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi;

The Big O notation is used to describe the limit of an algorithms performance as it approaches infinity or some other value.

wikipedia wrote:

big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Any example of it?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

This is very simple and very watered down.

Supposing you wanted to add two two digit numbers. It would take you 2 additions to do it. If you had two four digit numbers it would take 4 additions. Notice as n ( the number of digits doubled the amount of work required also doubled. 4 additions to 2.)

We say that algorithm is linear and assign it O(n).

Now how about multiplication the way you were taught?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I think multiplication should be linear too

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

**Online**

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi;

When you multiply two two digit numbers it takes 4 multiplications. When you two 4 digit numbers it takes 16 multiplications rather than the expected 8. When we triple the amout of digits 6 x 6 it takes 36 multiplications.

n

2 digits = 4 mults

4 digits = 16 mults

6 digits = 36 digits.

You can see that the relationship is n^2. We say that the operation of schoolboy multiplication is O(n^2).

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**mathgogocart****Member**- Registered: 2012-04-29
- Posts: 1,426

bobbym wrote:

Hi Agnishom;

The best way to learn anything is to solve problems. Dry lectures you will forget within a week, but a solved problem shows you how.

what about a wet lecture?

Hey.

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Yes...I see

Whats next?

*Last edited by Agnishom (2012-12-09 03:55:38)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi;

Did you check out the thread anonimnystefy mentioned?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Yes but I dont understand the problems over there

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Can you say what is the part you do not understand?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Okay but tomorrow Gotta sleep! Good Night!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,394

Hi;

Okay, see you tomorrow.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Sarah Rebekah 16****Member**- Registered: 2012-11-12
- Posts: 73

sup guys?

Love is Golden.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,382

hi Sarah,

How are you today?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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