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**daijoubu****Member**- Registered: 2013-09-28
- Posts: 8

Hello i'm daijoubu. I'm currently at an elementary maths level but what to get to the point where I can solve olympiad problems. I hope that you can help me and I can help you.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi daijoubu;

Welcome to the forum. It is good to have that as an ambition but whether you get to be an Olympiad winner or not is of secondary importance. Mathematics plays a big part in technology and science and there is an ever increasing demand for those skilled in it. Also it is beautiful and captivating and can bring you many hours of joy. So whether you become a champion or a mathematician or a hobbyist you can still enjoy it for its own sake.

That is reason enough to be here. So welcome!

**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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**daijoubu****Member**- Registered: 2013-09-28
- Posts: 8

Can you suggest any fun parts of maths that aren't beyond pre calculus?

*Last edited by daijoubu (2013-09-28 11:25:03)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Hi;

You want precalculus?

The fun comes when you work on a problem as hard as you can and it finally cracks and you solve it. And you know what? The more you solve the more joy you get.

**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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**daijoubu****Member**- Registered: 2013-09-28
- Posts: 8

basic algebra, geometry, trig or precalculus. I'm basically in between GCSE and AS level math in the UK so I wont be able to deal with the higher level topics. The problems on exams I have encountered don't last long and aren't really challenging as long as you know the formulas. You don't have to think much and just follow the rules.

I am interested in basic proofs but never really understood them that well. We moved from demonstration to basic proof but the teachers never really explained it well.

prove that the sum of 4 consecutive numbers is odd.

n

2n = even

2n + or - 1 = odd

(n-1)+n +(n+1) + (n+2)

1/2(4n+2)

2n+1

therefore 2n+1 is odd.

I'm interested in proofs but barely know the basics. I am going to look at proof by induction soon but proofs seem more difficult to understand than anything I have done so far.

*Last edited by daijoubu (2013-09-28 11:40:43)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

First have you seen Mathopolis? Are you good at solving everything over there?

**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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**daijoubu****Member**- Registered: 2013-09-28
- Posts: 8

No I have never seen that site before. The questions seem slightly more difficult than what i'm used to but manageable. Thank you for the link. I am just going to practice these sites for a few months then lol.

Do you know anymore? I also would like to know of websites with practice questions with solutions, tutorials, or information that goes into depth. It may seem counter intuitive but the more information i'm bombarded with about a topic, the easier it is for me to understand and remember.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,365

Mathopolis has over 8200 questions and yes they are good practice for you.

Here are a few more.

http://www.wyzant.com/help/math/precalculus

http://cims.nyu.edu/~kiryl/precalculus.html

https://www.math.ucdavis.edu/~marx/precalculus.html

You can always come in here and ask when you do not understand something.

Also, you might want to head down to brilliant.org and signup there too. They will rate you and give you olympiad style questions each week.

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

Hi daijobou

Welcome to 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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi daijoubu

Welcome to the forum.

You might enjoy some of the problems here:

http://nrich.maths.org/frontpage

I didn't follow your proof in post 5.

prove that the sum of 4 consecutive numbers is odd.

n

2n = even

2n + or - 1 = odd(n-1)+n +(n+1) + (n+2)

1/2(4n+2)

2n+1

therefore 2n+1 is odd.

Four consecutive numbers will have two odd and two even.

As ODD + ODD = EVEN

and

EVEN + EVEN = EVEN

surely the four will sum to an EVEN result.

You have this total: 4n + 2 and show that it divides by 2. Doesn't that mean you have proved the EVEN result?

I'm puzzled ...

You can learn about induction here:

http://www.mathsisfun.com/algebra/mathe … ction.html

Bob

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

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,530

Hello and welcome to the forum! I had ambitions like being a gold medalist at an olympiad (maybe Putnam) until a few months ago when I realized the true beauty of maths. If you are at that level, google "Yale university SMSG books" and you will find some online copies of those books which are old yet ideal for high school students (it covers many proofs as well).

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**daijoubu****Member**- Registered: 2013-09-28
- Posts: 8

@ bob bundy prove that 'half' the sum of 4 consecutive numbers is odd.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi daijoubu

Arrh. I see. In that case I'm happy with the proof.

Bob

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

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**karategirl1925****Member**- Registered: 2013-11-28
- Posts: 7

Hello!

I'm Tina and I'm like the same as you- GCSE to A level ish.

Yeah I really want to get into the olympiad too and do a kangaroo, so I posted this thing asking for help - it's called "JMC and IMC (or SMC) takers?!" and it's located in the 'Help' section of the forum. It's like, the first or second one down. You might wanna read the replies and

you might want to see it, I'm only doing IMC next year cause I'm young but I can manage. I know what calculus is.

Yeah aside from that let's be friends together!!!! Are you Japanese by any chance 'daijoubu' sounds like from anime XD

Mathopolis username: Karategirl2012

top ten in four different competitions! XD

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