x Turn on thread page Beta
 You are Here: Home >< Maths

# The Proof is Trivial! watch

1. (Original post by Jkn)
You're not just doing that for another shot at the IMO, are you? :/ I can picture you getting into a rather strange situation if you started university in the first year... perhaps you could take 2/3 years of exams all at once though hmm...
Clearly not; at least, I will be twenty years old before the first day of IMO 2014..
Roughly speaking, at our most prestigious university i.e. Sofia University, De Rham coholomogies are taught in year 4 and this is the most advanced course; this course, however, is senseless, as there is no further study of Crystalline cohomology. Not to mention that things such as Lie Groups (that is, the very basic real geometry) are only for the masters, but owing to lack of candidates such courses are taught rarely. Hence, the whole thing appears to be pointless.

By the way, has anybody seen this before? I am gobsmacked.
Clearly not; at least, I will be twenty years old before the first day of IMO 2014..
Roughly speaking, at our most prestigious university i.e. Sofia University, De Rham coholomogies are taught in year 4 and this is the most advanced course; this course, however, is senseless, as there is no further study of Crystalline cohomology. Not to mention that things such as Lie Groups (that is, the very basic real geometry) are only for the masters, but owing to lack of candidates such courses are taught rarely. Hence, the whole thing appears to be pointless.

By the way, has anybody seen this before? I am gobsmacked.
Actually know a little bit about something you said. That's made my otherwise **** day.
3. (Original post by bananarama2)
Actually know a little bit about something you said. That's made my otherwise **** day.

Obiter, I can't say that I understand even to the least extent the recently discussed physics problems, so you are in a better position.

Problem 244**

Prove that for any integer there exist infinitely many positive square-free integers such that .
4. Problem 244**

Let

Show f(x) is constant, and find its value.

Problem 345**/***

Evaluate
5. (Original post by bananarama2)
Solve it using bananas. (Say this in Rowan Atkinsons' voice)
6. (Original post by Ateo)
That's exactly what I was thinking of when I said it
7. Solution 245

We differentiate ; Hence, is constant over .

Let -

Solution 246

Rewrite,
i.e. Sofia University ...
I am not-so-motivated to study french - so I can't enroll at LLG although I have aced their mathematics exam.
UK is possible, but I am not quite sure.
I have no chance to be accepted into a university in the USA; their criteria is a bit vague for me (a friend of mine applied to several universities there last year, and he was not admitted even though he had participated in RSI).
10. Solution 246 (alternative)

11. We obviously have:
.

Problem 247**

Evaluate .
12. Solution 247

13. A friend just sent me this link, are many those questions actually do-able?
14. (Original post by james22)
A friend just sent me this link, are many those questions actually do-able?
they're certainly doable, but some are pretty hard.
I have no chance to be accepted into a university in the USA; their criteria is a bit vague for me...
Well, admissions are usually quite individual, so don't try to predict the outcome of your potential application based on other people's experience or results. It does not cost much to apply to universities anyway, so I don't see why not try it. If you have strong grades and achievements from competitions, together with a passion for the subject (which admissions tutors can identify), then you do have a chance. It might not be as great a chance as somebody who rocked IMO (or IOI, or something), but it is still a chance. Do you just let it slip?
...
Well, admissions are usually quite individual, so don't try to predict the outcome of your potential application based on other people's experience or results. It does not cost much to apply to universities anyway, so I don't see why not try it. If you have strong grades and achievements from competitions, together with a passion for the subject (which admissions tutors can identify), then you do have a chance. It might not be as great a chance as somebody who rocked IMO (or IOI, or something), but it is still a chance. Do you just let it slip?
I would very much agree with this. Please consider applying to a UK university (most likely, the right choice for you is Cambridge, but also look at Oxford, Warwick and Imperial too). Getting in front of an admissions tutor might be the hardest step - if you get to an interview and perform to your abilities, you should fly through the admissions process. Have you ever looked at STEP? If you feel like that's reasonable then definitely look into Cambridge.

I also think you should look into the US too - MIT seem to be international friendly
17. (Original post by james22)
A friend just sent me this link, are many those questions actually do-able?
This is the opitome of why I didn't do maths. I just can't get my head around stuff like that. I can apply calculus and maths to physics amd chemistry no problem, but not stuff like that.

Posted from TSR Mobile
18. (Original post by bananarama2)
This is the opitome of why I didn't do maths. I just can't get my head around stuff like that. I can apply calculus and maths to physics amd chemistry no problem, but not stuff like that.

Posted from TSR Mobile

The real question is. Can you apply Calculus to English?
19. (Original post by Zakee)
The real question is. Can you apply Calculus to English?
My mistakes in that are justified by the fact I was on my phone
Well, admissions are usually quite individual, so don't try to predict the outcome of your potential application based on other people's experience or results. It does not cost much to apply to universities anyway, so I don't see why not try it. If you have strong grades and achievements from competitions, together with a passion for the subject (which admissions tutors can identify), then you do have a chance. It might not be as great a chance as somebody who rocked IMO (or IOI, or something), but it is still a chance. Do you just let it slip?
(Original post by shamika)
I would very much agree with this. Please consider applying to a UK university (most likely, the right choice for you is Cambridge, but also look at Oxford, Warwick and Imperial too). Getting in front of an admissions tutor might be the hardest step - if you get to an interview and perform to your abilities, you should fly through the admissions process. Have you ever looked at STEP? If you feel like that's reasonable then definitely look into Cambridge.

I also think you should look into the US too - MIT seem to be international friendly
Thank you, I highly appreciate your advices and will take them into consideration.

I am reading some number theory and here is an exercise I made.

Problem 248**

Let be an arbitrary integer, - prime number, pick random divisor of , - integer which is not divisible by , and .

If , show .
Next, prove that .

Now, let and . Show that , where and satisfy .

We next let and define to be an arbitrary reduced residue system modulo such that . Set . Show that .

Let and be integers, , , ( is defined as above). Further, let be an arbitrary complete residue system modulo , and - reduced.

Denote and , where , .

Let

Show that .

Let , and , . Prove that , and that .

In the case show that and .

Prove that , where is independent of .

Problem 249**

Let be a prime number. Show that for all , there exists integer such that .

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 22, 2018
Today on TSR

### Did he block me?

What should I do?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams