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Primarygun

Maths Paper

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Is there a web site giving out a lot of difficult questions about the additional mathematics or just mathematics?

I appreciate who helps me :) very much.

I want to have far more troublesome questions:P

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Why don't you just get hold of a book ! I don't think the web is the best place to try and learn maths from.

 

Whats Riemann's hypothesis ?

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That the zeroes of a certain L-function all have real part =1/2 (lie on the critical line, in the parlance), the L-function is the Riemann Zeta function, and is detailed on many web sites.

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ok this is a bit beyond the scope of any maths I have done till now.

I have only heard of the riemann zeta function at times (Its what we once needed to derive some law in black body radiation - for some integration purposes)

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My school books are not very tricky and open-ended.

Pulkit, studying engineering have a lot of physics to study?

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I studied physics in first year - electrodynamics, optics and quantum mechanics.

 

Presently doing a course in applied mechanics called engineering mchanics which is quite difficult i must add.

 

Now i have just one course left called physics of materials, that has a lotta quantum mechanics. But since my major is in computer science that'll be the end of physics for me.

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I see.

I think I may make up my mind to study engineering several years later.

Since it has physics to study ( the most useful ones), also, the return is quite delicious ( I think)! Otherwise, I think I will choose studying medicine.

Moreover, the computing engineering or engineering get more studies on science?

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There is a branch of engineering we have here called engineering physics. It has physics courses in all four years, and later on you may choose to diversify into one of several branches of engineering.

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maybe you could independently verify Fermats Last Theorem perhaps. or the Fundamental theorem of Algebra

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maybe you could independently verify Fermats Last Theorem perhaps

 

Maybe if he starts doing that today, he might be done in 20 years or so.

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Fundamental theorem of Algebra

 

We did this in the two weeks of university? Or at least I did.

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Can you state this theorem.

I am sure I have heard of it, just can´t relate the name to anything.

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Any natural number greater than or equal to 2 (not sure about the "or equal than") can be written as a unique product of prime numbers.

 

For example, 8 = 2*2*2; 18 = 3*3*2: no other combination of prime numbers can make those numbers.

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hang on. is that what u think it is?? Cos in our course, it was called, the Fundamental Theorem of Arithmetic

 

What I meant by the fundamental theorem of Algebra

 

goes something like this

 

a polynomial of degree n has n roots.

 

or a polynomial of nth degree has n linear factors in C

 

yadda yadda yadda. u know what i mean

 

I still couldnt be bothered proving the prime thingy. maybe do it later

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Ah, got the wrong one ;) Saw FTA and assumed the wrong thing :D The proof is a bit convoluted although fairly straightforward.

 

Haven't heard of that one yet.

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The unique prime factorisation theorem is something I did in the first year too. I did it using ring theory ................

 

It was quite an easy proof I must say.

 

Polynomial of degree n has n roots is not too dissimilar, can be done using ring/group theory too.

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We did this in the first few weeks. Not heard of ring theory yet, probably come next year.

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A ring is a set that has an additely written abelian group structure with operation + and identity 0 which also possesses another binary operation, *, commonly called multiplication such that some obviously useful axioms hold (distribution, note * is not nec commutative, nor is there nec. an identity or inverses).

 

The fundamental theorem of arithmetic is simple to prove but subtle. If you think you understand it then you ought explain why Z[x] has unique factorization, but Z[sqrt(-5)] doesn't. It's to do with certain poperties of primes that aren't true in all rings.

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Acctualy my course steered clear of most properties of polynomials, so I am not sure of that proof. We went on to do vector spaces and matrices after ring theory.

 

What i found extremely intriguing was that ring theory had made the proof of unique prime factorisation much easier than it seemed to be intuitively. Often during group and ring theory the proofs of several theorems were trivialised. (Another example is fermat's little theorem)

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We did this in the first few weeks. Not heard of ring theory yet, probably come next year.

Rings are groups with fancier properties. Fields are rings with more fancy properties. Algebras are even fancier and so on I think.

 

Primarygun: I have a list of tough discrete maths. questions which I haven't answered yet. I can send it to you if you want to. Just PM me.

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Algebras are not fields, your implicit ordering fails at this point (i'm not sure what the "and so on"might be about)

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Primarygun: I have a list of tough discrete maths. questions which I haven't answered yet. I can send it to you if you want to. Just PM me.

 

I do believe that most of discrete maths is well beyond the level of the school going community. Certainly the learning groups, rings, fields, vector spaces, algebras etc. etc. should only be attempted once one has grasped well the more basic concepts in maths.

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