Redcoats
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What the title fails to encapsulate is that I am doing an EPQ on mathematics. In particular, I would really like to conduct such on the Riemann Hypothesis (i.e. its entailing history, progressions made, arguments for and against it, its implications and consequences if it is correct).

Enter title; I need a question to be the fulcrum of my project. The question needs to open up opportunity for debate but also should not detract from all the wonderful maths the Riemann Hypothesis ensues, such I really want to include in the project in all its glory. The question also should primarily focus on the Riemann Hypothesis itself.

To all those wonderful souls willing to help, thank you.
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CPW2016
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(Original post by Redcoats)
What the title fails to encapsulate is that I am doing an EPQ on mathematics. In particular, I would really like to conduct such on the Riemann Hypothesis (i.e. its entailing history, progressions made, arguments for and against it, its implications and consequences if it is correct).

Enter title; I need a question to be the fulcrum of my project. The question needs to open up opportunity for debate but also should not detract from all the wonderful maths the Riemann Hypothesis ensues, such I really want to include in the project in all its glory. The question also should primarily focus on the Riemann Hypothesis itself.

To all those wonderful souls willing to help, thank you.
I know the name of a wonderful soul who could help with all you desire to know. His name is Marcus Du Sautoy, he wrote a book called the Music of the Primes. It is a great book and deals directly with The hypothesis itself, its importance, its implications whether true or false, progress on a solution and a wonderful history of the mathematicians who strived to capture the elusive proof.
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Redcoats
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(Original post by CPW2016)
I know the name of a wonderful soul who could help with all you desire to know. His name is Marcus Du Sautoy, he wrote a book called the Music of the Primes. It is a great book and deals directly with The hypothesis itself, its importance, its implications whether true or false, progress on a solution and a wonderful history of the mathematicians who strived to capture the elusive proof.
Apologies to bring rain on your rather poetic answer, but I know the 'wonderful soul' of whom you speak. I am actually planning on getting out the very book and shall use it as a reference to my project.

What I currently need is an actual question, not necessarily information on the topic. Do you have any question ideas? Thank you nonetheless however.
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CPW2016
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(Original post by Redcoats)
Apologies to bring rain on your rather poetic answer, but I know the 'wonderful soul' of whom you speak. I am actually planning on getting out the very book and shall use it as a reference to my project.

What I currently need is an actual question, not necessarily information on the topic. Do you have any question ideas? Thank you nonetheless however.
Do you require the question to pertain to the hypothesis itself?
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Redcoats
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(Original post by CPW2016)
Do you require the question to pertain to the hypothesis itself?
Indeed
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Gregorius
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(Original post by Redcoats)
What the title fails to encapsulate is that I am doing an EPQ on mathematics. In particular, I would really like to conduct such on the Riemann Hypothesis (i.e. its entailing history, progressions made, arguments for and against it, its implications and consequences if it is correct).

Enter title; I need a question to be the fulcrum of my project. The question needs to open up opportunity for debate but also should not detract from all the wonderful maths the Riemann Hypothesis ensues, such I really want to include in the project in all its glory. The question also should primarily focus on the Riemann Hypothesis itself.

To all those wonderful souls willing to help, thank you.
One of the features of the Riemann zeta function that connects it with other parts of mathematics is the way in which the distribution of its non-trivial zeros seems to be connected with the "density" of the prime numbers distributed among the integers.

The Riemann hypothesis itself implies a nice strong bound on the error term of the prime number theorem. But more than that, and following the historical development of the subject, the error term in the prime number theorem can be related to how the zeros of the zeta function sit in the critical strip (even if the Riemann hypothesis were not to be true).

One line of investigation into the Riemann hypothesis has been to try to "squeeze" the location of the zeros in the critical strip closer and closer to the critical line - this then has implications for the error term in the prime number theorem.

So, your title might be something like "The implications of the Riemann hypothesis for the prime number theorem" or more generally, "The effect of the location of the zeros of the zeta function on the prime number theorem".
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Redcoats
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(Original post by Gregorius)
One of the features of the Riemann zeta function that connects it with other parts of mathematics is the way in which the distribution of its non-trivial zeros seems to be connected with the "density" of the prime numbers distributed among the integers.

The Riemann hypothesis itself implies a nice strong bound on the error term of the prime number theorem. But more than that, and following the historical development of the subject, the error term in the prime number theorem can be related to how the zeros of the zeta function sit in the critical strip (even if the Riemann hypothesis were not to be true).

One line of investigation into the Riemann hypothesis has been to try to "squeeze" the location of the zeros in the critical strip closer and closer to the critical line - this then has implications for the error term in the prime number theorem.

So, your title might be something like "The implications of the Riemann hypothesis for the prime number theorem" or more generally, "The effect of the location of the zeros of the zeta function on the prime number theorem".
Many thanks for such great advice. I definitely intended on talking about the PNT in the project and its relations with the zeta function. The former suggestion (i.e. "The implications of the Riemann hypothesis for the prime number theorem") seems great but I need the title question to allow for partial debate, giving scope for different concepts and arguments per se. Do you have any further suggestions, or indeed anyone else?
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Gregorius
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(Original post by Redcoats)
Many thanks for such great advice. I definitely intended on talking about the PNT in the project and its relations with the zeta function. The former suggestion (i.e. "The implications of the Riemann hypothesis for the prime number theorem" seems great but I need the title question to allow for partial debate, giving scope for different concepts and arguments per se. Do you have any further suggestions, or indeed anyone else?
I'm not familiar with the requirements for EPQs, but that having been said, perhaps something more speculative may suit. A title like "Is the Riemann Hypothesis true or not?" would allow you to survey the heuristic arguments that various mathematicians have advanced in support of each side.
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Redcoats
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(Original post by Gregorius)
I'm not familiar with the requirements for EPQs, but that having been said, perhaps something more speculative may suit. A title like "Is the Riemann Hypothesis true or not?" would allow you to survey the heuristic arguments that various mathematicians have advanced in support of each side.
I was contemplating such a question myself; I will inform my supervisor of it and see what the reception is, and, depending on the outcome, this thread will either be laid to rest or will be further fueled.
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Andy Lau
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Interesting enough, I've done my EPQ on the Riemann Hypothesis too !!!! Did you finish it and how did it go?
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Redcoats
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(Original post by Andy Lau)
Interesting enough, I've done my EPQ on the Riemann Hypothesis too !!!! Did you finish it and how did it go?
I'm doing it this year. What was your question?
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Andy Lau
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(Original post by Redcoats)
I'm doing it this year. What was your question?
Me too i finished it just before half term! My topic is What is the relationship between the Riemann zeta function adn the distribution of prime numbers? What about you?
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Redcoats
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(Original post by Andy Lau)
Me too i finished it just before half term! My topic is What is the relationship between the Riemann zeta function adn the distribution of prime numbers? What about you?
Mine is to do with whether the Hypothesis is likely to be true or not and what the best methods for proving (or disproving) it are.

I didn't know they did EPQ in China?
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Andy Lau
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(Original post by Redcoats)
Mine is to do with whether the Hypothesis is likely to be true or not and what the best methods for proving (or disproving) it are.

I didn't know they did EPQ in China?
Studying in a UK private school. Came here in fifth form lol....Is yours very mathematical and what additional knowledge did you learn?
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Redcoats
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(Original post by Andy Lau)
Studying in a UK private school. Came here in fifth form lol....Is yours very mathematical and what additional knowledge did you learn?
Pretty mathematical. I've learnt quite a bit (Riemann Spectrum, Mill's formula etc.). Yourself?
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Andy Lau
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(Original post by Redcoats)
Pretty mathematical. I've learnt quite a bit (Riemann Spectrum, Mill's formula etc.). Yourself?
I don't think I heard of these two, but I started off by doing multivariable calculus and worked through complex analysis briefly (now revising it just in case get asked during interviews). I included things like the functional equation of the Riemann zeta function and Prime number theorem(with a proof) etc.
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Redcoats
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(Original post by Andy Lau)
I don't think I heard of these two, but I started off by doing multivariable calculus and worked through complex analysis briefly (now revising it just in case get asked during interviews). I included things like the functional equation of the Riemann zeta function and Prime number theorem(with a proof) etc.
I would really like to know about the PNT proof. Could you send me a link to the one you studied?
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yudothis
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Are you doing a maths EPQ or a history EPQ? Granted I don't know about EPQs but it seems silly that you can do it in maths and yet write a history.
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_gcx
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(Original post by yudothis)
Are you doing a maths EPQ or a history EPQ? Granted I don't know about EPQs but it seems silly that you can do it in maths and yet write a history.
history of maths is silly? :P
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(Original post by _gcx)
history of maths is silly? :P
Not at all, I love me the music of the primes amongst other books.

The point was that fits under history as a subject rather than maths, no? Just summarizing and evaluating this topic without doing any sort of actual mathematics (apart from potentially copying formulae/proofs) doesn't seem like maths.
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