Enhance Your Calculus Skills with Recommended Books for Riemann Zeta Function

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Discussion Overview

The discussion centers around the Riemann zeta function, with participants sharing their experiences and seeking recommendations for books to enhance their calculus and mathematical skills. The scope includes topics related to calculus, real analysis, complex analysis, and analytic number theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses interest in the Riemann zeta function and inquires whether Tom Apostle's Calculus I would be beneficial for improving their skills.
  • Another participant suggests a progression of study: starting with real analysis, then moving to complex analysis, followed by basic number theory, and finally analytic number theory, emphasizing the importance of multivariable calculus for understanding complex variables.
  • A recommendation is made for the book "Hardy and Wright" as a suitable starting point for those interested in analytic number theory.
  • A participant warns that the links provided by the original poster lead to content from a mathematical crank, suggesting that the conclusions drawn by such individuals are often incorrect and not to be trusted.
  • Another participant notes that, as of now, no proof of the Riemann Hypothesis exists.

Areas of Agreement / Disagreement

Participants express differing views on the validity of certain online resources, with some cautioning against cranks in mathematics. There is no consensus on the best path forward for study, as different participants suggest varying sequences of topics and resources.

Contextual Notes

There are unresolved assumptions regarding the prerequisites for complex analysis and analytic number theory, as well as the credibility of online mathematical resources. The discussion does not resolve the status of the Riemann Hypothesis.

sparsh12
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i am interested in Riemann zeta function. i am in a high school.
i have good hold over calculus(at least what's required for physics).
Would Tom Apostle's Calculus I be good to further improve my skills.

What should i do next?
Real Analysis or Complex Analysis or directly analytic number theory?

Are L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle good at my level?

By the way, has Riemann hypothesis been proved?
have a look at http://www.coolissues.com/mathematics/Zeta/zeta.htm.

There are several pages by same author, on several unsolved problems,here:
http://www.coolissues.com/mathematics/Zeta/zeta.htm
 
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sparsh12 said:
i am interested in Riemann zeta function. i am in a high school.
i have good hold over calculus(at least what's required for physics).
Would Tom Apostle's Calculus I be good to further improve my skills.

What should i do next?
Real Analysis or Complex Analysis or directly analytic number theory?

Are L Ahlfors' complex analysis and Analytic Number Theory by Tom Apostle good at my level?

Real analysis first, then complex analysis, then basic number theory, then analytic number theory. And a strong grounding in multivariable calculus will help a lot with complex variables, so don't skip that.

If you're interested in analytic number theory, there's a book you can start reading right now and grow into as you learn more. Hardy and Wright. It's a classic.

https://www.amazon.com/dp/0199219869/?tag=pfamazon01-20
 
Hi sparsh12, I wish you all the best in your mathematical endeavors.

Just want to mention that the links you included are by a mathematical crank. There are lots of them out there, doing their own "research", and producing results, that if true, would cause well establish facts to be wrong. James Constant is a quite sophisticated crank, he knows a fair amount of math, he can write coherently, but his conclusions are just wrong. When a crank gets a result that contradicts hundreds of years of work by the best minds on the planet, they do not pause and ponder "where did I go wrong?", instead they have an urge to inform us all about their discoveries. I Just remembered that cranky stuff isn't allowed here in the forum, so I should stop.
 
There is a lot of valid info on the net as well as invalid info.

Keep learning and reading. So far no proof of RH that I know of exists.
 

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