DJBruce

I ask because if you have prove the Riemann Hypothesis as you claim I would be very interested in at least hearing the details of your methods you use in the proof yourself. Also although I am not sure if there are any members on this forum who are researching analytic number theory there are quite a few members who are quite good mathematicians, and could more than likely work through your argument. I am sure there are individual mathematicians working towards proving the Riemann Hypothesis, however, I doubt there are many actively working directly on the problem, and I would be very surprised if there was a research group focused solely on the problem. The Riemann Hypothesis is a problem, which has been worked on for over 150 years now, and like many longstanding open problems many mathematicians avoid directly trying to tackle such problems -- especially before a well path to a solution is formed. Consider that Wiles only began working on Fermat's Last Theorem after not only had Frey laid a clear plan to prove it, but after epsilon conjecture was proven -- also after having secured tenure at a top research university. See my previous post on how to increase your chances of getting your work read by professors. As a final note, and please do not take this the wrong way, but the Riemann Hypothesis is a problem, which has vexed some of the greatest mathematicians of the last 150 years. Not only has it done this, but little as far as I know no one has even been able create a reasonable program for approaching a proof to the problem. With this in mind I find it somewhat hard to believe that the proof of the Riemann Hypothesis is as easy as you suggest; especially because you have done little to support your claim other than say you used a "natural physical process".

Yes, but what "natural physical process" does it describe? Is it something along the lines of this?

From my talks with various math professors it seems that many of them -- if not most of them -- ignore most work sent to them on major open problems unless it is immediately clear that the author is aware of current work on this problem, and the work being presented clear states its methodology. So with that I would not expect to hear back from a professor soon, however, to improve your chances of a researcher actually taking the time to read your paper make sure you have a strong title, abstract, and introduction. What are you suggesting is the physical nature of the Riemann zeta function?

When using the standard formula for covariance with a sample the statistic is in fact biased due intuitively to the fact that the covariance depends upon the mean, which in turn depends on the sample. To correct this, and form an unbiased statistic we must multiple the standard formula for covariance by [latex]\frac{N}{N-1}[/latex]. This is called Bessel's Correction.

I understand the idea that the opening ceremony, and in fact the Olympics as a whole are meant to transcend conflict, politics, and violence and unify the world through sport. As such I agree with the sentiment that normally the opening ceremony should not be used to commemorate tragic events, and if for nothing else because there are so many that could be rememberer. However, that being said I completely disagree with the IOC's decision not to commemorate those who died in Munich. That is because this tragic massacre occurred at the Olympics, and so is part of the history of games. Those who perpetrated the act of terrorism were trying to shock the world by destroying the unifying vision of the olympics. So at very least the IOC should take a moment to remember that those who died in '72 in part did so for this vision. That being said IOC President Jaques Rouge did hold a moment of silence in an impromptu ceremony earlier this week, but in my mind that is to little. I find it somewhat disgusting that the Olympics, which preaches begin above political strife is playing politics instead of what in my mind is right. Honoring the 11 olympians who were murdered during the '72 games. Two final points: Bob Costas will hold his own moment of silence in honor of those murdered in '72 during the US broadcast of the opening ceremony. Here is a quite powerful video about the massacre.

This video is exactly what I was talking about. Rep. West says something controversial on the campaign trail, and so he then gets a ten minute interview on Fox News. This type of increased media exposure is what I believe has caused his rise to fame, and not that he's is recognizable the media becomes a self fulfilling prophecy since he now gets invites to shows since he is one of the more recognizable representatives.

Honestly, the thing I think that has led him to conservative stardom is his ability to say controversial things in ways that start media fire storms surrounding him. I am not saying that conservatives like the crazy things he says -- I would speculate that a majority of conservatives would actually disagree with some of his statements -- but rather by making a spectacle out of himself he draws a lot of media attention, and this high level of media exposure is the major cause of his popularity. I do not have any evidence to support this, but it certainly seems he comes up in a fair number of articles on Politico and ThinkProgress especially considering he's only a freshmen representative. Although I am not sure how to explain his amazing fundraising.

Had Hitler never existed I have strong feeling that there would still have been some sort of armed conflict in Europe. Germany in the late 1920's and early 1930's was quite a mess in many ways. Politically the Weimar Constitution was I believe in the long term untenable due to its inefficiencies caused by it representation system and how it delegated powers. Economically Germany was unstable, and suffered from numerous set backs and hardships. Socially the Weimar period was very tumultuous in that it was a time during which there were many competing forces trying to shape the culture of the Germany in drastically different ways. When taken in total I high doubt that Germany would have escaped the 1930's or 1940's without some sort of drastic change. I easily could invasion a revolution replacing the Weimar Republic with some other sort of government, and with how tenuous the peace was such a revolution could easily have caused an armed conflict with either Germany invading after a more conservative hardline government begin implemented, or France invading out of fear of a new government. Regardless, I doubt this would have escalated to anywhere near the level of World War II. It took Hitler roughly six years to form a strong enough national identity to rally the German people to fight. I doubt without the presence of a long term unifying force that German would have the will to engage in a long war. Obviously this prediction suggests other predictions regarding things like the state of technology and global standing, however, I doubt really feel like playing the what if game much further than my above thoughts.

Moderators are members of this forum just like you and I, and as Cap'n pointed out they are thus subject to all of the forum rules. In addition, SFN has published the moderating policy that all mods follow here. However, your question of whether or not moderators must follow the rules is only really applicable if there have been instances of moderators abusing their powers and breaking the rules. In my experience the moderators here on SFN do a great job, and work very hard to make sure all of their decisions are transparent and impartial. Are their specific instances you can cite where you believe moderators were breaking the rules because if not I am not sure I understand the point of discussing what would then be a non-issue.

I agree that the idea seems ridiculously idiotic since it is just renaming a current institution. However, if it would pacify some of those who are upset about same sex marriage, and at the same time extend equal rights to a portion of the population currently being discriminated against wouldn't it be better than our current situation? I am not sure I agree with your analogy here iNow. In the my idea no one losses and real privileges, and in fact a large portion of the people gain the ability to marry. A more apt analogy would be deciding to paint all the separate water fountains purple, call them all springs, and then let whoever wants to use them use them. Again this seems ridiculous because it is just changing the name of one thing to the other, but would't having purple springs be better than segregated water fountains? The church would not be dictating who you can marry instead the government would take the legal contract that is marriage cross out the word marriage and right partnership.

Why not do away with governments recognizing marriages, and instead simply have them recognize partnerships in whatever form they may be. While this might seem liking playing semantics it appears -- at least to me -- that many of those who oppose same sex marriage do so because to them regardless of the origin of marriage they feel marriage does carry a religious connotation. So by completely removing the government from recognizing marriages people are free to view marriage as they please, but it means that everyone is granted equal status under the law.

What are your questions?

Check your math here. [latex]x^{2}-1-3=x^{2}-2[/latex]?

If you really wanted you could read up on something like the Elo Rating System, and try and modify this for your use. Another option that is similar to how some high school sports teams are ranked would be that if [latex]x[/latex] and [latex]y[/latex] are players then the players ranking would satisfy: [latex]P_{x}-P_{y}=\frac{R_{y}}{R_{x}}S_{x}-\frac{R_{x}}{R_{y}}S_{y}[/latex] Where [latex]R_{x}, R_{y}[/latex] are the ratings of their respective teams, and [latex]S_{x}, S_{y}[/latex] are their respective scores. You want to write a program that iteratively finds the players rankings to minimize the error in the above equation for the entire league. This method can be modified to include whether a person beats a really strong player and so on, but again it might be a bit complicated for what you want. Not sure how it would work, but one simple formula that might give a rough idea of rating would be: [latex]P_{x}=W_{x}\frac{\overline{R_{op}}}{\overline{R_{x}}}[/latex] Where [latex]W_{x}[/latex] is the winning perectange of player [latex]x[/latex], [latex]\overline{R_{op}}[/latex] is the average team rating for all of [latex]x[/latex]'s opponents, and [latex]\overline{R_{x}}[/latex] is the average team rating of [latex]x[/latex]. As I said I have no idea if this will give anything resembling decent rankings, but it should be easy to implement in Excel, is normalized, and should at least in theory reward the right things i.e.: the more you win against good teams with bad teams the higher your rating should be.

Certainly there is a homomorphism from [latex]M_{n\times n}(\mathbb{C})[/latex] to [latex]M_{2n\times 2n}(\mathbb{R})[/latex], however, what I was referring to was the fact that you can think of [latex]M_{n\times n}(\mathbb{R}) [/latex] as a subset of [latex]\mathbb{R}^{2n}[/latex], and so we can consider it as a topological space. In fact many matrix groups such as [latex]GL_{n}(\mathbb{R})[/latex] have the "special" property of also having differential structures that work with the group structure aka Lie Group. However, none of this theoretical stuff is probably strictly needed for Axioms problem. All they really need to do is multiple two complex numbers, and figure out how to write a matrix such that the matrix multiplication corresponds to this complex multiplication, and from their just generalize.

So I was clicking around the Mathematics forum, and I noticed some strange thins in the tutorial on differentiation. Namely, I never knew that "the Basics of Limits" was related to "Conservatives Beating War Drums on Foreign Policy" or that the "Chain Rule" had something to do with ydoaPs pointing at photos of planets. I think the links in the table of contents do not link to the right posts for some reason, or Capn has some devilish plan to confuse Calc I students.

No idea about whether or not your calculator can handle complex matrices. However, since there is a natural homeomorphism from [latex]\mathbb{C}^{n}[/latex] to [latex]\mathbb{R}^{2n}[/latex], and so also a nice homeomorphism from [latex]M_{n\times n}\left(\mathbb{C}\right)[/latex] to [latex]M_{2n\times 2n}\left(\mathbb{R}\right)[/latex], you can just use real matrices to try and solve your system.

Dividing by zero is not defined. If you are asking the mathematical question what is zero, and looking at the rational or real numbers as fields -- i.e.: a place where you can add, multiple, have multiplicative and additive inverse, have additive and multiplicative identities, and other "natural" properties -- then 0 is simply the additive identity. If you are asking the philosophical question whether zero exists, then I don't think mathematics really has an answer for you, other than the fact that many mathematical objects have nice properties if we assume they have a "zero".

Not as exciting as some of the chemistry accidents, but the commons in the math department recently got a glass wall with fancy frosted glass intended to be used as a dry erase board. Well, one side of the glass was a dry erase board if you wrote on the frosted side it is apparently permanent. So now the commons has a fancy glass mural depicting the struggle of students working with Mayer-Vietoris and the Snake Lemma.

Sorry I was sloppy when I stated what I had done towards a solution: I did get that [math]f(0)-2f(1)+f(2)=-f'(a)+f'(b)=f''©(b-a).[/math] where c is in [0, 2]. But the there is still the (b-a) term that needs to be taken care of somehow, and that is where I was stuck. Sorry for the poor description in the OP.

So I've been trying to prep for an upcoming math competition by going through some problems. This one has me a little stuck, "Suppose [latex]f[/latex] is a differentiable function function on [0, 2] then there exists a point [latex]c\in [/latex] such that: [latex]f''©=f(0)-2f(1)+f(2).[/latex]" I am not sure this statement is true under these conditions, and think twice differentiable is probably required. Assuming that [latex]f[/latex] is twice differentiable I have tried applying the mean value theorem, and have been able to show that there exists [latex]a,b\in [0,2][/latex] and [latex]c\in [f'(a), f'(b)] [/latex] such that: [latex]f(0)-2f(1)+f(2)=f'(a)+f'(b)=f''©.[/latex] However, I am not seeing that that [latex]f'(a), f'(b)\in [0,2].[/latex] Any ideas on how to continue in this problem?

As people have previously said, it really depends on what you courses you are taking, and what area of mathematics you plan on studying, and your mathematical maturity. If you are planning on majoring in "pure" maths then at some point you will need to begin taking rigorous proof based courses. If you have little experience to proofs and theoretical mathematics you might want to consider a intro to proofs book such as "How to Prove It" by Daniel Velleman or "Mathematical Proofs" by Gary Chartrand. Although to be honest the best way to learn "how to do proofs" is by doing them yourself. As has been said if you have already taken basic calculus, i.e.: single variable, you may want to consider reading up on introductory real analysis. Personally, I really like Spivak's Calculus or little Rubin for this. However, these books are more expensive than the one Dr. Rocket recommended. If you are looking for a good complete Linear Algebra book I would recommend Hoffam and Kunze's Linear Algebra. Although be forewarned that this book is a fairly theoretical approach, and so if you are new to theoretical mathematics you might want to use a book that is a little more concrete.

Prove that .999...=1 and then generalize your argument.

Kavlas, what is the definition of convergence?

As I pointed out in a previous thread a 1999 paper by Esswaran Etc All. found that it is possible to feed 19.82 billion people. So while this doesn't mean that an increase in population won't cause other problems, but it certainly suggests one thing that many Malthusians point to, food shortages, may not be that big of an issue. http://soils.usda.gov/use/worldsoils/papers/pop-support-paper.html