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Everything posted by DJBruce

  1. Proving the generalization to any numbers might be more difficult, but actually doing the problem or generalizing without proof shouldn't be horrible. The question asks for numbers of the form: [math]x \equiv 6mod(9)[/math] [math]x \equiv 12mod(21)[/math] So this is similar to the Chinese Remainder Theorem, but since [math]gcd(9,21)=3\neq1[/math] we cannot you the apply the regular chinese remainder theorem, but [math]6 \equiv 12mod(gcd(21,9))[/math] So we can apply the special case where we know that we want to look at numbers congruent to the lcd(21,9)=63. So this tells us that our ring has 63 equivalence classes, and so every 63 number must meet the desired conditions of the problem. You can fairly easily find that 33 is the smallest number that meets the desired criteria, and so then we see that between 33 and 1111 we have 17 multiples of 63, and so you now that you have a total of 18 between 11 and 1111. This process should generalize to certain other situations fairly easily, but I'll let you work that out if you want.
  2. Pretty much just an application of a modified version of the Chinese Remainder Theorem, where your moduli are not pairwise coprime, which I guess is pretty cool in a way. See about 1/3 from the bottom of the "Theorem Statement" section. http://en.wikipedia....mainder_theorem
  3. Correct. Mathematics has developed a language all of its own that includes words, which have very precise and technical mathematical definitions. "And" and "Or" are two of these words, which when read by a mathematician in a post relating to mathematics would instantly mean something very precise to the reader. I believe this is what DrRocket said, '"and" is well-understood in mathematics.' This technical language is nothing special to mathematics, as almost all sciences have a very well developed and precise "language". For example, the word force has an everyday definition, but if one were to read "force" in a physics article one would instantly know that they are more than likely referring to the technical definition. Also the technical definitions of "and" and "or" is definitely used in computer science and physics.
  4. No, the word and in the technical sense of mathematics means the intersection of two events or sets. So in your example you would have: [math]\{x<3 | x \in R\}[/math] and [math]\{x>8 | x \in R\}[/math] [math]\{x<3 | x \in R\} \cap \{x>8 | x \in R\}=\{\}[/math] The second interpretation you gave is actually the interpretation of "or" ie: the union of two sets.
  5. No, what you have are two different expressions. Since [math]2=(1*2)[/math] you could write 48/(1*2), which would be 24. Ahh, not it cannot. No it could not unless you completely change the standard convention of what the notation of [math]/frac{a}{b}[\math] means.
  6. Yes, you can do the rearranging part since [math]log(a)[\math] just represents a real number you still have the commutativity of multiplication.
  7. Yeah conjectures that turn out to be false. :/

    1. lucykk


      this look cool

  8. So many cool facts about the US Electorate in such pretty pictures: http://www-personal.umich.edu/~mejn/election/2008/
  9. My bad, wasn't quite thinking there.
  10. I am not really sure what you were trying to do, because your work is not correct the second line is not really needed to solve this equation. As for solving this why not try so of the properties of logs. For example, [math]log(a)-log(b)=log(\frac{a}{b})[/math] might be useful since you could then combine the entire left side of the equation into one log meaning you could "delogify" ie: take the inverse of both sides to end up with a fairly easy equation to solve. This is to much like homework for me to do any more, but if you post you work, or have any question feel free to ask. Yep, thats right, but your second step is really not needed.
  11. So I have an SFN blog, and when I go through SFN it shows that I have a certain username attached to a certain email address, but when I go to login at Wordpress directly it does not think that this email address is registered. Are the SFN blogs separate from Wordpress and if so is it possible to combine them so that you can access them from Wordpress?
  12. In my experience most professors I have encountered are more than willing to not only help students who ask for help, but are also willing to go above and beyond for their students. So to paint the image that all professors don't care about their students is in my opinion a little hasty generalization. From what I have seen often those who have problems with professors do so not because of the professor, but often because of their own actions. Students often do not seek help until it is to late -ie: the day before or day of an exam-, expect professors to spoon feed them material, want professors to go over the lectures because they are continually absent, or expect professors to magically fix their grade at the end of the semester. In any of these situations I do not blame professors for being less than helpful, and these are the things that often get professors the rap of being "bad". On the not of professors making the exams hard and curving it is necessary because if the purpose of the purpose of an exam is to delineate between those who have mastered the material, and those who haven't then an incredibly easy exam where everyone does well does not actually fulfill its purpose. I know at least in mathematics department at my university upper level undergraduates are hired to be course assistants. These course assistants are required to hold office hours and give a out of class lecture on something related to the class. They also grade some of the homework, occasionally fill in for the professor, and serve as a general mentor to all of the kids in the class. I found them really helpful because they are great resource to go to about general questions that you might not want to ask a professor.
  13. is studying some convex geometry.

  14. I am not an expert on monetary policy, however, I feel that the USD will rise out of the current trouble it is in. If we look at the USD Index we see that over the last half a month the dollar has made a slight comeback hitting right above 75. Granted that this is by no means a huge rally, nor is 75 great, however, we have not dropped bellow our lowest index point, and I would like to give it a little time to see if this rally continues. I doubt that we will rebound to a great level, but I would bet that the dollar will increase and stabilize in the near future. Also some experts are believe that the USD will increase on the EUR in the next year, which will definitely help our currency. As for the dollars relation to oil I do think there is some relation between the two, but I am not sure how strong this is. Also I feel that oil prices will also drop once the Middle East calms down. Who knows when this will be, but when it does I expect oil prices to fall just as they did earlier in the decade, and I would expect that you help the dollar as well. To some extent our economy is built upon future and/or "imaginary" funds, but then the entire idea of money and an economy is built upon peoples belief in it. In my opinion some level of imagery funds is healthy, and important for our economy the problems occur when people purposely use creative/fraudulent accounting to hide losses, and people then lose their confidence in the market. http://www.bloomberg.com/apps/quote?ticker=DXY:IND http://video.cnbc.com/gallery/?video=3000021724
  15. So I am trying to create a Mathematica program where I will give it a set of data, and a desired radius. The program will then create a new data point at each a position on a circle with desired radius, and calculate the spatial median median for the original data set, and the that new point. It will then create a new point on the circle, and calculate the spatial median for the the original data set and this second point. It will continue to do this going all around the circle, and then when it is done it will graph the original data set, along with all of the spatial medians it calculated. My code is: << MultivariateStatistics` f[r_, Data_] := (temp = 0, x = 0, y = 0; While[temp > 360, {x = r*cos (temp Degree), y = r*sin (temp Degree), Med = {SpatialMedian[Data, {x, y}]}} temp++]; Med) Can anyone help, or provide some good resources for programing in Mathematica?
  16. Well yes if a lot of people spoke Cherokee then it would be useful, but currently there are not many Cherokee people around -yet alone people who fluently speak Cherokee. The Cherokee Nation has roughly 300,000 members, which means that they make of roughly .09% of the US population, and they are generally located in Oklahoma so the usefulness of the language, and the chance of meeting someone in the bar who speeks Cherokee is incredibly slim for most people. Everything does not have to be about personal gain, but teaching someone Cherokee really has no overall gain in my opinion.
  17. Yep, thats how you would do it! Since if do that you would have: [math]\frac{Charge}{\frac{Charge}{Electron}}=Electrons[/math]
  18. Look at the units. You have a charge in C, and you know the charge per electron so what would you do to have your answer come out in electrons?
  19. India in the modern sense of the country did not exist, but the region referred to as the Indies certainly did. As for the origin of the word Indian I am not sure how it was derived, but Christopher Columbus did write in his log, "En 33 días pasé de las islas de Canaria a las Indias" and "A la primera que yo hallé puse nombre San Salvador [isla Watling] a comemoración de Su Alta Majestad, el cual maravillosamente todo esto ha dado; los Indios la llaman Guanahaní." So we see that it does appear he used the what we would translate as Indian to describe the inhabitants of the New World. http://abc.gov.ar/docentes/efemerides/12deoctubre2009/descargas/europa/carta_colon.pdf http://es.wikisource.org/wiki/Carta_de_Cristobal_Col%C3%B3n_a_los_Reyes_Cat%C3%B3licos_anunciando_el_descubrimiento_de_Am%C3%A9rica North America has significant portions of its history where Spanish, English, French, and numerous Native American dialects have been spoken should we not respect the people who were here before us by learning all of those languages? Also if you are going to learn a Native American dialect, which one would you learn? Surely, you could not expect everyone to learn them all, and this means that numerous different distinct cultures would not receive the respect you think studying these languages would give them. Finally, I believe you can show respect for other cultures without mandating that people learn their language. For example, studying their history and culture -which most schools already do- would in my opinion show respect to those that came before us.
  20. Why mandate those languages? What makes those more important/useful than Spanish, Chinese, German?
  21. Look at your third line of equations; you simplified your factorials incorrectly. [math]\frac{(2n+1)!}{(2n+3)!}= \frac{(2n+1)(2n)...}{(2n+3)(2n+2)(2n+1)...1}[/math] If you correct this you should notice that it works out correctly. However, don't forget to check your endpoints.
  22. Personally I feel that for the most part our schools, America, have a fairly good balance between the various subjects. At least in my area the basic high school ciriclulum requires: -2 Years of Foreign Language -4 Years of English Literature, Language, and Composition -3 Years of Science and Math -2 Years of History/Civics I believe that there is a lot to be gained in a well rounded liberal arts education because through exploring various different subjects we allow students to practice various patterns of thinking and argumentation. To be fair I admit that not all of this has a practical application. For example, literary analysis does not have a practical purpose in most peoples lives, but then again neither does calculus, however, both of these subjects help teach students how important ways to think and analysis things that are invaluable in the real world. That being said the thing I would do to the curriculum is to first shift everything forward about 2 years meaning that by time students graduate high school the average student should have complete calculus, and a fairly rigorous science and language requirement. While the advanced students -currently those who take AP's- graduate having finished multivariable, linear algebra, and what is currently college level sciences. While doing this I would also want to raise standards in two ways. First I would actually like to have a good process of holding those kids back who do poorly, without having them drop out. Secondly, I would want to separate students based on ability since this would then force the best students to actually have to work since they can no longer count on the fact that the worse students will just make them look good. A final thing I would like to do is make it so to fulfill graduation requirements students must actually take a rigorous course in that area. For example, currently at my University every student is required to take 10 credits of humanities, social sciences, and natural sciences, however, for some reason it is possible to fulfill your natural science requirement with mini-courses like "Dinosaurs and Other Failures" and "Aliens". If I had my way students would actually have to take things like physics, chemistry, or biology instead of simply taking blow off classes since science might be hard for some.
  23. So what areas, and/or topics in mathematics are you all interested? Analysis, Algebra, Algebraic Geometry, Number Theory, Applied Maths, etc.. Personally I am not at a point where I am absolutely sure what I am interested in, but from my limited experience analysis, algebraic geometry, and number theory all seem to be towards the top of my interest list.
  24. In this instance there is really only one distributive property, and that is the distribution of multiplication over addition ie: a(b+c)=ab+ac.
  25. Personally, I find that often knowing who I am talking to is very useful and important. Knowing who I am talking to allows me to some extent judge the reliability of the information they are posting and to better understand their tone and where they are coming from. For example, if Swans where to respond to a physics question I would consider his response to be fairly reliables, since he has though his other posts shown to be an expert in the area. I feel that similar information can know about most who post here regularly, which makes debates in my opinion better. As for the overall tone of this forum I find that SFN strikes the right balance of keeping things civilized and on topic without ruling with an iron fist. The negative reputation seems to be used for the most part fairly, and when not there are often members who will correct this by giving positive reputation. Overall, SFN has a much better atmosphere than most forums I frequent thanks to the quality of members we have, the hard and tireless work of the mods, and the design and forethought of the admins. However, if I could suggest one change I did enjoy how back with the vB forum you could leave a comment with your rep point. I felt that this A) Inspired people to give positive rep since they are reminded of it when they receive it, and B) Allows people to give constructive criticism or explain their praise so that people can continue to improve the quality of their posts.
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