Dapthar

What kind of engineering reference are you looking for? Chemical, Electrical, Mechanical, Nuclear, or something else? If you could be a tad bit more specific, it would help.

I've been wondering about the benefits of noise cancelling headphones. For those who aren't familiar with these devices, they essentially generate a sound wave that is [math]180^o[/math] out of phase with the low-frequency noise that is picked up by the microphones that are present in the headset. For example, see the attached picture. If the noise waveform was the red sine wave, the waveform generated by the headphones would be the blue sine wave, and when added together, these waveforms cancel out, resulting in no sound. (Note this is an idealized view, in reality the headphones can't generate the "anti-noise" waveform immediately, resulting in an incomplete cancellation, which is perceived as a quiet hissing sound.) However, my question is, is this addition of waveforms done in the air, or by one's ear? The reason I ask is if the cancellation is done in the air, then no sound actually reaches one's ear, and thus the ear does no work. But, if and the summation is done inside one's ear, i.e. biologically, then the ear is working twice as hard as it has to, leading to the twice the damage that constant exposure to the noise would inflict.

The number of Calculus classes usually varies by institution. A typical division is: Calculus I: Covers limits, continuity, symbolic and numerical derivatives, and applications of these topics. (Restricted to one dimension) Calculus II: Covers symbolic and numerical integration, advanced integration techniques, Taylor series, and applications of these topics. (Again, restricted to one dimension) Calculus III: Extension of differentiation and integration to n dimensions (with most of the time being spent on functions of two independent variables), vector calculus, and applications of these topics. The above topics are sometimes shifted between classes, but usually maintain the same relative order, e.g., basic symbolic and numerical integration may be shifted to Calculus I, but differentiation is in all but the rarest cases, taught before integration. Also note that the above structure is closely follows that of the text I learned Calculus from, authored by Edwards and Penney.

It depends on what you mean by "best". If you want a simple' date=' and quick way to get a reasonably accurate estimate of a square root, try the first method on this page: http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html If you want a more accurate approach, you could use the Binomial Theorem, and the details of how to use such a method are also on the aforementioned page, under the heading [b']Square Roots Using Infinite Series[/b].

I suggest reading the "2001" series by Arthur C. Clarke. Namely: 2001: A Space Odyssey 2010: Odyssey Two 2061: Odyssey Three 3001: The Final Odyssey In general, anything Clarke has written by himself is worth reading, while books he co-authors tend to be lackluster.

I wonder how this will play with Intel's decision to begin embedding Digital Rights Management hardware into their dual core processors. But then again, Apple seems to have dealt with the DRM/iPod issue in a manner that hasn't alienated their user base.

Could you please make the SFN logo at the top left of the page link to the SFN homepage once again? Apparently the link was broken/forgotten when the style was updated. Thanks.

There's Java. Not much else immediately springs to my mind besides C#, but that's a variant of C++.

I'm not Swansont, but I hope you don't mind my input. Also, all of my suggestions are based on my experience from universities in the US. From my consultations with professors before entering graduate school, I found out that Masters programs generally have much looser entry requirements than Ph.D. programs (In the sciences, at least. I've not researched graduate programs in the Arts). For the most part, you can enter a Master's program, and go to a Ph.D. after you finish, but it's not advisable to do so unless you are not able to be admitted to the Ph.D. program. The primary reason for this is because the classroom portion of the Ph.D. (as opposed to the thesis portion) usually satisfies almost all of the coursework one would have completed for a Master's degree. However, the same stringent admission requirements for a Ph.D. will be applied to your Master's coursework, so if you need to pick up your grades, doing a Master's first will give you an opportunity to shine, so long as you can get admitted to the program. It depends. If your GPA for classes in your major is above 3.0, but your overall (i.e. including liberal education electives) GPA is lower, then you don't have much to worry about. Otherwise, you're going to have a hard time getting admitted unless your recommendations are very good. Remember, the best recommendations you can get are from professors in the department you wish to study, e.g., if you're going for Math, only get recommendations from Math professors. Also, an important note on recommendations. I suggest you waive your right to see them, since the reviewers of your application tend to lend more credence to these recommendations. Why? If you can see them, the professors 'have to write something nice'. Professors tend to take on multiple students' date=' so there really isn't a 'first dibs' process as it were. You tend to talk to your intended advisor directly and make your case, as opposed to having it dictated via some committee. Also, the advisor really doesn't do much until you've finished the classsroom portion of a Ph.D., aside from possibly advising you on what classes to take. Thus, if you [i']really[/i] need to, you can delay choosing an advisor until you've nearly finished your coursework, but I don't suggest that you follow such a course of action. If the professor you wish to study under wants you to attend, and you have a decent application, (i.e. you show some promise, perhaps your freshman and sophomore grades were poor, but your subsequent grades were stellar) then you won't have much trouble getting in, unless the professor doesn't have tenure, or something in that vein. Regarding funding, I'm sorry to say this, but if you don't have at least a 3.0 GPA in the classes in your major, your chances of being funded via a fellowship, Teaching Assistantship, or Research Assistantship, are slim to none.

It looks right to me. I would have worked out this problem in the same manner, since it seems to call for an algebraic approach.

I don't really have a personal version per say, I'm just quoting from memory. If you'd like, I can dig up my old Abstract Algebra book and post those field axioms here. Alternatively, I can just tell you the page number if you already have access to his book; Algebra by Michael Artin.

I believe associativity and commutativity are all that's left.

Yup. My mistake. I've fixed the original post.

A set that is closed under addition and multiplication (both operations are commutative and associative), where multiplication distributes over addition, has multiplicative and additive inverses, and multiplicative and additive identity elements. The axioms are not 'absolute truths' as it were, for they cannot be proven to be true, you just have to 'believe' that they are. I suppose it injects a bit of faith into Mathematics. You know that the '0' and '1' I referred to are not integers, or reals, correct? They're just names given to members of the field. If you like, you can call them 'x' and 'y', or whatever you want. It doesn't, because I'm only saying that this is true for elements of the field with one element. As what I've said earlier indicates, I'm doing no such thing. What I mentioned does not apply to the real numbers, since the reals are not a field with one element.

Because it doesn't have to hold in a field. In a field with one element, the additive identity equals the multiplicative identity.

I think that's there just to make people feel better about taking a while. RedAlert: Consider the following questions: What is the rose? What are the petals? Also, examine the situation where there are 0 petals around the rose very carefully. Finally, the pattern is not very complicated, so don't overthink it. If a mod thinks this post gives too much away, feel free to edit it.

A small note, the New Scientist link that you reference is dead. You might want to replace it with Google's cached page. Link: http://64.233.161.104/search?q=cache:YxzXUxtnee8J:www.newscientist.com/article.ns%3Fid%3Ddn3488+&hl=en

I'm sorry if this sounds a bit pro-establishment, but I think the guy is a little shady. First, note Wiles's reply: Sounds a bit sarcastic, don't you think? (Italics and bold are my own.) Also, what tipped me off is that the man found fault with the trichotomy axiom of the real numbers. For those who are a bit rusty, the trichotomy axiom of the real numbers states that all real numbers are either negative, positive, or zero. It's a bit difficult to fault with that. Finally, the whole "The result is a new real number system that is free from defects and contradictions," reeks of pseudoscience, since as Godel proved: Thus, you can't make the real numbers, "free of defects", as it were. Source: http://www.math.hawaii.edu/~dale/godel/godel.html#FirstIncompleteness According to the Mathematics Geneology Project, the Mr. Escultura does have a legit Ph.D., but apparently, something went horribly wrong between 1970 and the present day. I'll reevaluate when some other news sources collaborate the story, but for now, I'm betting on a hoax.

That my friend, is 7 shades of messed up. It's a shame that people can just fall through the cracks just like that. On a lighter note, regarding the first article: Doesn't this seem like a bit of an odd thing to report in an article? One can almost hear the voices now... Austrailian Govt. Official: "Now we can abide people smoking marijuana, but doing so while sewing?! This kind of reckless behavior can not be tolerated in civilized society!" At least, that's the mental image I got when I read that passage.

I used the same alias at Sciforums as I do here. Yup.

[Tootsie pop narrator voice] The world may never know. [/Tootsie pop narrator voice]

[geek] Count Dooku hovers in one of the Clone Wars animated shorts. [/geek]

You have to be able to create a non-Lebesgue measurable subset of the object of interest, and for physical objects, this is not possible, since they are composed of atoms. From a Banach-Tarski perspective, it doesn't matter if the space shares all the properties of Euclidean space, if the objects that inhabit that space cannot be divided into non-Lebsegue measurable subsets.