What is the best way to write math equations on the internet?
There are three ways which work well in practice and emit very well set mathematics. The first is to generate static s (great contrast). The second is to dynamically generate s in the browser. The software is called MathJax () which produces the highest quality output (vector fonts when possible --- it uses webfonts if it can or the user's fonts of they exist and even support the STIX fonts). It is also verypatible with browsers and dynamic. The trade-off is that it will need to do all the layoutputations client-side which often causes the browser to seizure as some people have said (in response to my website in particular). You can see a sample of set math at this post on my blog (observe the loading it needs to do) I do NOT rmend MathML. While it is a standard it is clumsy (e.g. requiring one to use
How can I convert LaTex (.tex) files to images (.png, .jpg)?
You can convert tex to pdf easily then convert that pdf file to other format. There lots of software like image magic inkscape etc or online services which will convert pdf to jpg or png file.
How can I write math formulas in a PDF document? I want to add some math formulas into my notes in PDF.
If you want to know how to write math formulas then you can use MathType or ms word equation tool (alt+enter). To convert this word into pdf you can use any online converter or download Total doc converter Some pdf manager like foxit or adobe Pdf managers like foxit can also allow you to add image equations s and shapes into direct pdf without any aid of conversion.
As a mathematician, do you feel comfortable using computers instead of papers and pens?
In my math programme programming has been a majorponent from the beginning. As skeptical as I was and as much as I worried about not doing Real Math I have to admit that this programme has the right idea. And while I can never see myself being a programmer full time I'm really glad to have that skill and I enjoy using it in math. Because you often are designing your own programmes you are being creative. You need to make something that will suit you and there's often many ways to go about it and you have to be precise. You still have to understand what it is your doing (otherwise how can you write instructions for aputer to follow) and it often points out flaws in your own thought process. It also changes the way math is taught at my university. There's much more concern that we really understand the inner workings than just understand how to calculate the problems. And of course everything we learn to do byputer we can also do by hand. ETA After reading the other answers yeah if you're talking about LaTeX that's pretty worthless. Sorry there's the ever present should programming be part of a math degree debate always going on here.
What are gravitational waves?
Let me begin my answer with a question What are electromagnetic waves? Before Maxwell in the 186s people knew about electricity; they knew about magnetism; and they knew that the two were connected. However they did not know exactly how the two are connected. In came James Clerk Maxwell who wrote down a set of equations that contained within themselves everything people knew about electricity and magnetism. But the equations also contained something else. They had non-trivial vacuum solutions electrical and magnetic fields present even when there were no charges no currents no magnets around. These vacuum solutions were wave-like solutions that had a specific propagation velocity. Maxwell recognized this velocity as the known speed of light and proposed that the wavelike solutions in fact describe light. But the equations also predicted that such waves at wavelengths very different from that of visible light can be produced by wiggling around magnets or electrical charges. This prediction was spectacularly confirmed by Hertz not too many years later. (Imagine this was not humans mimicking nature. Nobody saw a radio in nature and the idea ofmunicating over a distance using invisible waves was akin to magic to any mid-19th century scientist. Yet this was a prediction of a beautiful theory that came in the laboratory.) Just as Maxwell developed a set of field equations for electric and magnetic fields Einstein developed a set of field equations for gravitational fields. And just as Maxwell's equations had vacuum solutions so did Einstein's field equations. And like Maxwell's Einstein's vacuum solutions also propagate as waves at the speed of light. These would be gravitational waves the gravitational equivalent of electromagnetic waves a prediction of our field theory of gravity. Electromagnetic waves are generated by wiggling around (accelerating) electric charges. Gravitational waves would be generated by wiggling around masses. Every mass that accelerates loses some energy and momentum by creating waves in the geometry of spacetime which travel at the speed of light. There is a crucial difference though. Because of the nature of Einstein's field equations and the smallness of the gravitational constant generating gravitational waves is exceptionally inefficient. It takes extremely large masses undergoing extreme accelerations to produce gravitational waves that carry meaningful amounts of energy. So whereas it is possible to generate a lot of light say by heating (and thus wiggling around) electrically charged atoms and electrons in the filament of a light bulb you'd need something the size of a planet wiggled about at relativistic speeds before meaningful quantities of gravitational waves are produced. This is one reason why we have been unable to detect them directly to date. But indirectly they have been detected by observing so-called binary pulsars. As two stars in a binary pulsar system orbit each other very rapidly they lose some energy due to gravitational waves and as a result their orbital period (which in the case of a binary pulsar can be measured very accurately) changes. This has been detected in several pulsars and the rate of change is consistent with predictions derived from Einstein's field equations.
What are some pseudo-scientific myths floating around in India?
You can find legions online. A good place to start will be places like What are some Indian traditions that have scientific reasons behind them and are valid and useful today? question qid 17544 nI will exhume a particular answer there (with a considerable number of upvotes- that should illustrate the extent to which such hogwash has penetrated the Indian internetmunity). Edit Looks like that answer has been edited a bit which I view as a very positive event. Logs keep the record as always. I was entertained at first and then nearly wanted to cry 1. Exhibit A n ' cowdung has been successfully tested for absorbing alpha beta and even gamma rays italic ' n I call Bullshit (literally). Sure cowdung can stop alpha rays--and so can 5cm of air italic . Such an extraordinary property! As for beta a few mm of any any metal is adequate to stop it and so it would not be too extraordinary if a few cm thick layer of cow-dung blocked them off. The claim about gamma rays however is almost certainly -Gamma rays need high density material to block them off and preferably high atomic mass as well. Lead is ideal for such purposes but not a loose packing material (made out of mostly carbon and hydrogen). There has been no study cited in that statement (and I can bet that nothing like this came out in a reputed peer-reviewed journal) and I call the last claim . I also fail to understand why would this even matter as life had 4.8 billion years to adjust to background radiation before the nuclear age came and screwed up the equations. Of course there is some BS about Pre-Iron age nukes as well-which is ridiculous on far too many levels to list. 2. Exhibit B n ' Cowdung is a great source of methane (CH4). Microbes found in this cowdung are mostly anaerobic and release methane as a byproduct of their oxidation activities. When this methane in the cowdung spreades in contact with air and sun's heat it is converted to Formaldehyde. Formaldehyde is antimicrobial and germicidal. It even kills spores of bacteria. Thus providing as a pretty good nature friendly disinfectant. italic ' nThe Equation CH_4+O_2=H_2CO+H_2O math as given in that answer is thermodynamically feasible I grant that. However it is a kinetic absurdity at room temperature as the C-H bond in methane is far too strong to undergo aerial oxidation. Hydrocarbons are actually fairly resilient to aerial oxidation else life itself would burn to ashes within nanoseconds. Heat can do nothing. Light Not going to happen either. The methyl radical is too unstable to allow this reaction and no such analogous ones occur for any higher hydrocarbon homologue. If this occured Industry would be using this to make tons of formaldehyde and not be using expensive transition metal catalysts ( Formaldehyde #Synthesis_and_industrial_production ). The last line in that article in fact clearly makes the point- conditions that oxidize methane to formaldehyde will also oxidize formaldehyde to carbon dioxide. BS again. Also methane happens to be a fairly potent Greenhouse gas. We would not be worrying too much about methane if the cited reaction was -instead we would be concerned about the high conc of carcinogenic formaldehyde in the atmosphere. You didnt think that a small molecule germicide will be benign as water did you? Check MSDS of a dilute solution if you want Page on EditnIn case anyone is interested to learn more about partial oxidation of methane-n Direct methane-to-formaldehyde route found article on C&EN (the ACS magazine) Catalytic Methane Oxidation at Low Temperatures Using Ozone (Look at abstract-low temp is under 675 degrees C) Partial oxidation of methane to formaldehyde by means of molecular oxygen (Another one in case you have access past the pay wall-I do not rmend paying money for these things) . Exhibit C n ' Here is one such s.' italic nI don't know what to say except to cry about the state of chemistry education in India. Silver and gold are near oxidatively inert-and so any antimicrobial property of thier ions cannot be in any form be connected to their use. Gold does not undergo aerial oxidation at all (which is why it is shiny and we waste ton of forex trying to import the most useless metal ever)-although Gold (I) and (III) are useful (if expensive) reagents. Silver does tarnish to the sulphide-but the problem is that too few Ag(I) salts are soluble. Flouridepercholrate sulphate (slightly) but not sulphide oxide etc-which is what we get from the atmosphere. There is no source of free Ag(I) thates from jewellery. Will add more as I find them. Few Edits Deleted direct to the answer on the request of the author. However the question is still ed. Also I found the Ken Ham-Bill Nye debate to be pointless and in case any of my 'avid followers' are avid enough to read the bottom footnote-I would request you to stop posting s to this answer on that answer for I think it is a fairly pointless exercise. The author has also asked me to stop my follower army. I am not sure that I have such an army-but if such exists same goes for you.