darklight03/StackMIAsub huggingface dataset:
I am currently a math major in college and my main problem is that it feels directionless. My college offers little in term of variety in undergraduate math so I moved on into taking graduate courses and I am actually loving it. But at this point I am just randomly taking courses that looks interesting and was wondering if there was specific directions to take within math. And even past that where will it lead. Thanks EDIT After reading the comments I decided to add extra info. On the courses that I like, I have taken Abstract Algebra and Linear Algebra and really enjoyed them and also Number theory. I have also taken the typical three semester Calculus courses, Differential Equations, Discrete Math, Probability, Numerical Analysis and Real Analysis. On these courses I like them though I am not as enthusiastic about them as I am for the other courses I have mentioned. Though I find their applications very interesting. And more specifically on the question it is on what paths are there to take in school and also what paths are there to take after graduation.
When creating a presentation, I sometimes create extra slides that contain additional information, a more thorough explanation, or an extra plot pertaining to certain parts of my talk. These extra slides are usually in a separate PDF and the document is usually only opened if an audience member asks a question or requests information and one of my extra slides supplements my response nicely. I am wondering if it's possible to insert these slides into my presentation with the two following options: The extra slides are skipped when progressing through the presentation unless... I click on a hyperlink placed somewhere on the slide. If clicked, we traverse to the extra slide. From this slide, continuing to the 'next' slide would send us back to the slide that got us here originally. The above can be accomplished with two (or more) PDFs (one with the presentation, one -- or more -- with the supplemental slides) via hyperref but ideally I would like to only have one document. I am not familiar enough with ifthen to know if it can be done with that package. Any help would be much appreciated.
Some time ago I learned the difference between a present participle and a gerund, so today I decided to pass any online test to make sure I understand it. I passed it having made only one mistake, which asked the difference between the two in this sentence: Nobody was surprised at John being absent. One needed to choose between present participle and gerund in reference to the word being. I chose present participle because the word being here plays a role of an adjective apart from a verb. I thought that if it had read John's being, then the word would have been a participle because it would be a noun in a form of a verb. I know, this question is a duplicate and I agree that it should be closed, but I just would like to find out whether it was me who made a mistake or whether it was the website that diddo.
Background: I was cooking eggs (very difficult) with a plastic spatula which was not very good, so when I set it on the border of the pan it began melting. In order to keep cooking, I reached for a wooden spoon which can touch the pan without melting. This led me to wonder about the behaviors of the materials. For example, if I had left the plastic spatula it would have melted, but if I had turned up the temperature enough it would have actually ignited and caught a flame. If I had done the same with the wooden spoon, it wouldn't melt as I turned up the temperature but it would ignite eventually. So why is it that certain materials (plastic in this case) will go through the process of melting, then igniting, but wood just seems to skip the melting and go straight into ignition? My only guess is that somehow wood has a melting point higher than its ignition point, but I am not even sure if that makes physical sense. A Google search led me to a strange-looking forum with disappointing answers. My understanding of thermodynamics is only as far as the math goes, but I am conceptually blind in this area. Maybe someone can shed some more light.
I think everyone should have seen a bowl of hot water moving by itself on a flat surface such as glass(seems like it is moving by itself but maybe there are some external force applied to it when it moves). What is the explanation of this phenomenon? Hypotheses : Since the bowl is heavy, for it to move the friction between the bowl and the surface must be very very low. I have heard that water may form a thin layer between the bowl and the surface, but l'm not sure whether it is the case or not. I think the bowl can move by itself because heat makes the air below the bowl expand. Edit : I will re-experiment those again and update the question in few days. Maybe I will take a video clip too. and I am not talking about a magic trick whatsoever.
For the absolute life of me, I cannot seem to wrap my head around the proofs given in my number theory and cryptography class. Maybe it's the teacher, or the textbook, both or neither, but this is causing me great concern for two reasons. First is obvious, since I hate solving math without a full comprehensive understanding of the concepts. Second, I have the feeling I'll be asked to prove concepts in my exams. So how do I go about this? Does anyone have any textbooks or something (or anything) that could help me grasp all this better? To clarify, the main concepts covered in class are GCDs, Euclidean algorithm, concepts of coprimes, Euler-Fermat theorem etc. Then these bleed into solving cryptosystems such as RSA, Chinese Remainder Theorem and others. Thanks!
"It is also my favorite quotation. " Does this sentence mean that this is my favorite quotation in addition to other quotations which are my favorites, or does it mean that I am a person who has this quotation as a favorite, in addition to the persons who have this quotation as a favorite? Does "also" indicate the presence of more (favorite) quotations, or more persons who have this quotation as a favorite? If it is the former, how what is the correct way express the later? I mean if a person says, "This is my favorite quotation", how should I express that I also have it in the list of my favorites? Should I say, "It is also my favorite."? I want it to be more formal than "Mine too". A side question which arose while asking the question above: Is the following sentence correct from the perspective of punctuation? I mean if a person says, "This is my favorite quotation", how should I express that I also have it in the list of my favorites?
I am trying to prepare a paper for submission to a journal that is not an AAS publication, but I would still like to use the AASTeX package for the tools it provides and stylistic reasons. The journal does not have its own LaTeX package, so I can use the AASTeX package as long as I make sure to conform to the few given guidelines. One of the guidelines I need to follow is using the in-text citation format of [n] where n is a positive integer. Each reference in the references section should be labeled with a corresponding number. If I were not using the AASTeX package, thebibliography environment would use this format. The modified version in AASTeX package forces you to use AAS format. How can I use LaTeX's default thebibliography with the AASTeX package? EDIT: In order to make this question more specific, I want to know what I can comment out of the class file (or add) in order for the default thebibliography to be used. Alternatively, what options can I add to a blank tex file to get a similar look and feel to AASTeX style without the AASTeX thebibliography? Alternative packages that are already made that are similar in style would otherwise be appreciated if I'm asking for too much.
This question actually came about from a discussion of another question posed here The neutron is known to be comprised of an electron and a proton, and there are observations that the neutron can be created by these particles or alternately decay into these particles. Furthermore the stability of the neutron is vastly improved if it remains bound within the nucleus. So presumably the nuclear force helps to maintain the neutron's stability. Once outside the nucleus the neutron has a much harder time keeping itself together, and once again becomes a proton and electron. And just to keep matters, and this post more simple and shorter, I'm neglecting the additional fact that the electron antineutrino is also produced in the decay. Now getting to my question, I'm wondering why we have to consider the neutron as a separate particle within itself rather than a proton-electron "system" of particles? Is there an experiment that refutes this way of looking at things? (note I'm asking for an experiment or set of experiments, not just theories)?
I have been performing an experiment at school in which I test the force on an iron surface from the magnetic field of an electromagnet. The electromagnet has a rectangular iron core. The theory predicts that the force increases linear with the surface area of the iron plate. This is because the volume between the plate and the magnet contains a certain amount of energy, which is equal to the force exerted on the plate times the distance between the plate and the magnet. I found that the force does not increase linear with the surface. This is because of the divergence of the magnetic field of a bar magnet, which is what the core of the electromagnet essentially is. Researching the magnetic field of a bar magnet, I discovered that there is a higher density of field lines at the edges of the poles, and thus a stronger force on the plate. There are some images on this website, such as the one below. I am curious as to why the field is stronger here. I know that the electric field is stronger at edges and corners because the electrons repel and end up at a higher concentration there, is it the same concept for magnetic fields?
I would like some help with what the word it in the paragraph below (with emphasis added; the word is not emphasized in this way in the original). Does it refer to the TV or the antenna outlet? The passage is taken from Haruki Murakami's TV People. Everything gets removed from the sideboard to make room for the television. The TV people plug it into a wall socket, then switch it on. Then there is a tinkling noise, and the screen lights up. A moment later, the picture floats into view. They change the channels by remote control. But all the channels are blank---probably, I think, because they haven't connected the set to an antenna. There has to be antenna outlet somewhere in the apartment. I seem to remember the superintendent telling us where it was when we moved into this condominium. All you had to do was connect it. But I can't remember where it is. We don't own a television, so I've completely forgotten.
I was finding the are the of hypocycloids. Then it struck me that apart from integration, there could be another method of finding the area of the hypocycloid with different curves. But the problem is I am not getting my answer right. So could somebody please help me tell if my logic is wrong altogether or if I am doing some other mistake. Here is the another method I am talking about:- Take case of a deltoid - we can make a deltoid by taking an equilateral triangle, and on all three of its vertices drawing circles whose radius is half the side of the triangle. Now the figure left in the middle is a deltoid. Similarly, we could use n number of sides in the regular polygon to draw hypocycloids with n cusps. (see the pictures below - the red coloured drawing in the middle is the hypocycloid) Is this idea wrong? Thank you so much :)
Materials in quantum information often emphasize that one and two bit classical reversible gates cannot achieve universality for the classical reversible computation, whereas universal quantum computing can be achieved only using one or two qubits gates. I want to understand why classical reversible computing cannot be achieved with only one and two bits classical reversible gates. I consulted with some of the materials, but all the materials I consulted with only 'illustrated' why it was difficult or seemed to be impossible to simulate some kinds of classical reversible gates only using one and two bits classical reversible gates, never giving a satisfactory clear mathematical proof as to that impossibility. Specifically, I wonder if there is any mathematically clear proof for the claim that Toffoli gate cannot be achieved only using one and two bits classical reversible gates. Thanks in advance.
If you make a straight cut through a square, one part can always be made to cover the other. (This is true by symmetry if the cut goes through the centre, and if it doesn't, you can shift it to the centre while taking from one part and giving to the other.) However, if you cut an equilateral triangle, it may or may not be the case that one part can be made to cover the other. In some cases it may depend on whether we're allowed to flip the parts; I'll leave that to you in case one or the other version has a more elegant solution. How can the cuts that allow one part to cover the other best be characterized? What is the probability that a random cut will allow one part to cover the other? Of course we need to specify a distribution for the cuts, and again I'll leave you to choose between two plausible distributions in case one yields a nicer result: Either Jaynes' solution to the Bertrand "paradox" (i.e. random straws thrown from afar, with uniformly distributed directions and uniformly distributed coordinates perpendicular to their direction), or a cut defined by two independently uniformly distributed points on two different sides of the triangle. Update: I've posted the case without flipping as a separate question.
I'm looking for an adjective that describes an object that, rather than is just the outside, is instead just the inside. Searching for antonyms of hollow, I have only found the word solid, which suggests both the inside and outside of an object. I really need a way to describe something as being just the inside of something. I can only think of words like core or heart to describe what I'm looking for, but those are nouns. When a tree has only its exterior, the tree is hollow. It is a hollow tree. When a tree has only its interior, the tree is _____. It is a _____ tree. Perhaps tree was a bad example, it was the only object I could think of at the time that made sense to be a hollow object. Any object where that description could apply is a reasonable substitute, it does not have to be specifically about a tree.
I've long wondered about the future of our species. Taking the long view, I find it very amusing to consider the challenges that humans will face and (hopefully) overcome on our journey to the end of time. The most vexing problem is the apparently insurmountable issue of Proton Decay and how this could put a premature halt to our species and in fact any complex baryonic structures. I know that Proton Decay has not been observed in practice, but the timescales involved for the effects to become appreciable have not and will not for a great long while elapse(d). The only possible solution I've been able to come up with is Anthropo-nucleosynthesis (this is the only term I could think of meaning "human caused matter generation" but maybe there already is a word/phrase for it that I am unaware of). That would only be effective if these newly forged protons/neutrons would have the same lifespan as those that were created from Big Bang nucleosynthesis. Anyways, I know this was a very long winded intro question/statement, but I'm curious as to your thoughts, solutions, refinements, or problems with anything I've laid out here. What do you think?
My aim is to produce an html-file with the same text as the pdf produced by LaTeX- The html shall represent the pagination and line-break structure of the pdf: When there is a linebreak in the pdf I want to produce a <br> in html, when there is a paragraph I want to produce a <p> in html, when there is a newpage in the pdf I want to produce a horizontal line in html. Handling of the paragraphs is easy since they are defined in the input file. But line-breaking and pagination depends on the font and on the width and height of the document (and maybe on some other things I cannot even imagine yet). Is there a way of getting LaTex to tell me where it broke the lines and where it started a new page?
I've been searching the internet all day for this particular case and can't find a single word on the subject - whether that's my poor searching or the subject is obscure, I do not know. I am also not particularly fluent with mathematical jargon, so forgive my fumbling explanation. Hopefully one of you may re-phrase my problem after I present it. This Tangent Chord Angle diagram is the closest visual representation I can find for describing my dilemma. I'll be referring to points from this diagram, although it doesn't demonstrate the problem itself, only the starting conditions of my problem. I have been trying to write a program that will rotate a vector TP from a point T tangent to circle O until that vector essentially describes a chord on the circle (possibly TA if the magnitude of A equals the magnitude of P). I know: T, the initial tangent point TP, the initial vector from T O, the circle on which T lies The radius of circle O I have no clue what to do to get that vector to "fit" inside the circle. I understand there are two possible chords depending on the direction of rotation - I'll be using whichever angle is closer to the vector's original angle. Again, forgive my inability. I'm afraid it would take considerably longer for me just to learn how to more appropriately describe the problem.
I have long found the Simulation Hypothesis to be better-able to answer questions that I have regarding the universe than the string theory and the quantum field theory. What I believe is that the notion of our universe being a simulation, especially in the last few years, has developed to the point where it should be seriously considered as a candidate for A Theory of Everything. Work on it, by the likes of Nick Bostrom (who proposed the Simulation Argument in his groundbreaking paper), has been cohesive and it has time and time again been proven to be just as plausible as any theory out there. Remember that a theory is just that, a theory. And as a theory, the Simulation Argument gives fitting answers to a lot of questions that physicists have found hard to answer for decades. Much to the dismay of pragmatists, the results yielded by the Double-Slit Experiment have been particularly insightful. The Simulation Hypothesis has much less irregularities than the other theories. It pays just as much heed to the laws of physics and mathematics, even being better able to address issues of epistemology and metaphysics. Then why is it that we don't even see it as a contender for A Theory of Everything?
An off-topic question posed at Mathoverflow by Andrew Stacey, but one which fits here: One thing that came out of Terry Tao's recent blog posts on this matter (first post and follow up) is that it's hard to get an overview of all the different ways of getting one's amazing mathematics onto the web. I thought it'd be useful to gather together a list of such. This meant to be a list of ways to do it, not examples of where it's already being done. Standard community wiki rules: one thing per answer and feel free to edit other's answers. Additional rules: it'd be useful to have a little more than just links. A brief description, pros and cons (be objective), platforms (does it only work on Linux, sort of thing) - things that might help someone decide which things to examine further.
To move charge from one point to another in an electric field, the force which we must apply is equal and opposite to the force due to the field. (Quoted from Engineering Electromagnetics by Hayt.) Here is my concern: To move a charge, shouldn't the force that we must apply be just a little higher than the force exrted on the charge by the field? I know that electric field intensity is the amount of 'kick' a test charge feels when placed in that electric field. Now if I apply the SAME amount of force against the force due to E field, the charge, according to my understanding, will just stay there and won't move. If I apply a force just a little higher than force due to E field, only then the charge should move. Why does the text say that to MOVE charge in E field, we should apply force EQUAL to that of the force experienced by charge because of E field.
I've come across a book that has this general questions about lines and planes. I can't agree with some of the answers it presents, for the reasons that I'll state below: True or False: Three distinct points form a plane - BOOK ANSWER: True - MY ANSWER: False, they cannot belong to the same line Two intersecting lines form a plane - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. Two lines that don't belong to a same plane are skew - BOOK ANSWER: True - MY ANSWER: True If three lines are parallel, there is a plane that contains them - BOOK ANSWER: True - MY ANSWER: False, they can be parallel and coincident lines. If three distinct lines are intersecting two by two, then they form only one plane - For this last one there's no answer and I'm not sure about the conclusion. If you could help me, I appreciate it. Thank you.
This question concerns the residual heat (if any) contained within the Earth's moon. At the time of the Apollo moon landings, it was widely reported that the boot marks left by the astronauts would last "forever", as there is no atmosphere to disturb them and because the moon was geologically "dead." Ignoring cosmic dust, moon quakes (which have since been confirmed) and the blast created by the Eagle lander top section as it left the moon, is this idea of extremely long term preservation of the boot prints really valid? Do we know if the moon is capable of creating convection cells, carrying heat to the surface and gradually erasing the boot prints and tracks left by the astronauts by stirring the dust particles surrounding them? Does the Earth create gravitational forces within the interior of the moon, even though I appreciate they may be a low order compared to the extreme example of Jupiter on Io?
As you know the active noise cancellation technology used in many application such as protection of aircraft cabins and car interiors to reduce engine noise also some headphones use this feature to reduce unwanted ambient sounds. Actually I don't know the details of how this feature works, but I do know that it has input (microphone) that receives noise waves, control unit that invert the incoming noise waves and output (speakers) to emit inverted noise waves and therefore they will cancel each other. What I'm not understanding is that If we considered the sound waves are traveling in air, then the inverted noise waves emitted from the speaker will reach the listener before they combine with the original noise waves so they cancel each other while the inverted noise waves are traveling in a solid-media (components of the microphone, speaker, etc.) faster than the original noise waves traveling in air. I'm I missing something or there is another feature they use to adjust the speed of sound in the active noise cancellation?