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I'm fairly well-versed in calculus but I would like to explore beyond calculus. I have looked into the basics of some topics in higher mathematics such as group theory and abstract algebra and they intrigue me. I am wondering if there are any recommended methods or resources I should use to learn more about these topics. And is there any recommended starting point? | 1 |
I'm a complete beginner at LaTeX, and I'm trying to typeset a complex layout. How should I go about building a page like the one shown below. Edit I was able to replicate the layout using minipages with the multicols package. The images were embedded using the graphicx package. | 1 |
I came across several forums and articles saying that criteria is plural and criterion is singular. Some gave me the impression that criterion is used to denote a set of rules. What is the correct use of these two words? | 1 |
I have somehow managed to lose all my document classes and hence cannot compile anything. I have tried re-configuring and re-installing to no avail. I am on a university computer and cannot edit the program files. | 1 |
"If they would have been painted this afternoon, the walls would be completely dry by tomorrow evening." The quoted sentence is ungrammatical. I believe it has something to do with tense, but I do not believe that the 'if...would be' structure requires parallelism. So what is wrong with this sentence? Thank you. | 1 |
Is solving problems quickly an important trait for a mathematician to have? Is solving textbook/olympiad style problems quickly necessary to succeed in math? To make an analogy, is it better to be a sprinter or a marathon runner in mathematics? | 1 |
I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. Are there any recommendations for a good text that might help me to do this? Or any suggestions for how to tackle these sorts of problems. Thanks | 1 |
Is there a word that works as a milder version of strenuous? Strenuous is defined by Oxford as something "requiring or using great effort or exertion." I'm looking for a word with a similar definition except for the "great" part. | 1 |
I am confused on how to properly describe an all expense paid vacation. Is it an all expenses paid vacation or an all expense paid vacation, and are there any hyphens between all, expense or expenses, and paid? I ask because it seems to be all over the place on google search. | 1 |
What exactly is meant by Lorentz invariance? Is it just an experimental observation, or is there a theory that postulates it? What quantities do we expect to be Lorentz invariant? Charge? Charge densities? Forces? Lagrangians? | 1 |
I've heard many people use the term "goose bumps"; in my family, they were "goose pimples," but I don't know if this was peculiar to us, or if others also use it. My wife's family's saying for this was "Chilly bumps." Are there others? Is one considered the "most correct"? | 1 |
I've read a few different explanations of how hovercrafts hover, and they all mention a low-pressure cushion of air. This confuses me though: If there is low pressure under the hovercraft, why doesn't it get sucked to the ground? Also, if air is being forced into the space under the craft, why is this air cushion not high-pressure? | 1 |
It is known that in general, a mixed state can have multiple pure state decompositions. However, it has a unique eigendecomposition in the absence of degenerate eigenvalues. What is the special significance of this eigendecomposition over other pure state decompositions for the same density matrix? | 1 |
As the title suggests, Can the effects of a person's mass upon the local gravitational field be detected and measured remotely? I am aware any mass produces and effects gravity but couldn't find anything in my searching if it is possible or theoretically possible to detect this effect remotely. | 1 |
I used to pronounce 'detail' as ['di:teil] with accent on the first syllable. However, these days I hear people (and on the radio) say [di'teil] with accent on the second syllable. Is my pronunciation incorrect? Is there a regional preference for this? | 1 |
I'm a high school teacher and someone asked me this in my class, and to be honest I'm quite stumped! I haven't done any high level math in such a long time, and I'm really not sure how to approach this. Is the solution even approachable to a highschool student? Thanks for the help. | 1 |
I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good introductory text for this topic. Any idea will be appreciated. | 1 |
That would not have happened if John had completed his work. That would have not happened if John had completed his work. The former seems correct. The latter doesn't seem incorrect. Are there any cases where one ought to use the latter instead of the former? | 1 |
For example I've written: "I have an interest in rock climbing and am a member of the mountaineers Society." My friend thinks it has to be: "I have an interest in rock climbing and I am a member of the mountaineers Society." which I think sounds bad. Which is right? | 1 |
What is the past perfect of "have"? Is it "have", "had", or "had had"? And if it is "had had", doesn't it sound weird and awkward? when and how do I use it? Thanks. | 1 |
I have a problem that I need to prove using induction. Prove that a surjective function has at least as many members in its domain as it does in its codomain. Do I begin by using the axiom of choice? Thanks. | 1 |
In Arabic, the expression "Summer cloud" is usually used to mean that "this is not going to last for a long time" or "it won't last as long as you think it will". Is there an equivalent phrase in English? | 1 |
So I'm essentially trying to find an explicit description of the smallest subfield generated by a subset of the field. I know that if s is an element of the subset, we must also have its additive and multiplicative inverse. Is there a succint way of describing the subfield set-theoretically? Again, the intuition seems clear, but I'm struggling with a formal description... | 1 |
This morning I heard the word "constitutionality" being used by a journalist with regard to the debate over the legality of health care reforms here in the US. This grates on my British ears as I would simply use 'constitutional' in this context. Does 'constitutionality' have a different meaning? Is this a recent Americanism? | 1 |
When measuring blood viscosity, the literature claims that we generally use a cone-and-plate viscometer. Why is this; is there any way to explain this mathematically in terms of the shear rate, etc? Does it have to do with the fact that the shear rate is constant in this device? Why won't it work with a parallel-plate viscometer? | 1 |
What does the phrase "begging the question" really mean? And does it even matter if I use it correctly? Almost everyone just uses it as a synonym for "posing the question" these days. | 1 |
Is there a good template for software release notes? I typically cover new features, bug fixes, and enhancements. I'm currently using HTML but its ugly and not easy to distribute. Ultimately, I'd like to produce a single PDF. | 1 |
I've been going over the algebraic topology part of Munkres and this question has stumped me. If we have a complete metric space that is not compact, must it be simply-connected (path-connected plus trivial fundamental group)? My intuition tells me no, but I can't come up with an example. | 1 |
This may be trivial, but I want to be sure I understand correctly: Is it true that the interior of a simple polygon is always a simply-connected subset of the plane? I.e, is it eligible for the Riemann mapping theorem? | 1 |
I am wondering if there's an English expression for making someone fall in love with you. In Hungarian there is a term that could be translated into something like "fooling someone into yourself" - meaning you make the person fall deep in love with you, and it is implied that it's thanks to some deceitful or dishonest behavior. | 1 |
I'm trying to get some intuition, I think it almost makes sense, since you can think of the area of a square is length multiplied by height. The volume of a cube is length multiplied by height, multiplied by depth. I don't understand how to find the volume of the hypercube. What's the correct intuition? | 1 |
I recently became interested in the solution to Hilbert's tenth problem, in reading about the succession of results that lead up to the proof I came across the notion of recursive sets and recursively enumerable sets. The distinction between the two sets is very subtle. I need some help in answering the question in the title. Thank you in advance. | 1 |
What is it called when a character knows something the audience doesn't? For example, if the character was stating something obvious like "today is your birthday", saying it only to inform the audience, what is that called? | 1 |
I know that the game which is called football in Europe is called soccer in the U.S. But I wonder to what extent this differentiation is strict. What do people from England call their favorite game in conversations with Americans? Is there a misunderstanding in this case? | 1 |
When reading certain books I will encounter names of places or people that have been abbreviated. An example is in Catherine Hutter's translation of Goethe's "The Sorrows of Young Werther": A few days ago I met a man called V., an ingenuous fellow with a very pleasant face. Why is this done? | 1 |
Let's say I'm trying to describe two things that change. The first changes often and the second changes less often. Is there a better word than "volatility" to use in the following scenario? Is it even proper in this use? The first thing has "high volatility" The second thing has "low volatility" | 1 |
I feel like when two conjectures are inconsistent with one another, it's a clear sign of our misunderstanding of deeper mathematics. I was wondering if anyone knew of a comprehensive list of conjectures that contradict other conjectures. | 1 |
An ice cream shop sells ice creams in five possible flavours. How many combinations of three scoop cones are possibles?[Note:The repetition of flavours is allowed but the order in which the flavours are chosen does not matter.] | 1 |
Consider the following sentences: If I had my own place, I could do whatever I want. If I had my own place, I could do whatever I wanted. She said I could do whatever I want. She said I could do whatever I wanted. Which ones are correct and why? Is the answer different in a conditional, or does that not matter? | 1 |
I am using sharelatex (great tool) but I haven't been able to find a way to show the ruler (blue numbers on the sides of the paper) that comes with the CVPR template. I was wondering if someone has had the same problem and how did they solve it. | 1 |
"It's precisely in contrast to the ordinary that the resurrection stands out." Could someone explain what the author meant by "in contrast to the ordinary"? Could I replace "in contrast" in this case with "opposite"? | 1 |
I'm fascinated by the fundamental questions raised by the Double Slit Experiment at the quantum level. I found this "Dr Quantum" video clip which seems like a great explanation. But is it scientifically accurate? | 1 |
I'm following my first course in field theory and the professor began, like many books do, by introducing the scalar field. However, I am a bit hesitant about the physical idea of fields. My question is: what is the physical meaning of the fields? Why they are introduced? I read the introduction of the books of Peskin and Weinberg but I'm not satisfied. | 1 |
I have an electric stove, and when I turn it on and turn off the lights, I notice the stove glowing. However, as I turn down the temperature, it eventually goes away completely. Is there a cut-off point for glowing? What actually is giving off the light? Does the heat itself give off the light, or the metal? | 1 |
In Flemish we have a saying "Vijgen na pasen". Translated: "figs after Easter". It means a solution comes too late to be of any use. What is the English equivalent for this? Some googling gives me "Closing the barn door when the cow has bolted", but the explanation seems to point more towards the wrong solution for a problem. | 1 |
I am an undergraduate physics student, and I wanted to study about interacting particle systems. I have studied probability theory, linear algebra, and statistical mechanics. I know basic measure theory and stochastic processes, but have very little knowledge of algebra. What more do I have to know to study interacting particle systems? (Please give names to some reference books if possible) | 1 |
I know that the zeros of analytic function (with one variable) over complex plane are isolated. However, I am not aware about the structure of the zeros set of analytic functions over complex plane with several variables. My question is: How I can understood this structure. | 1 |
According to this Fritinancy entry, the demonym for Norfolk, England is "North Anglian," rather than "Norfolker" or "Norfolkite," for historical reasons. What about Norfolk, Virginia, in the United States? I suppose you could argue for the same historical reasons, since it was named after Norfolk in England, but that just feels wrong to me. | 1 |
I am using sidewaysfigure for many of my figures. When I print out my document, for reasons I don't understand, the figure captions are on the inside and not the outside. Is there a quick way to flip all the sideways figures without affecting anything else? | 1 |
Does the current acceleration of the universe imply that our universe is open? If the universe is closed, from the Friedmann equations, the acceleration of the universe wouldn't be possible, would it? (Of course, except for the very early inflation era.) | 1 |
I know how to use a .bib file to add BibTex and use that in the main document. Is there a way I can include the bib-file in my latex document and not use an external bib-file? | 1 |
Do magnets (permanent) become weaker as they are exposed to para-magnetic objects? I was thinking about this after seeing this. I am buying a magnet and wish to know if a magnet (permanent) loses its magnetic domain structure or alignment when exposed to para magnetic materials. | 1 |
If I understand correctly, scientists were able to find strong evidence for the existence of quarks by using deep inelastic scattering. If quarks (hypothetically) are composed of preons, could we use similar methods to detect the preons? If so, how would we have to modify the scattering experiments used to detect quarks? | 1 |
I have a funnel and I notice when I try to pour powdered sugar through it, it blocks up unless I tap it. If I put sand in the funnel, it goes through. Is there a theory of funnels that can predict what materials will pass through a funnel of given dimensions? | 1 |
If I project a circle over the Z-axis, I'll get a cilinder. If I project a square over the Z-axis, I'll get a parallelepiped. If I project an ellipse over the Z-axis, I'll get a... whatsitsname? I can't find the name of this object, and I can't believe it doesn't have one to begin with. | 1 |
If I write a paper, is it acceptable for me to use a title like "analysis of PDEs related to blah blah blah" instead of "analysis of partial differential equations related to blah blah blah"? I intend on using in the abstract the words partial differential equations and writing (PDE) in brackets next to it. Is this reasonable? Thanks. | 1 |
In my high school and college math classes, I've always seen graphs drawn with either no arrows on the ends of the axes or with arrows on both ends. A colleague recently argued with me that this was crazy and arrows are always placed on one side of each axis to indicate the positive direction. Like so: Which style is more prevalent? | 1 |
In a normal double slit experiment, I'm told that sunlight doesn't produce a visible interference pattern because there is no stable phase relationship between the two slits. However, sunlight bouncing off a CD does produce interference-based rainbows, so sunlight can interfere if the slits are close enough. How close do the slits need to be to see interference when direct sunlight falls on them? | 1 |
I'm sorry if this was asked before but with all the stars and dark matter and all the other stuff, curently in the Universe, what's the avarage temperature of the Universe? Is it like extremely high or extremely low? | 1 |
Let's say we have a given wavefunction and we want to find a particle that will fulfill the properties for that wavefunction. How can we do that? Is it possible? I was thinking of using Schrodinger's equation.. would that work? (please tell me if there is anything wrong with this question so I can fix it!) | 1 |
I need to find a word which means "the town or city in which one lives". Words like "residence" or "domicile" appear to have this meaning, but because "residence" and "domicile" can also mean "the home in which one lives", my readers will be confused. Is there a word which only refers to the geographic location? | 1 |
The standard Bernoulli Equation has three terms on each side, a kinetic energy term, a potential energy term and a pressure term. I've never seen an extension of this to also include a rotational kinetic energy term. Do things get too crazy when fluids rotate for a simple extension to the equation? | 1 |
I don't know why, but despite having read the definition over too many times to count, its one of those words that just doesn't click. I see it being used in sentences and have never been able to fully understand it either. Could someone help explain it, and use it in a sentence? Thanks! | 1 |
I think I should use broke because it is in past tense. Am I correct? If incorrect, can you explain to me briefly which case is correct? I was thinking about punching him and breaking his teeth. I was thinking about punching him and broke his teeth. | 1 |
I would like to get into a career that uses alot of applied math. I took a numerical analysis course in undergrad and liked it, so I plan to self-learn numerical methods for PDEs. Other than the MIT OCW, are there any good textbooks or lectures notes that can be viewed online? Particularly those that are geared towards engineers/scientists, since I'm not into theorems/proofs | 1 |
I read here that a major ingredient in Whitney's strong embedding theorem and later Smale's celebrated h-cobordism theorem is the Whitney trick. Can someone give an intuitive description of the trick? To be more specific, I would be happy to know why and where the trick was applied ? Thanks. | 1 |
So I am learning LaTeX and I find it slow to test changes. So I'd edit the .tex file, then go to command line, and run pdflatex, wait for it to complete, and then open total commander, and then open the .pdf file. Does anyone know a faster way to test changes? (WYSIWYG?) | 1 |
I'm looking for a word to describe the final flight of an aircraft (or other vessels if there is no direct equivalent) such as the final flight of the space shuttle. Does anyone know if a word like this exists? Thanks! | 1 |
We have a project at school to develop an idea about how we can generate electricity. My question is: do collisions between matter and antimatter particles generate heat, so that one could harvest it using turbines? | 1 |
I want to show that the domain of any partially defined recursive function is equal to the range of some ( totally defined ) recursive function. I haven't understood which is the difference between a partially defined recursive function and a totally defined recursive function? Could you explain it to me? | 1 |
Why are measurable functions called "measurable"? What exactly is being "measured"? For measurable sets, I can intuitively understand that the measure of the set "measures" how large is the set. Thanks for any help! | 1 |
I have recently falled into an error because I didn't use % when I was supposed to. My question is now: When do I have to use % at the end of the line and when should I leave it out? | 1 |
Can we add an uncountable number of positive elements, and can this sum be finite? I always have trouble understanding mathematical operations when dealing with an uncountable number of elements. Any help would be great. | 1 |
I have seen this phrase do not pass go a couple of times reading Internet forums, but I don't remember figuring it out in context, as I've never played the game Monopoly. What does it mean? | 1 |
Under normal lens operation, a beam is sent through the centre of the lens along the optical axis (ie perpendicular to the lens's plane). What happens when a beam is sent through a lens at an angle to the optical axis? Does it simply exit the lens at the same angle? | 1 |
You get taught about matrices and how they work but nobody ever tells you WHY they work in the way that they do. What was the idea that sparked the creation of matrices? | 1 |
In crystallography, we always speak about the direct and reciprocal lattice spaces. One property about these spaces in mentioned here, as follows: Each point (hkl) in the reciprocal lattice corresponds to a set of lattice planes (hkl) in the real space lattice. Can anyone give a proof for this statement? | 1 |
What I am asking is this: Why can't a body be solid, then solid-ish, then solid-like, then liquid-like, then liquid-ish, then liquid, then vapor-like and then vapor? Why is there a rigid temperature boundaries between solid, liquid and vapor? Why doesn't water simply change "states" in a continuous manner? | 1 |
I was wondering what is the difference between I wasn't knowing and I didn't know? If I say, I wasn't knowing, I am talking about something unknown in past, the act of not knowing is finished, it means that I know it now, but before it was unknown to me. | 1 |
Suppose I have a graph and I calculate the eigenvalues of the adjacency matrix and find that there are some number of zero eigenvalues. Do zero eigenvalues have any significance? Also is there a good way to interpret the inverse (when it exists)? In some cases the inverse is called the Green's function. Thanks! | 1 |
Verbs can be conjugated to past/future tenses. Nouns can be pluralized. Adjectives also have comparative and superlative forms. For example fast, faster, and fastest. What is the word that describes converting between the base form and the comparative and superlative forms? | 1 |
I was wondering where the noun punk stems from. Obviously, it's used for members of a certain subculture, but has the word been in use before the invention of said subculture and been adapted for it, or has it been made up specifically for it? | 1 |
Say I have a rigid body in space. I've read that if I during some short time interval apply a force on the body at some point which is not in line with the center of mass, it would start rotating about an axis which is perpendicular to the force and which goes through the center of mass. What is the proof of this? | 1 |
I've been doing some maths work using the rate of flow of liquids. I've used various models for the flow and various methods to integrate these models. The one thing that is confusing me is the difference between constants of proportionality, and constants of integration? | 1 |
With today's computers having several gigabytes of memory, why does TeX still have such limited capacity, and why are modern TeX installations not adjusted for higher capacity by default? Why is adjusting TeX capacity only recommended as a last resort? | 1 |
State the domain and range of the following graphs. Express each domain using interval notation and express each range using set-builder notation. I think I'm beginning to understand using interval notation and set builder notation, but I'm still having trouble with the endpoints. | 1 |
British English makes the distinction between 'practise' (verb) and 'practice' (noun). Based on this, I would judge the following sentence as incorrect: In practise, computers often crash. Nevertheless, I see it frequently. Could 'practise' possibly be a verb in this phrase? | 1 |
I read the definition of a hereditarily compact space in topospaces.subwiki.org, it says: A topological space is termed hereditarily compact if every subset of it is compact in the subspace topology. I don't understand how this is any different from saying: every subset is compact. Can someone explain the difference? | 1 |
Excerpt: In developed countries, running water is available everywhere and air-conditioning is expected not just in our homes but in our cars. We don't realize that these are luxuries. My sentence: The author mentions "running water" and "air-conditioning" as examples of things we take for granted. Are the quotation marks required? | 1 |
Imagine a body in a tub which is in a lift. When the lift is stationary, the body is floating. If the lift accelerates upwards with a constant acceleration, what will happen to the buoyancy? Will its value change or not? I do not think it shouldn't. But my friend says it will. But why? | 1 |
I have researched a little on loop quantum gravity (LQG), but all I got were very ambiguous explanations about loops and nodes that all end with mathematical equations. If someone could give me a non-mathematical, clear idea of LQG, I would really appreciate it. | 1 |
Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which depends only on the electric and magnetic fields and which will have Maxwell's equations as its Euler-Lagrange equations? | 1 |
I have seen the phrase used in this form or as a template for other rhetorical questions - e.g., "what's an honest economist to do?"; "what's an honest business owner to do?";"what's an honest Nigerian to do?" I cannot find any reference to its original use in literature, but was asked recently "who said that?" - and didn't have an answer. | 1 |
I have tried to find this out through google and searching this site with no luck. Basically, are the terms 'law' and 'identity' interchangeable in Mathematics? What is described as 'logarithmic identities' in one place is referred to as 'log laws' elsewhere. Similiarly, 'index laws' and 'exponential identities'. | 1 |
I'd like to create a custom design for my beamer presentations. How could I achieve this? I have neither found any resources for that nor does the official beamer documentation talk about it. Are there any good resources to start with? | 1 |
What's a word for an inaccurate artistic representation that doesn't retain all the qualities or features of the original subject? For example: There is a painting of a king but it doesn't have the expected semblance. It looks like him but there are oddities, like an elongated nose, or bigger eyes and ears. | 1 |
The energy required to remove an electron from the surface of a metal is less than that required to remove an electron from a free atom. Why?The electron is bound to the nucleus in an atom by electrostatic forces. How is an electron 'free' on a metal surface? | 1 |
What is the difference between the following sentences? Even in those days he played golf on Wednesday. Even in those days he played golf on every Wednesday. Even in those days he played golf every Wednesday. In a non-progressive sentence, which adverb phrase (in those days, or every Wednesday) is used to refer a serial state (habitual)? | 1 |
I've long been familiar with crenulated edges, but until today I wasn't aware of crenelated. Looking at the definitions, they seem to describe the same kind of feature, that of notches on an edge that are more rounded in contrast to, say, serrated. What are the differences in nuances? When would be a "wrong" time to use one over the other? | 1 |
Each shop in a town has an odd number of customers and each pair of shops shares an even number of customers. Prove that there are at least as many customers as there are shops. Any hints are appreciated. | 1 |
Subsets and Splits