# Questions tagged [soft-question]

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### What should I do to make up for my negligence as an undergrad?

This is a long one so please bear with me. I am not happy with where I am as a math student at the moment. So far, most of my courses have been conducted entirely online and the importance and ...
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### Notation: minimum for all (sub) elements

Have an element list \Delta, these Elements have sub values, \alpha, \beta, ...
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If we have a number of independent events in probability, we can calculate it's likelihood : $$\prod_{\forall i} p_{i}$$ We can also consider ( where $H$ is the Heaviside step function ) $$\int L(t) H(... -4 votes 0 answers 26 views ### Could you please answer this short survey (30 seconds) about guessing the weight of a chair from an image? [closed] We are a group of engineering students who are performing a statistical survey and we would like your help! Could you please answer this short survey (30 seconds) about guessing the weight of a chair ... 0 votes 0 answers 24 views ### Undecidibily of the Word Problem for Groups and First Order Logic I am trying to derive the undecidability of the Word Problem for an arbitrary group, let's call this Problem WP(G). It is clear to me that FOL and higher are undecidable and I want to reduce the WP(... 0 votes 1 answer 39 views ### Intuition behind the notation of differential operators \frac{\partial}{\partial z} and \frac{\partial}{\partial \overline z}. I am a graduate student of Mathematics.In this semester I am studying complex analysis.Stein Shakarchi's complex analysis book defines differential operators \frac{\partial}{\partial z} and \frac{\... 1 vote 2 answers 81 views ### Utility of the coordinate free definition of the derivative on manifolds. Preface: I am not an expert on the topic of smooth manifolds, nor do I have the perspective gained from knowing many theorems proven on smooth manifolds. Please try to look at the problem from the ... 1 vote 1 answer 63 views ### About Exercise 3.D.13 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. I am reading "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. 3.69 Suppose V is finite-dimensional and T\in\mathcal{L}(V). Then the following are equivalent: (a) T is ... 1 vote 0 answers 22 views ### Proving a uniform bound given that 0<A-f\leq B I've been working in the following problem. The problem itself is quite large and involves many steps, but the point is that I'm in a step where I have a certain open set \Omega \subseteq \mathbb R^n... 1 vote 0 answers 60 views ### If 𝑓∘𝑔∘ℎ=𝑓 ∧ 𝑔∘ℎ∘𝑓=𝑔 then must ℎ∘𝑓∘𝑔=ℎ? If not, then What can be said of each 𝑓,𝑔,ℎ and are there any simpy-definable minimal conditions imposable upon one or more of the indexable functions that would ensure this symmetric closure? ... 1 vote 0 answers 40 views ### Getting better at Geometry - soft question I am a high school student in the UK (year 12 UK, grade 11 US. I am very interested in maths and so have been doing some STEP papers (2 and 3) in my spare time. I have become reasonably proficient at ... 2 votes 1 answer 69 views ### Can Hilbert's Hotel be explained by a difference between ordinal numbers and cardinal numbers In taking a philosophy of maths course I have been very curious about the notion of infinity, and whether or not it is paradoxical. One thing I have frequently thought is that "infinity" as ... 0 votes 0 answers 26 views ### What software can I use to graph a solid of revolution between 2 functions? What software is used to graph solids of revolution between 2 functions like the ones below? 5 votes 0 answers 87 views ### Examples of Substructures that "do not know they are that substructure" Just learned \mathbb{L}\vDash \mathbb{V}=\mathbb{L} and was warned that this property is not obvious with the counterexample mentioned being HOD. I can think of a few examples of definable ... 1 vote 2 answers 70 views ### Intuition for fibers over a point in \operatorname{Spec}(A) This is a rather soft question, but I would like to see what I get. I'm currently reading/working through Atiyah Macdonald, and I just did exercise 21 of Chapter 3. I won't repeat the entire exercise ... 3 votes 1 answer 102 views ### A Reference From Andrej Bauer's Recent Talk on Countable Reals Andrej Bauer gave a talk today in the topos institute colloquium (video here) announcing a proof that the dedekind reals can be countable in the absence of LEM and CC. At roughly the 27 minute mark, ... 4 votes 1 answer 35 views ### Practical uses of p norms for p\notin \{1,2,\infty\}? We all love normed spaces, but it seems like the 1-, 2-, and \infty-norms get the lion's share of the love. That's not admittedly not without good reason, but what of the other unsung norms with ... 1 vote 1 answer 58 views ### Integrating Dirac delta distribution from 0 to 1. Let \delta be rigorously defined as a generalized function (lim of a function). I am guessing that \int_{-1}^0\delta(x)d x=\int_0^1\delta(x)d x=\frac{1}{2}? Also, let E denote a set contains 1/3 ... 6 votes 0 answers 24 views ### What are some good sources for probability heuristics? I've studied rigorous probability theory at university but I find myself struggling to solve questions in probability as quickly as some of my peers. I think that what I try to do is 'translate' the ... 6 votes 1 answer 124 views ### What is expected from a Master's thesis, especially contrasted with a Bachelor's or PhD thesis? [closed] I'm thinking of enrolling in a Master's degree in Mathematics and it culminates with a thesis rather than being purely course-based. I am wondering what is expected of students writing a Master's ... 4 votes 1 answer 95 views ### A Collection of Bogus Proofs Hello M.S.E. people, This question is just for fun, don't take it seriously :). We have all encountered Bogus Proofs, which seem logical and reasonable, but they prove some claims which are completely ... 0 votes 0 answers 12 views ### PUCT Analoge for Adversarial Bandits Many people are familiar with PUCT, the multi-armed bandits algorithm that produces good results (logarithmic regret) in the stochastic regime that utilizes 'predictions' of the best arm. This ... 7 votes 1 answer 146 views ### Does "Entropy" explain why the Normal Distribution is so "Popular"? Recently, I have learned about the Principle of Maximum Entropy with regards to Probability Distribution - in particular, when certain "information" (i.e. constraints) is available about ... 0 votes 0 answers 5 views ### variational methods of semilinear elliptic problem with critical sobolev index There are many exitence results of semilinear elliptic problem with critical sobolev index, for example, the Brezis-Nirenberg problem:$$-\Delta u =\lambda u+u|u|^{2^{*}-2}.$$However, it seems all ... 1 vote 1 answer 71 views ### Vectors as arrows Given some vector space, can we take vectors as arrows to form a category? I mean, I am not thinking the vectors spaces as objects, and linear transformations between them as arrows. In the monoid ... 4 votes 0 answers 28 views ### Understanding compatibility of PDE THEOREM 1: The equations$$f(x, y, z, p, q)=0\qquad (1)$$and$$g(x, y, z, p, q)=0\qquad(2) are compatible on a domain $D$ if (i) $J=\frac{\partial(f, g)}{\partial(p, q)}=\left|\begin{array}{ll}f_{... 2 votes 0 answers 60 views ### Proofs and Types: Girard's remarks on Theoretical Computing In the first chapter of Girard's Proofs and Types (1989) one finds the following remarks: Theoretical Computing is not yet a science. Many basic concepts have not been clarified, and current work in ... 0 votes 1 answer 14 views ### How to reduce a straight line - of known equation and passing by two rotating points - to a line segment : which condition should be imposed on$x$? Let point$P=(cos(\alpha), sin (\alpha))$and point$Q = (cos(\alpha+ \pi), sin (\alpha+\pi))$be two points moving on a circle ( of center$(0,0)$and of radius$1$). The straignt line passing ... 0 votes 0 answers 38 views ### About Exercise 5.B.20 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. I am reading "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. Exercise 5.B.20: Suppose$V$is a finite-dimensional complex vector space and$T\in\mathcal{L}(V)$. Prove that$T$has ... 0 votes 0 answers 55 views ### Intermediate Linear Algebra Text I have been struggling to find an intermediate-level linear algebra textbook. I have tried Strang's Introduction to Linear Algebra and found it convoluted. Additionally, some of the books like Axler's ... 0 votes 1 answer 78 views ### Soft Question: Introductory books on Algebraic Number Theory I am a high school student in Britain. I have recently studied elementary number theory and absolutely loved it. I got as far as to prove results like quadratic reciprocity, Fermat's sum of two ... 1 vote 0 answers 70 views ### Should I still pursue math? [closed] I'm a sophomore studying physics in the US. I have always liked math and physics, and as a high school student I've always aced in both subjects, in fact they are the only subjects that I get good ... 8 votes 0 answers 76 views ### Externalizing Statements about the Effective Topos (or: what is it good for?) Say we prove some theorem constructively (by which I mean, without choice and without LEM). Then it's true inside an arbitrary topos, and in the case of sheaf topoi we can externalize our theorem into ... 0 votes 0 answers 12 views ### terminology : Big difference between basic real analysis and basic calculus over reals? [duplicate] Im a bit confused by terminology: What is the difference ( if any ) between Basic Real Analysis without measure theory. and Basic Real Calculus ( calculus over the reals , not complex analysis nor ... 0 votes 2 answers 53 views ### Let$h$be such that$h(x)=\int_a^x f'(t)dt$. For which value of$a$is function$h$identical to function$f$? An informal reasoning had led me to the ( erroneous) conviction that: "the integral of the differential$f'(x)dx$is identical to$f(x)$, because the (infinite) sum of the infinitesimal linear ... -2 votes 2 answers 61 views ### How much time should I spend on a problem when preparing for a timed exam? [closed] I'm preparing for a university entrance exam that has different subjects (like Biology, Mathematics, Physics, Chemistry ,...). In the Math section, there are$30$problems for$47$minutes ($94$secs ... 1 vote 2 answers 38 views ### Is the boundary of singleton set in$T_1$space is empty? The singleton set in$T_1 $topological space is closed so, I wonder how i use this information to prove that boundary of this set is empty. 0 votes 0 answers 31 views ### When to use Remark and Note I am writing notes for some topics of Math in details. I am confused about one thing that when do we use word 'Remark' and 'Note'. I referred some texts.. but couldn't figure out the exact difference. 2 votes 4 answers 122 views ### What breaks down when generalising from sets to classes? I have been familiarising myself recently with some basic definitions in category theory, where we work with classes of objects and morphisms, as opposed to just sets. It feels like I am long overdue ... 25 votes 5 answers 2k views ### Are there are any inherent mathematical reasons some proofs are difficult? This is not a complaint about my proofs course being difficult, or how I can learn to prove things better, as all other questions of this flavour on Google seem to be. I am asking in a purely ... 0 votes 1 answer 55 views ### Analytic works versus synthetic works in mathematical research With the purpose to clarify my ideas about terminology I would like to ask in Mathematics Stack Exchange what is the difference of two verbal expressions: when a professional mathematician understands ... -3 votes 0 answers 58 views ### Why do we split the Number System into Even and Odd? [closed] I started thinking about this whilst learning that the difference between a Baryon and a Meson is their possession of an odd or even number of quarks; I couldn't think of the name for the odd-even ... 11 votes 7 answers 712 views ### The vertices of a tetrahedron lie on a sphere I am struggling a bit with the following (elementary) question: How to prove that every regular tetrahedron admits a circumsphere, i.e. there exist a sphere on which all four vertices lie. I would ... 2 votes 1 answer 49 views ### How to graph the elasticity function ( knowing the - linear-demand function and the price function )? What goes wrong in my Desmos graph? My goal is to visualize the graph of the elasticity function for a linear demand curve . The problem I face is that the elasticity function graph I came up with looks unfamiliar. I suppose my formula ... 0 votes 0 answers 19 views ### Does any weak form of compactness can force the conclusion of the closed graph theorem to be true? Closed Graph Theorem (Topological Version , necessary condition ) :$X,Y$be two topological space where$ Y $is a compact Hausdorff space and$f:X\to Y$be a map with$G_f=\{(x,f(x)):x\in X\}\subset ...
Everyone knows that integrating a function $f(x)$ from a to b can be represented by the area under $f(x)$ graph from a to b. But If we are integrating lets say $f(y)$ from $h(x)$ to $g(x)$ what will ...