# Tagged Questions

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

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### Is convexity the most general dividing line between “easy” and “hard” optimization problems?

Just got started with Boyd's Convex Optimization. It's great stuff and I see how it directly subsumes the all-important linear programming class of models. However, it seems that if a problem is non-...
177 views

### Are there important situations where we study false statements as if they were true?

I know of two situations resulting from asserting that a false mathematical statement is true (by this we assume that the statement has been made to be a mathematical axiom and that it must be true ...
72 views

### Big Rudin directly after baby rudin?

I'm a high school student who went through Rudin's Principles of Mathematical analysis a while ago in its entirety, except for the last two chapters. I bought Real and Complex Analysis too, and ...
125 views

### Are there any modern mathematicians whose research interest is in “Probability Theory”? [closed]

I have seen professors in universities list "stochastic calculus", "stochastic analysis", "stochastic processes", "stochastic geometry" and "applied probability" as research interests, but are there ...
59 views

### What will happen if evolve metric under Ricci flow on general manifold? [closed]

Because the scalar curvature under Ricci flow evolve by $$\partial_t R=\Delta R+ 2|Ric|^2$$ I treat it as heat equation with heat source . So, no matter the heat source is very hot or not , the ...
66 views

This question is almost a duplicate of this one, but not quite. There the person asked about examples and intuition, I am asking about terminology and applications, and I am addressing my question ...
95 views

I have been reading Massey's Algebraic Topology and on page 158 came across the following "semi-mystical principle" which he says guides much mathematical research: Whenever we wish to gain ...
53 views

### Redundant proof in Math paper [on hold]

Recently, I read a published math paper and I found that in the excessive argument in the proof of one of its theorem. In fact, in my opinion, the redundant part is not even correct, because it ...
327 views

### Corollaries of the Yoneda Lemma in Analysis?

I am looking for some simple examples of how the Yoneda Lemma can be applied in analysis and probability theory and related fields. A simple candidate example that I can think of and somewhat ...
217 views

### Is any real-valued function in physics somehow continuous?

Consider the following well-known function: $$\operatorname{sinc}(x) = \begin{cases} \sin(x)/x & \text{for } x \ne 0 \\ 1 & \text{for } x =0 \end{cases}$$ In physics, the sinc function has ...
59 views

### What is the Star of David theorem?

I came across a MathWorld entry for the Star of David Theorem, but it doesn't provide much context. I have never heard of this before, can somebody explain its significance and any applications it ...
59 views

### Next book in in learning Analytic Number Theory

I have just finished the book "Tom M. Apostol - Introduction to Analytic Number Theory". My aim is to reach to graduate level to do research, especially on Rationality/Irrationality and Algebraic/...
61 views

### Is every finite category identifiable with a directed multigraph? (and vice versa?) [duplicate]

What seems implicit in this talk on youtube, is the claim that every directed multigraph (with loops) can be identified with a finite category and vice versa, if we consider the paths of the directed ...
184 views

### How to know if you are “tough enough” to study Algebraic Topology [closed]

I am graduating with a BA this summer and I am very interested in topology. I admit it, I never went that deep into topology and all I know is about point-set topology (metric spaces etc.) but from ...
105 views

### Is a pure mathematics degree worth it from a financial standpoint? [closed]

I know this isn't a math question but this has been on my mind for quite some time. I am a second year university student who is planning on getting a degree in pure mathematics. I really enjoy the ...
171 views

### Lonely theorems [closed]

What are some instances of theorems which are especially unique in mathematics, i.e. for which there are not many other theorems of a similar character? An example I have in mind is Pick's theorem, ...
23 views

### Maximum data storage in a paper sheet? which theory should I look for?

I'd love to study a problem: How much information can be stored in a blank paper sheet. with those considerations: "store in a sheet" means writte letters or numbers or equations, with a pen and a ...
862 views

### How do I tell if I am able to go to graduate school in math? [closed]

This is my first question on this site, and this question may sound disturbing. My apologies, but I truly need some advice on this. I am a sophomore math major at a fairly good math department (top ...
118 views

### Can Local Martingales be characterized only using their FV process and BM?

Prove or Disprove: A process $(X_t)_{t \ge 0}$ is a (continuous) local martingale if and only if it can be represented in the form: $$\int_0^t \xi dB = \large B_{\int_0^t \xi_s^2 ds}$$ where the ...
33 views

### How can I remember whether finite or countable cartesian product of countable set is countable

I always forget this result Is cartesian product of countable set countable under finite or countable cartesian products? Is there a good way to remember this? Like a proof sketch where the ...
41 views

### How can I study probability?

I want to have a deep understanding of probability. I've tried William Feller's first book on Probability, and E.T Jaynes' Probability theory - the logic of science (which is very different from most ...
81 views

### Are there any “default” properties which hold for almost all topological spaces in analysis?

What is the simplest/most general commonly used (type of) topological space in analysis? For instance, every example I can think of in analysis is first-countable. I don't think it can be metric ...
119 views

### Should a high schooler be concerned with the abstraction of mathematics? [closed]

I'm currently studying precalculus in high school and have no hands-on experience with advanced mathematics (calculus and beyond). Every time I learn something new, I feel the need to connect it with ...
84 views

### Topology on $\mathcal{C}(X,Y)$ to work with homotopy.

We know that the compact open topology on $\mathcal{C}(X,Y)$ is a good choice for topology on the set of continuous maps, but this seems really efficient, both naively and with respect to existence of ...
54 views

### Is the infinitesimal generator for Lie groups the same as the infinitesimal generator of a Markov semigroup?

Is the infinitesimal generator for Lie groups related to the infinitesimal generator of a Markov semigroup? Or are they totally different concepts? https://en.wikipedia.org/wiki/Lie_group#...
143 views

### Can we characterize all infinite Euclidean-domains having exactly one invertible element?

$\mathbb Z_2$ and $\mathbb Z_2[x]$ are two euclidean-domains having exactly one invertible element ; my question is ; Can we characterize all euclidean domains $D$ having exactly one invertible ...
54 views

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### Self Study of number theory

I have always wanted to learn about number theory. There is actually no one here who can teach me and it's also not in my regular school syllabus, but the greatness of number theory attracts me ...
53 views

I am thinking of making a model or whatever name i don't know. Idea is this that I suffers from headache, say twice in a month. What i want to do is that i want to make some kind of system in which i ...
27 views

### The best known bounds for spectral radius of a graph

There are many bounds for the spectral radius of graphs in terms of no. of vertices, maximum degree, chromatic number etc. I wish to know till date what are the best lower and upper bound for the ...
34 views

### What are some other operators like infinite sums and products? [duplicate]

I've heard of the sigma and capital pi notations (hasn't everyone?), but I know there are some other ones, like the ones signified E, F and K. What are these? Are there any more related to infinite ...
33 views

### Recommendation in orthogonal polynomials

I am searching for a good book in orthogonal polynomials (for good I mean detailed and with all the basic results one has to know before doing some research in that branch ) for beginners ( nothing at ...
88 views

### On the HoTT Cauchy Reals

In the Homotopy Type Theory Book there is a construction given of a kind of Cauchy reals via higher inductive type and the authors remarked, that this construction is preferred to other notions (reals ...
651 views

### Tough integrals that can be easily beaten by using simple techniques

This question is just idle curiosity. Today I find that an integral problem can be easily evaluated by using simple techniques like my answer to evaluate \int_0^{\pi/2}\frac{\cos{x}}{...