# 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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### Why are alternating divergent series generally easier to evaluate? [closed]

Why is it that alternating divergent series tend to be easier to evaluate or that there are more ways to evaluate them? Is there a particular reason for the difficulty to evaluate series that don't ...
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### a healthy perspective on “knowing everything” [closed]

This is a question about attitude, but related to math studies. I have trouble with two things: 1. making "normal" progress in my learning and 2. having the satisfaction that I understand what is ...
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### Comparing Patrick Billingsley's Aniversary Edition to previous editions, and to Robert B. Ash's book.

I'm reading some of the reviews at amazon to the Anniversary edition of Billingsley's 'Probability and Measure', and several users state that the book is riddled with new typos, and plain errors, ...
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### Reference request for Grothendieck's work on “Integration with values in a topological group”

Recently I was reading the available part of the second part of W. Scharlau's book on Alexandre Grothendieck (see here). There I found, An anecdote survives about Grothendieck's arrival in Nancy: ...
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### How should one characterize mathematical conclusions? [closed]

I have posted this in Philosophy SE as well because I feel that it is appropriate both here and there. As practiced, mathematical proof seems not to be an explicit formal deduction within a formal ...
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### Topics in Geometry and Dynamical Systems

Dynamical Systems/Fractal Geometry and Differential Geometry/Topology are really interesting areas of study. My question is whether there is any direct connection between them? In other words, are ...
51 views

### Sum of integers [duplicate]

I cannot accept that $\sum_{n=1}^\infty n = -\frac{1}{12}$. It should be that such a sum is divergent. That it is divergent is useful for the Test for Divergence in many such problems. I feel like ...
67 views

### Axioms of Geometry?

I have taken the generic low level undergraduate classes, such as Calculus 1-3, Differential Equations, and Linear algebra. Since I never learned Geometry past a basic high school level, I thought it ...
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### A Pure Maths Approach to Thinking About Vectors

Introduction Generally most students are introduced to the concept of Vector as something that has both a "magnitude and direction" and Scalars as something that only has a "magnitude and no ...
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### Is linear algebra developed any further? [duplicate]

I heard an opinion that linear algebra has ceased to develop 100 years ago because there's nothing else to "discover" in this branch of mathematics, and no scientific activity other than teaching ...
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### Calculating the gradient of a scalar field. Am I missing something?

Question Find the gradient of $f$ at each point where it exists. $f:\Bbb{R^3} \to \Bbb{R} ~,~f(x,y,z)=xy^3z-\sin(x).$ Attempted solution $\text{grad } f=\nabla f=(y^3z-\cos(x),3xy^2z,xy^3)$ ...
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### Understanding order and countability

I am confused with how to defining the order of countable set. Let me express my thoughts by some examples: $\Bbb{N}$ has a 'natural' order, namely $1\lt2\lt3...$ For any countable set, we can define ...
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### Does excluding or including zero from the definitions of “positive” and “negative” make any consequential difference in mathematics?

I was absolutely certain that zero was both positive and negative. And zero was neither strictly positive nor strictly negative. But today I made a few Google searches, and they all say the same ...
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### Persistent Homology. Missing points

I'm working on a project with a professor. This project involves Persistent Homology methods over a point cloud. Recently we found some inconsistencies in the point clouds that we were reading, ...
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### Need some suggestion for an introductory talk on 'Local Cohomology'?

Next week i am to give a talk on 'Local Cohomology' and i am writing to request suggestions for some basic interesting results for the talk.The relevant information is as follows: (1) The audience ...
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### Is basis change ever useful in practical linear algebra?

In layman's terms, why would anyone ever want to change basis? Do eigenvalues have to do with changing basis?
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### Gauss: The study of Euler's works…

I keep coming across this quote by Gauss but I haven't actually been able to locate the original source: “The Study of Euler’s works will remain the best school for the various fields of mathematics ...
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### Good book for self study of Continued Fractions

Does anyone have a recommendation for a rigorous while readable book to use for the self study of continued fractions? PS - As examples of "rigorous while readable book" for self-learning, A. ...
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### Is a Quotient the number of times one value fits inside another, or the value of one of the groups produced by the operation

My question is a simple one, but one I haven't been able to figure out through research. When a simple division is performed suppose 10/2 = 5, is that 5 classified as the frequency or the number of ...
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### Why are we interested in cohomology?

I've been studying algebraic topology for over half a year now and came across alot of different topics of it (fundamental groups, Van Kampen, singular homology, homology theory, Mayer Vietoris, ...
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### Importance of guide/advisor in a PhD [closed]

I am really in a fix in my career. I completed my Masters in 2014. I qualified in a PhD Scholarships Test in 2015 and in the same year joined in a University for research work. My interest lies in ...
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### hyperbolic spaces and fractals

Is there a relation between hyperbolic spaces and fractals? In group theory, if we take the Cayley graph of a free group on two generators, we get a fractal quaternary tree, which I'd like to think as ...
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### Recommendations: Any Good books to study Path-Integration from 0 again?

I was researching and talking with some friends about I want to start from zero studying path integral, this question, and they recommended I start by studying "Quantum Mechanics and Path Integrals". ...
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### Soft question on the notion of connections

We have met the notion of connection in different places: 1.For a vector bundle $E\to M$,a connection is defined to be a way of diffentiating a section of $E$ along a vector field of $M$,by which we ...
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### what broad topics in game theory are likely discussed when you say 'game-theoretic analysis' of something?

I actually do not know anything about game theory, and in my current research I think I need to start knowing what it is all about. In the meantime, I always read papers that say they did a 'game-...