# 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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### Things you've believed for a long time were true, but are false in reality [duplicate]

Do you have any things (mathematical statements, statements about mathematics) you've believed for a long time were true, but now with enough mathematical knowledge you realize were wrong? For ...
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### Is $0$ the midpoint of $(-\infty,+\infty)$?

Is $0$ the midpoint of $(-\infty,+\infty)$? Intuitively, I'd think so, and trying to refine my intuition as to why I'd think so, I would say that this is the case because there is a one-to-one ...
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### Books and/or online resources on solving problems.

What are some good resources(online, books) that teach you how to tackle difficult and ugly problems in higher math arranged by subjects(analysis, topology, ODEs, groups etc) or topics(polynomials, ...
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### Starting Calculus with a weak foundation in Pre-Calculus

I am struggling in Pre-Calc mathematics, and I want to know is it ok if I start Calculus I with a weak foundation in Pre-calculus mathematics? I understand the general gist of limits, function ...
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### good lecture series for complex analysis?

I was wondering if i could teach myself complex analysis. Any good lecture series out there on the internet available for free (preferably)? One that would be suitable for an undergraduate student?
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### Low Level Books on Conjectures/Famous Problems

I am currently an undergraduate math/CS major with coursework done in Linear Algebra, Vector Calculus (that covered a significant amount of Real 1 material), Discrete Math, and about to take courses ...
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### What do people mean by “(this piece of maths) is hard/difficult”?

Sometimes when I talk to my maths professors, they would say "this piece of maths (e.g. differential geometry) is hard". What do they exactly mean by "hard" (difficult) - when clearly they're the ...
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### How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
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### What languages to learn for maths? [closed]

For people with "hands-on" experience in mathematical research, what languages are the most beneficial to learn? I know that many graduate programs require some degree of non-native lingual ...
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### Evolution of Relations

In Frege, one finds relations treated as predicates in complex terms. However, modern set theory appears to treat them as two-place relation. Is this correct? If so, when did this shift occur and to ...
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### contact point and point of intersection

I am just unable to understand the definitions of contact point and point of intersection.My doubts can be summed up into the following two questions : 1) Suppose $f(x)=x^2$ and $g(x)=0$ are two ...
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### Path to Differential Geometry

What do I need to learn to start on the rigorous study of differential geometry? I'm about to start my 3rd undergrad year at school, and have taken Cal 1-3, Linear Algebra, Elementary Number Theory, ...
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### How does one explain basic probability theory to a layman?

I have recently been involved in a number of discussions with people with little or no background in mathematics when we considered a problem of the following shape. A random event is going to ...
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### Less Terse alternative to Advanced Calculus by Folland.

I am currently in an advanced calculus class in university. We use Advanced Calculus by Folland. When I try to follow along the book I find that it is not verbose enough, and has too few examples. I ...
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### What level of rigour is expected in Real Analysis?

I fail to find a duplicate. I am wondering what level of rigour is needed in a typical undergraduate course in Real Analysis. To clarify my question, I provide an exercise from Rudin and my proposed ...
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### How can I know which theorem to use to prove another one?

In class this year a part of what we do is re learning theorems etc from previous years, but a more rigorous way. However, when I suggest a way to prove those theorems/properties/..., I often get an ...
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### Relations between definite integrals not having a known closed form

Are there any known cases, when there are two (or more) definite integrals, none of them having any known closed-form expression on its own, but there is still a non-trivial$^\dagger$ elementary ...
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### Is the exclusion of uncountable additivity a drawback of Lebesgue measure?

A friend and I were having a discussion about Lebesgue measure. I attempted to be profound by making the following points: Analytic geometry has been a fantastic tool, but the concept of ...
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### Why is a straight line the shortest distance between two points?

The first application I was shown of the calculus of variations was proving that the shortest distance between two points is a straight line. Define a functional measuring the length of a curve ...
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### Why are all non-polynomial functions are basically exponents?

There's paucity of really "original" functions in Math. Aside from power functions/ polynomials, really the only other function widely used is exponential. For example, $\log$ is simply inverse of ...
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### The role of 'arbitrary' in proofs

Generally, when one is going to prove a result regarding a set of elements, they begin their proof with those first few pleasing words: "Suppose...is an arbitrary element in..." My question is, why ...
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### Follow up to Pinter's abstract algebra

I wanted to learn abstract algebra this summer so I bought Pinter's A book of Abstract Algebra. I was planning on reading it over the course of the summer, but just finished the last problem of its ...
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### Are there high performance computing applications for symbolic integration?

Currently there are a number of applications for numerical integration in applied mathematics and physics. Many of these are integral transforms (often Fourier or Laplace), or solving definite ...
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### Most dificult concepts in mathematics [closed]

(Sorry, last soft question!) Borwien, in The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, (probably quite rightly) says of the Riemann Hypothesis, that No layman has ever ...
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### What was the book that opened your mind to the beauty of mathematics? [closed]

Of course, I am generalising here. It may have been a teacher, a theorem, self pursuit, discussions with family / friends / colleagues, etc. that opened your mind to the beauty of mathematics. But ...
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### Varying definitions of symmetric and selfadjoint operators

There seems to be some disagreement (at least when consulting textbooks), what constitutes a symmetric operator and what constitutes a selfadjoint operator (of course, only the unbounded case is of ...
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### Trying to translate the paper “COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS” by J P Loday J Alg (54) 178, 1978

I am trying to translate the paper "COHOMOLOGIE ET GROUPE DE STEINBERG RELATIFS" by J P Loday J Alg (54) 178, 1978 using google traslator. In section 1, he writes Un morphisme d’extensions relatives ...
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### Name of quantity that is not invariant, but only changes in one direction

How do you call a quantity that is not an invariant, but only changes in one direction during the process? Example: The degree of the polynomials go down when Euclidean division is applied, so the ...
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### Anyone worked with this particular orthogonal matrix

In my recent studies of quaternions, the following orthogonal matrix has come up. For example, it is related to the matrix representation of quaternion multiplication. Has anyone seen it come up in ...
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### Mathematical research of Pokémon

In competitive Pokémon-play, two players pick a team of six Pokémon out of the 718 available. These are picked independently, that is, player $A$ is unaware of player $B$'s choice of Pokémon. Some ...
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### Are there categorifications of prime or irreducible elements (of a ring, say)?

I'm very sorry if this is a duplicate in any way or is otherwise a stupid question. I've looked around (for quite a while) but . . . no luck. There's a categorification of what it means to be an ...
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### What background is required to understand Random Matrix Theory

I would like to be able to understand RMT but after "reading" many articles I have found that I have a limited capacity. I just see complicated equations. I guess I know linear algebra, classical ...
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### Pythagorean like theorem for general spaces

There are laws, for example Pythagorean theorem, for calculating distance of two points, say $d(a,b)$, using third point and knowing $d(a,c)$ and $d(c,b)$ in vector spaces. My question is that for ...
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### having great difficulty in understanding long math problems ! any advices !!! please [closed]

I'm not an English origin I'm good at direct math exercises But I'm having great difficulty in understanding long math problems Such as described below Which contains many sentences and many terms ...
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### Abstract Objects in Logic

I am confused on the concept of extensionality versus intensionality. When we say 2<3 is True, we say that 2<3 can be demonstrated by a mathematical proof. So, according to mathematical logic, ...
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I read this question How can Zeno's dichotomy paradox be disproved using mathematics? . The first (ie the one on the top) answer uses the fact that $\sum\limits_{n=1}^\infty\frac{1}{2^n}=1$, ...
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### Where should I go for translations of mathematical texts?

I am currently trying to read Applications algébriques de la cohomologie de groupes. II: théorie des algèbres simples by J-P. Serre. It is very hard for me to read this article since I'm not a native ...
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### Is Courant's Introduction to Calculus and Analysis still up-to-date?

I just found this marvelous book and I think that it's the best book in this category, but I'm worried that it is not up-to-date. I've heard that Hardy's A Course of Pure Mathematics has some switched ...
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### Book series like AMS' Student Mathematical Library?

I had the joy of discovering AMS' Student Mathematical Library book series today, and I have been pleasantly surprised by how enticing some of the titles seem: exciting and expositionary, a perfect ...
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### Book ref. request: “…starting from a mathematically amorphous problem and combining ideas from sources to produce new mathematics…”

I couldn't find Charles Radin's Miles of Tiles at the local university library or the public library, and cannot afford its Amazon price right now. Thus, while sorely disappointed for the moment, I ...
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### How can I choose the best algorithm to integrate ODE's numerically?

I have studied in a course several algorithms to integrate ODE's numerical: Runge-Kutta, Predictor-Corrector methods, Taylor... However the teacher failed to show which is the best for every ...
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### I want to learn math from ground-up, basic to advanced, beginner to expert

I want to learn math. I've learned math long time ago, but i hardly remember anything. I really want to relearn but have no idea where to begin. I want to learn math by reading through good books, ...