Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [soft-question]

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.

For questions whose answers cannot be objectively evaluated as correct or incorrect, but which are still relevant to mathematics.se.

12079 questions
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Contour Integrals, why give them a name?

I must ask because I can't find an answer, it's a bit of a soft question and for that I apologise. Why are they called contour integrals? In all the subheadings I've checked there is no special reason. My "guess" is that a contour cannot cross…
Alec Teal
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Is it bad for a potential grad schooler to take Abstract Algebra and Real Analysis my last year?

I'm taking Abstract Algebra and Real Analysis my last year. I've already taken the following: Calc 1-3 DiffEQ Complex Analysis Operations Research Linear Algebra Mathematics Foundations Theory of Numbers Advanced Stasticis I'm worried that grad…
user142883
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What should I study to understand knot theory?

I want to ask for some advice :) I am aware that it might be a little early to get interested in specific areas/subareas at his stage, but the theory of knots interests me a lot. I've went through PMA, topology at the level of Munkres and 《Basic…
user48078
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Differential in Math

Differential is a term, I first learned, in Mathematics Analysis. Now I have some problems about this term: (1) Can we generalize differential to norm space? (2) Can we generalize it into topological linear space? (3) Can we generalize it into more…
gaoxinge
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Rules for modulus of a (|a|)?

So I am wondering about this statement: $|a| = a$ if $a \le 0$ and $-a$ if $a<0$ Why is it $-a$ if $a<0$? Shouldn't the modulus always be positive?
Sab ಠ_ಠ
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How should pen-significance be distributed?

At present, when POTUS ceremoniously signs an important bill, he typically does so with a multitude of pens, rendering each stroke of his signature with a different pen. These pens are later handed out to those present who had important connections…
Senex Ægypti Parvi
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Validity of Problem Solving Methods

I was in class the other day, and I was suddenly concerned with the idea that some methods don't work for solving certain problems. I'm working on integration right now, so some of the problem solving methods that I'm talking about involve…
Adam
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Help finding an area for my Masters

Next year I will be doing my MSc. in mathematics at the University of Toronto. I, however, am not sure whether after I will want to pursue my PhD. or not. So I was wondering what branch of mathematics would be good to study for my MSc. if I am…
ndege
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Is the cesaro sum any less valid than the formal sum? (And the arbitrary nature of mathematics.)

The title basically says it all. I've just watched a video explaining (without any formal definitions) that the 'sum' of the natural numbers is equal to -1/12. Now, the more I read about mathematics the more it seems to be quite arbitrary - but then…
Tito
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Can anyone recommend books for self learning calculus which focus on developing understanding?

I am trying to learn a little basic mathematics by myself with help from a few books and this site. So far I have read 3 excellent books: Algebra, Trigonometry and Method of Coordinates by Gelfand et al. Since finishing them I am left wondering what…
mikoyan
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Big oh property

Suppose that $f(x)$ and $g(x)$ are two non negative functions and suppose that $$f(x)=O(g(x)).$$ Can we conclude that $$-g(x)=O(-f(x)) ?$$ I think is false but i'm not sure. Thank you and sorry for this dumb question.
user42503
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Question about equation

I have a basic question. If I have an expression(Polynomial,logarithm,etc.) and it is told to me it's an equation, but it's is not written to what it's equal to, do we consider it by convention equal to 0 ??? For a certain reason, I don't remember…
user108343
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General questions about grad school, REU's, etc from a freshman

I am a freshman at a top-20 university majoring in math. My dream is to be a college professor. I am currently taking a combined multivariable calc/linear algebra class restricted to freshmen. It is very proof intensive and is supposedly considered…
Jimbo James
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Is differential geometry useful for algebra?

Is differential geometry useful for algebra? Or are they not very related? I don't need a complicated answer; I just want to know if it would be useful for learning algebra. Thanks in advance
user58289
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How can one avoid small errors and mistakes in easy calculations.

I have a problem for a long time now which is I always make small stupid errors and mistakes in calculations when the question is easy or. This issue caused me a lot of problems in exams that I was known for having bad grades when the exam is easy…
pie
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