# Tagged Questions

The process of studying mathematics without formal instruction. _Don't_ use this tag just because you were self-studying when you came across the mathematical question you're asking; it is only for when the fact that you're self-studying is what your question is _about_.

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### What are the books that I should study for college? [closed]

Baccalaureate exam approached Real Analysis (limits, differentiation and integration), Abstract Algebra, Functional Algebra, Linear Algebra, Combinatorics, Complex numbers, Vector Geometry, Analytical ...
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### Non-Inductive formula for subdivision operator

This problem is from hatcher 2.1.25. Find an explicit, noninductive formula for the barycentric subdivision operator. I have no idea how to get that formula. The only way I see it geometrically is ...
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### A very detailed book for calculus 1-3.

Is there a very good book covering the whole calculus in detail, explaining all topics in calculus 1-3 for self-learning? I'm in geometry I, so I will start calculus in two years, and finish in five ...
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### Prove the continuity on an open interval

I need to show, that function $f(x) =\frac{2x +3}{x-2}$ is continuous on the interval $(2,\infty)$ My attempt: We should find the right-hand limit to prove the continuity: and this limit is equal to ...
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### What exactly does f'(x)=0 imply from the definition of differentiability?

Let f be a real valued function satisfying $|f (x) −f (a)| ≤ C|x−a|^γ$, for some γ > 0 and C >0. (a) If γ = 1, show that f is continuous at a; (b) If γ > 1, show that f is ...
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### What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
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### Showing $\mathbb{Q} \times \mathbb{Q}$ is not a field

I am revising and have come across the question Show that $\mathbb{Q} \times \mathbb{Q}$ with element-wise addition and multiplication is not a field I don't understand how to go about this, do i ...
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### How should one without any university mathematics background study mathematical logic?

How should someone who hasn't studied any math at a university level start studying mathematical logic? (There are already questions like this but they mostly focus on book recommendation for people ...
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### Does equality of the sum of two such series imply equality of each term of that series?

Let a(1)< a(2) < ..< a(m) and b(1)< b(2)<..< b(n) be real numbers such that $$\sum_{i=1}^m |a(i)-x| = \sum_{j=1}^n |b(j)-x|$$ for all x belonging to R. Show that m=n and a(i)=b(i),...
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### Find dimension of a Vector Space.

Let $E=\{1,2,\ldots,n\}$, where $n$ is odd. $V$ is the vector space of all functions mapping from $E$ to $\mathbb R^3$. Find $\dim(V)$. Consider $T:V\to V$ such that $$Tf(k)=[f(k)+f(n+1-k)].$$ ...
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### Are there powerful ways to use the topological definition of continuity in real analysis?

In the lectures for introductory real analysis, my professor repeatedly told the class that the topological definition of continuity (preimage of open is open) is the most powerful version of ...