# Questions tagged [self-learning]

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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### Proof Validation: Let $f: A \to B$. Then $f^{-1}f$ is the identity on $\mathcal{P}(A)$ if 1-1, and $ff^{-1}$ the identity on $\mathcal{P}(B)$ if onto.

I am attempting some self-learning of proof based texts, and I'm a little confused on what's "allowed". Specifically, I am trying to prove the below claim, and I am unsure about a few steps ...
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### Is it worthwhile to redo problems where an arithmetic mistake has been made?

When learning new concepts in math, is it worth my time to redo problems if my mistakes were purely arithmetic mistakes (or very simple algebra mistakes)? If I made sign errors, or added fractions ...
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### Verifying Proof: If $L$ is a poset with a bottom element, and $\exists \sup(S)$ for every subset $S \subset L$, then $L$ is a complete lattice

I am currently working through Kaplansky for self study and was hoping to get some feedback on this proof. I would appreciate comments on clarity and legability as well. Claim: If $L$ is a poset with ...
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### Study multiple subjects at the same time or deep dive into one?

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense ...
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### Learning Mathematics: unique knowledge of math.

I've come to a point where I now more fully (like 99%) understand that math is about specialized/unique knowledge which can't be summarized by some grand scheme or united principle. So my question is, ...
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### find the pure strategy Nash equilibrium with 3 players

There are three players and each stakes 10 dollar. The players simultaneously choose a number from the set {1, 2, 3, 4}. If three numbers are different, the player choosing the middle number wins the ...
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### Find the Nash equilibrium for the given question

Consider there are two players in a simultaneous game. Each of them chooses and pays integer multiples of one dollar to play the game. The player with the highest bid wins 100 dollar and the loser ...
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### Verifying examples of definition of field extension

Let K be a field containing F as a subfield, written as $K/F$. Call $F$ the base field of $K/F$ and $K$ the extension field of $K/F$. Definition: Let $K/F$ be an extension of fields. K is a vector ...
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### Is the following sentence contrapositive of the sentence “If it's spring, the birds will sing”

I need to find the contrapositive, which is "If the birds do not sing, it is not spring" But if it's written like, "If it's not spring, the birds will not sing", can this be ...
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### Creative approoach to understanding advanced math notation

I was very pleased when I saw Hilbert curves and as a student I am interested to learn advanced mathematical concepts such as Hilbert spaces in an interesting and creative way. In many papers I am ...
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### Calculate if an expression is uniformly lower than another?

I have two expressions $$\frac{2}{n-1} \quad \text{and} \quad \frac{2n-1}{n^2}$$ and I need to prove that $$\frac{2n-1}{n^2} < \frac{2}{n-1}$$ for all $n \in \{2,3,\ldots\}$. How can I do this?
### area to the right of $r\cos\theta=6$ and $r=10$
I have been trying to solve this question for a while and I seem to get stuck although it does not seem hard Given $r\cos\theta=6$ and $r=10$ we need to find the area inside the circle and on the ...
Given a group action of $G$ on $M$, we have the notion of the stabilizer of a point $m$ : $Stab_G(m)=\{g \in G | g(m)=m \}$ , and we could extend this to a definition of the stabilizer of a generic ...