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47 votes
7 answers
4k views

When working proof exercises from a textbook with no solutions manual, how do you know when your proof is sound/acceptable?

47 votes
1 answer
2k views

What did mathematicians study as an undergraduate/graduate before modern mathematics such as modern algebra and analysis?

40 votes
2 answers
48k views

What exactly is the difference between weak and strong induction?

21 votes
8 answers
53k views

Calculator similar to Desmos but for $3$D

20 votes
4 answers
2k views

Is the number $333{,}333{,}333{,}333{,}333{,}333{,}333{,}333{,}334$ a perfect square?

16 votes
2 answers
759 views

Do quotient rings have geometric meaning, or geometric intuition?

15 votes
5 answers
1k views

Is 'Algebraic Number Theory' the study of the theory of algebraic numbers, or is it the study of the theory of numbers from an algebraic viewpoint?

13 votes
5 answers
1k views

How many prime numbers are there in between $1000!+1$ and $1000!+1000$, inclusive?

10 votes
1 answer
1k views

If continuity preserves convergence, and Cauchy sequences are convergent sequences, why do we need uniform continuity to preserve Cauchy sequences?

9 votes
4 answers
5k views

Is every Closed set a Perfect set?

9 votes
2 answers
4k views

Let $G$ be a group, and $H$ a subgroup of $G$. Let $a, b \in G$. Prove $Ha=Hb$ iff $ab^{-1} \in H$.

8 votes
2 answers
2k views

Prove in any integral domain, if $a^2=b^2$ then $a=\pm b$

8 votes
2 answers
7k views

Prove every maximal ideal of $A$ is a prime ideal (Hint: Use the fact that $J$ is a maximal ideal iff $A/J$ is a field.)

8 votes
1 answer
19k views

Difference between parentheses and angle brackets in vector notation

8 votes
1 answer
545 views

How does this nursery rhyme pertain to power series: “There was a little girl Who had a little curl Right in the middle of her forehead..."

7 votes
1 answer
2k views

Let $G$ be a $p$-group: $|G| = p^r$. Prove that $G$ contains a normal subgroup of order $p^k$ for every nonnegative $k \le r$.

7 votes
2 answers
138 views

Minimal polynomial of $\sqrt{3+2\sqrt{3}}$

7 votes
2 answers
4k views

Give an intuitive explanation for polynomial quotient ring, or polynomial ring mod kernel

7 votes
2 answers
917 views

Should I study projective geometry or commutative algebra as prerequisite to start algebraic geometry?

7 votes
4 answers
347 views

If $\{q_\alpha: X_\alpha \to Y_\alpha\}$ is a family of quotient maps, then $q:\coprod_\alpha X_\alpha \to \coprod_\alpha Y_\alpha$ is a quotient map.

6 votes
1 answer
327 views

How does $\mathbb R^n\setminus \{0\}$ being simply connected follow as a corollary from $\mathbb S^{n-1}$ being a strong deformation retract?

6 votes
2 answers
2k views

Let $a$ be an element of order $n$ in a group $G$. If $a^m$ has order $n$, then $m$ and $n$ are relatively prime.

6 votes
2 answers
256 views

How do I formally show that the Zariski tangent space of the intersection of two closed subschemes is the intersection of the tangent spaces?

5 votes
0 answers
85 views

Exercise $\textrm{3.2.O}$ from Vakil's notes on AG: Is this statement/picture correct? How to interpret a map of spaces as a map between Spectrums?

5 votes
2 answers
248 views

If $R$ is a reduced Noetherian ring, then every prime ideal in the total quotient ring $K(R)$ is maximal.

5 votes
2 answers
615 views

How to prove finite abelian group is direct sum of cyclic groups by using matrices over Euclidean domain?

5 votes
3 answers
397 views

Is there a name for categories whose objects are sets?

5 votes
3 answers
206 views

If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?

5 votes
3 answers
518 views

What is the fibered coproduct of abelian groups?

5 votes
0 answers
172 views

Can we find the GCD of two polynomials in $\mathbb Q[x]$ by representing the coefficients as vectors?

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