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109 votes

Studying for the Putnam Exam

big-list contest-math self-learning learning asked Feb 16 '13 at 19:28
math.stackexchange.com

84 votes

Cute Determinant Question

linear-algebra determinant asked Jun 8 '12 at 3:45
math.stackexchange.com

52 votes

Why the emphasis on Projective Space in Algebraic Geometry?

algebraic-geometry intuition riemann-surfaces teaching projective-space asked Nov 24 '11 at 23:04
math.stackexchange.com

46 votes

A $\{0,1\}$-matrix with positive spectrum must have all eigenvalues equal to $1$

linear-algebra eigenvalues-eigenvectors alternative-proof asked Dec 20 '12 at 1:01
math.stackexchange.com

43 votes

What is the importance of the infinitesimal generator of Brownian motion?

probability-theory stochastic-processes brownian-motion markov-process asked Feb 28 '14 at 17:19
math.stackexchange.com

41 votes

Find $f(x)$ such that $f(f(x)) = x^2 - 2$

contest-math functional-equations asked Sep 1 '13 at 3:13
math.stackexchange.com

40 votes

Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?

linear-algebra matrices trace asked Feb 22 '13 at 22:28
math.stackexchange.com

37 votes

What is the modern axiomatization of (Euclidean) plane geometry?

geometry reference-request euclidean-geometry axioms asked Nov 10 '11 at 20:07
math.stackexchange.com

35 votes

How to resolve Simpson's paradox?

simpsons-paradox asked Dec 2 '13 at 1:39
stats.stackexchange.com

34 votes

Square matrices satisfying certain relations must have dimension divisible by $3$

linear-algebra matrices contest-math asked Feb 10 '13 at 19:59
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Top Answers
157
Can an irrational number raised to an irrational power be rational?
math.stackexchange.com

48
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$
math.stackexchange.com

39
Are most matrices invertible?
math.stackexchange.com

33
Find $A^{1000}$ by using Cayley-Hamilton Theorem
math.stackexchange.com

23
How to define a bijection between $(0,1)$ and $(0,1]$?
math.stackexchange.com

21
Prove that transcendental numbers exist: Are there less paniful ways of doing it?
math.stackexchange.com

21
Is $3 \ge 1$ or is it just $3 > 1$?
math.stackexchange.com

20
Probability of 3 Heads in 10 Coin Flips
math.stackexchange.com

20
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
math.stackexchange.com

20
Very good linear algebra book.
math.stackexchange.com

18
why 0=0 is not possible??
math.stackexchange.com

18
Prove properties of $A^2 = -I$
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18
Best Fake Proofs? (A M.SE April Fools Day collection)
math.stackexchange.com

15
Is there any mathematical or physical situations that $1+2+3+\ldots\infty=-\frac{1}{12}$ shows itself?
math.stackexchange.com

15
Good motivation for the introduction of Lebesgue integral?
matheducators.stackexchange.com

14
Prove that $\frac{b^2+c^2}{b+c}+\frac{c^2+a^2}{c+a}+\frac{a^2+b^2}{a+b} \ge a+b+c$
math.stackexchange.com

14
Is there a non-constant smooth function mapping $\mathbb{R}$ into $\mathbb{Q}$
math.stackexchange.com

14
Show that holomorphic $f_1, . . . , f_n $ are constant if $\sum_{k=1}^n \left| f_k(z) \right|$ is constant.
math.stackexchange.com

13
If $\int_0^1 f(x)x^n \ dx=0$ for every $n$, then $f=0$.
math.stackexchange.com

13
Are there any books that take a 'theorems as problems' approach?
mathoverflow.net

13
Is there a power series which converges to $f(x) =| x|$ for all $x$?
math.stackexchange.com

12
$\sum\limits_{\text{prime }p} 2^{-p}$ is an irrational number
math.stackexchange.com

10
If $AB=BA=0$ and $A+B$ is invertible, is $A-B$ invertible?
math.stackexchange.com

10
Initial and terminal objects in $\textbf{FinVect}_R$
math.stackexchange.com

10
Branch cut for $\sqrt{1-z^2}$ - Can I use the branch cut of $\sqrt{z}$?
math.stackexchange.com

10
Continuous and additive implies linear
math.stackexchange.com

9
Research done by high-school students
math.stackexchange.com

9
Bijective holomorphic map
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9
Definition of neighborhood and open set in topology
math.stackexchange.com

9
Is there a field extension over the real numbers that is not the same as the field of complex numbers?
math.stackexchange.com

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