| MathSE ID Math Question Tag
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| 2488771 What is the general formula for the coefficient of $x^k$ in the expansion of the trinomial $(1+x+x^2)^n$? Unambiguous
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| 746518 How do I do question 8(i) in this picture? I have $x=\delta\tan(\theta)$, but I'm not sure how to turn this into a PDF. Ambiguous
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| 215089 Subset of Power Set of Natural Numbers Ambiguous
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| 219343 How can I Prove that $[(p \to\neg q) \wedge q] \to \neg p$ is a tautology? Ambiguous
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| 1054529 What is the purpose of mathematical induction in proving statements about integers? Unambiguous
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| 1898365 What are the properties of the tensor product of two abelian groups? Unambiguous
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| 2274060 If $x$ and $y$ are positive real numbers, what is the minimum value of the expression $(x+y)\left(\frac{1}{x} + \frac{1}{y}\right)$? Unambiguous
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| 3198849 Evaluate the limit as $x$ approaches $0$ of $(sin(x) - x) / x^3$ using power series without L'Hospital's Rule. Unambiguous
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| 1779361 How to prove $\cos^4x - \sin^4x - \cos^2x + \sin^2x$ is always $0$? Ambiguous
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| 2152735 "What does ""open set"" mean in the concept of a topology?" Ambiguous
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| 1101966 Provide a step-by-step proof that the definite integral $\int_0^1 \frac{x^3\arctan x}{(3-x^2)^2\sqrt{1-x^2}} \, dx$ equals $\frac{\pi\sqrt{2}}{192}(18-\pi-6\sqrt{3})$. Unambiguous
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| 160327 What is the mathematical symbol for the universal quantifier 'for every element' in predicate logic? Unambiguous
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| 2596764 If a differentiable function $f: \mathbb{R} \to \mathbb{R}$ satisfies $\lim_{x \to \pm\infty} f(x) = -\infty$, must the function have a global maximum? Unambiguous
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| 590489 What are some topologies that work on functions? Ambiguous
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| 1761660 How to proceed from the discriminant $1+4y(y+a)\geq 0$ to find the number of integral values of $a$? Ambiguous
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| 279233 Is $m^4+4^n\equiv 1\pmod 8$ an iff condition? Ambiguous
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| 769619 For which Banach spaces $X$ is the closed unit ball of the dual space $X^*$ strictly convex? Unambiguous
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| 3806534 If $\lim_{x\to 0}\left(f(x)+\frac{1}{f(x)}\right)=2,$ show that $\lim_{x\to 0}f(x)=1$. Ambiguous
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| 1890614 What are the mathematical definitions of infinity in set theory and calculus? Unambiguous
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| 217291 How do I find the mathematical expressions for the red and green lines in my image to put into pgfplots? Ambiguous
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| 1726540 How do I find the derivative of the function $f(x) = x^{1/x}$ with respect to $x$? Unambiguous
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| 1409828 How to get the center point of the red area where my ellipses intersect? Ambiguous
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| 1568161 Evaluate the limit as $x$ approaches $\pi$ of $\frac{(\pi - x) \sin(x)}{1 + \cos(x)}$. Unambiguous
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| 884228 For the density f(x) = 1/(b-a) on [a,b], what is R(t)? Ambiguous
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| 2170954 Let $p(n)$ denote the productivity of the most productive $n$-state Turing machine, where productivity is the length of the output string if the machine halts in standard position and $0$ otherwise. Prove that $\forall n\, [p(n+11) \ge 2n]$. Unambiguous
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| 2657826 Given $P(x) = ax^3 + 3x^2 + bx + 3$ with $P(1) = 0$ and remainder $15$ when divided by $(x-2)$, find $a$ and $b$, and solve the inequality $P(x) \le 0$. Unambiguous
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| 2426632 What is the difference between curvature and torsion for a space curve in differential geometry? Unambiguous
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| 571232 Show that a natural number $a$ with base-$10$ representation $(r_k r_{k-1}\cdots r_1 r_0)_{10}$ satisfies $4 \mid a$ if and only if $4 \mid (r_1 r_0)_{10}$. Unambiguous
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| 2007373 Basic Geometric intuition, context is undergraduate mathematics Ambiguous
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| 541081 In the Martingale betting strategy, when is it mathematically optimal to stop doubling down on losses? Unambiguous
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| 2323384 equation of common tangent touching circle and the parabola Ambiguous
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| 1594324 Find all real numbers x such that $|x|<x$. Unambiguous
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| 1902450 What is an easy way to prove that the integral of $\frac{1-y^2}{(1+y^2)^2} \, dy$ equals $\frac{y}{1+y^2} + C$? Unambiguous
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| 43945 What is a shortcut method for calculating the probability distribution of a 1D symmetric random walk after $n$ steps? Unambiguous
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| 3151361 Prove that $\sqrt{7} + 2\sqrt{5} < 2 + \sqrt{35}$ for positive real numbers. Unambiguous
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| 2887105 How do I write $\dfrac{1}{1-i-z}$ as the sum of a series? Ambiguous
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| 92962 Suppose $a$ is a number, and for some $n$, $a^n$ and $(a+1)^n$ are both rational. Is $a$ rational? Ambiguous
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| 1285663 Area of region inequality Ambiguous
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| 1537426 Is it true that sums of several roots are never integers? Ambiguous
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| 2007946 Why don't the limits for the angles both go up to $2\pi$ in this integral? Ambiguous
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| 1214106 Find all polynomials satisfying a certain functional equation involving $x^2-y^2$. Ambiguous
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| 1372825 What is the numerical value of the improper integral $\int_0^{\infty}e^{-t^2 /100} \sin(\pi t) dt$? Unambiguous
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| 2540002 Prove that for any $\sigma > 0$ and $N \in \mathbb{N}$, the sum $\sum_{i=0}^{N} \frac{1}{\sqrt{2\pi\sigma^2}} e^{-(i+0.5)^2/(2\sigma^2)} < 0.5$. Unambiguous
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| 3984395 How to prove my integral $\Gamma(x)$ decays exponentially bounded by $A_d e^{-|x|/L}$? Ambiguous
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| 1524225 Find the least $n$ such that the expression is divisible by $700$. Ambiguous
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| 685435 How can I find an upper bound for the remainder term of the Riemann zeta function series for $\zeta(2)$ after $n$ terms? Unambiguous
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| 4841809 Why is it a problem that the echelon form isn't unique? Ambiguous
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| 612241 Evaluate $\lim_{x\rightarrow 0} \frac{\sin x}{x + \tan x} $ without L'Hopital rule. Unambiguous
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| 2617141 Why is the equation of a circle not a function of $x$, and how do I show this algebraically using the vertical line test or solving for $y$? Unambiguous
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| 44348 Simplify $||x-5|-10|<\epsilon$. Ambiguous
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| 483708 How to prove the identity $\frac{\eta^{14}(q^4)}{\eta^{4}(q^8)}=4\eta^4(q^2)\eta^2(q^4)\eta^4(q^8)+\eta^4(q)\eta^2(q^2)\eta^4(q^4)$ where $\eta(q)$ is the Dedekind eta function? Unambiguous
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| 571232 How do I show that 4|$a$ iff 4|($r_{1}$$r_{0}$)$_{10}$? Ambiguous
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| 1896418 For $n\ge5$ points in the plane with no four collinear, find a closed-form expression for $f(n)$, the maximum number of points guaranteed such that no three of them are collinear, over all such configurations. Unambiguous
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| 3330117 Limit involving prime and composite numbers Ambiguous
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| 3390858 Find the range of values of $k$ for which $kx^2 + 8x + k <6$ for all real values of $k$ Ambiguous
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| 4726367 How do people create trigonometric questions from scratch? Ambiguous
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| 1025196 Let $f:[-1,1]\to\mathbb{R}$ be continuous with $f(-1)=f(1)$. Prove that there exists $y\in[0,1]$ such that $f(y)=f(y-1)$. Unambiguous
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| 4351550 Intersection of perpendicular bisector and circle in a triangle. Ambiguous
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| 3026909 How many presentations are there for $D_8$ using permutations, and can it be done with other groups? Ambiguous
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| 4734106 Are there numerical approximations or algorithms for computing the square root of a number that are computationally faster than the standard library function? Unambiguous
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| 1730258 What is the formula for the arc length of a parabola given by $y = ax^2$ from $x = 0$ to $x = b$? Unambiguous
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| 2092731 Find the radius of convergence of $\sum_{n=1}^\infty \frac{(3n+1)^{10}x^n}{2n^n}$ using the root test. Unambiguous
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| 2587259 How many permutations are there for a 9-player baseball batting order? Unambiguous
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| 215332 Coefficent of an equation Ambiguous
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| 3149675 Open ball in $M=\mathbb{R}\setminus\{-1,1\}$ Ambiguous
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| 2669535 I can show that $\overline{R(A')} \subseteq N(A)^{\perp}$, but I'm not sure how to prove the converse using the fact that $R(A)$ is Banach. Ambiguous
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| 1150363 Is the real number $\pi$ equal to the angle $180^\circ$ in terms of their numerical value? Unambiguous
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| 1810374 How many distinct 7-note musical scales can be formed by choosing subsets of notes from the 12-note chromatic scale? Unambiguous
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| 1745083 What is the optimal path between $2$ fixed points around an invisible obstructing wall? Ambiguous
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| 360449 What does $x \ne y \ne z$ mean? Ambiguous
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| 2660495 Probability of Choosing Exactly 1 pair out of 4 Ambiguous
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| 4083792 Conditional expectation based on two bivariate normal RVs? Ambiguous
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| 3017130 How do you factorize the quadratic expression $m^2 + 2ABm + B^2$? Unambiguous
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| 348715 Evaluate the limit as $x$ approaches infinity: $\lim_{x \to \infty} \left( \sqrt{x^2+x} + 2\sqrt{x^2+2x} - x \right)$ Unambiguous
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| 4520880 Why does the distributive law not apply to the expression $2(2.49 \times 10^8)$ when there is only one term inside the parentheses? Unambiguous
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| 1114879 How to algorithmically detect if two ellipses in a 2D plane intersect? Unambiguous
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| 102524 Finding the formula of an nonlinear function Ambiguous
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| 2334855 What are the bounds of $$\frac{x+1}{xy+x+1}+\frac{y+1}{yz+y+1}+\frac{z+1}{zx+z+1}$$? Ambiguous
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| 1325994 What is the last digit of 347 raised to the power of 61 in base 10? Unambiguous
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| 956087 I found that y' = (1-y)/(x-2). How do I find the tangent line from here? Ambiguous
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| 3542957 What is the difference between $-i$ and $j$? Ambiguous
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| 68897 What are the properties and definitions of a symmetric positive definite matrix in linear algebra? Unambiguous
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| 188945 What are the epistemological and pedagogical disadvantages of relying exclusively on computer algebra systems for mathematical proof and computation compared to manual derivation? Unambiguous
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| 2894360 Provide a step-by-step proof to show that the equation $\frac{x + \frac{1}{2}}{\frac{1}{x} + 2} = \frac{x}{2}$ holds for all $x \neq 0, -\frac{1}{2}$. Unambiguous
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| 1513096 Prove that the stereographic projection of the upper hemisphere from the North Pole is orientation-preserving if and only if the dimension n of the sphere $S^n$ is even. Unambiguous
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| 2140493 Counterintuitive examples in probability Ambiguous
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| 3178233 Prove that there is $c \in (0,1)$ such that $e^{f'(c)}f(0)^{f(c)}=f(1)^{f(c)}$ Ambiguous
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| 1668681 An example that a 2D shape with its centre of mass on its boundary Ambiguous
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| 767709 How to show a function with $x^n$ is uniformly convergent on $[0,1]$? Ambiguous
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| 1040278 Nobody told me that self teaching could be so damaging... Ambiguous
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| 3772635 Find all real solutions to the system of equations $\sqrt{x} + y = 7$ and $x + \sqrt{y} = 11$. Unambiguous
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| 2431076 Prove that if $\sigma^r$ is an $n$-cycle for some permutation $\sigma \in S_m$, then $\sigma$ itself must be an $n$-cycle. Unambiguous
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| 2867689 For the equation $6x^2+8xy+4y^2+17y-6=0$, use implicit differentiation to find $\frac{dy}{dx}$, isolating all terms containing $\frac{dy}{dx}$ on one side. Unambiguous
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| 1901862 For what smooth functions is there a nice closed form for a certain exponential integral, invertible in terms of the upper limit? Ambiguous
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| 2445959 find all natural number such that $n-2\mid n^2-2$ Ambiguous
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| 982093 Proof for $\lim_{n \to \infty}(1+\frac{a_n}{n})^n = e^a$ given that the sequence $a_n$ converges to $a$ as $n \to \infty$. Unambiguous
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| 1554069 On a cubic curve $C$ defined by an elliptic curve group law, prove that the tangent at a point $P$ intersects $C$ at $P$ with multiplicity 2 and at the point $4P$, and that the tangent at $5P$ intersects $C$ at $5P$ with multiplicity 2 and at the point $2P$. Unambiguous
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| 3804598 In a building with elevators following uniform distributions, if the average wait time with two is 1 minute, what is it with one? Ambiguous
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| 128823 What is the limit of $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$ for a continuous function $f$ on $[0, 1]$? Unambiguous
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| 3570162 $\exists b\in S_2\ \forall a\in S_1: p(a,b)$ Ambiguous
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| 3024780 Given three points forming a triangle in the Cartesian plane, how do you calculate the coordinates of the Fermat point (the point minimizing the sum of distances to the vertices)? Unambiguous
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| 2062239 How to construct the polar decomposition for Wegge-Olsen Exercise 1.A.c? Ambiguous
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| 2599280 How to find $m$ and point $P$ for a tangent line without using differentiation at all? Ambiguous
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| 2538727 Show that the space $X = [0,1]^{[0,1]}$ (the set of all functions from $[0,1]$ to $[0,1]$ equipped with the product topology) is not sequentially compact. Unambiguous
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| 574475 Given the points $P=(2,1)$ and $A=(-1,5)$, find the correct parametric equations of the line through $P$ in the direction of $A$. Unambiguous
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| 2490647 What is the asymptotic behavior of the number of involutions on a set of n elements as n approaches infinity? Unambiguous
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| 2296759 How to prove $B$ is a symmetric matrix from its inner product? Ambiguous
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| 590489 What are the most common topologies used on function spaces, such as the compact-open and product topologies? Unambiguous
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| 3906075 Number of non-identity elements of order $2$ in this set. (Related to abelian group of order $34.$) Ambiguous
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| 1762325 Is the formula $\neg \neg p \rightarrow p$ a tautology in classical logic, and is it provable in intuitionistic logic? Unambiguous
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| 1222768 In the context of mathematical analysis, why are vector-valued functions considered well-defined functions, whereas multivalued functions are not considered functions in the strict set-theoretic sense? Unambiguous
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| 547928 What is the minimum value of $a+b+\frac{1}{ab}$ for positive real numbers $a, b$ such that $a^2 + b^2 = 1$? Unambiguous
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| 1051513 What is the probability that three of the selected items had values less than or equal to five? Ambiguous
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| 1405562 What is the method for calculating the remainder of a large integer when divided by a modulus (modular exponentiation or modular reduction)? Unambiguous
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| 1429993 What is the value of an infinite factorial tower? Ambiguous
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| 541081 When to stop doubling down? Ambiguous
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| 3962287 Find the Maclaurin series expansion of the function $y(t) = (t^2 + t - 2)e^{t^2 + 1}$ centered at $t = 0$. Unambiguous
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| 2332969 Find the radius of convergence of the power series $f(x) = \sum_{n=2}^\infty \log(n) x^n$. Unambiguous
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| 1695625 Does $h_{a,b}(x) = ((ax + b) \bmod 2^w)/2^{w-M}$ satisfy the Uniform Difference Property? Ambiguous
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| 2051197 Can someone explain this formula? Ambiguous
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| 602143 Find the area bounded by the curves $y=e^x$, $y=xe^x$, and $x=0$ Ambiguous
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| 1799824 Determine whether the function $f: \mathbb{R}^2 \to \mathbb{R}^2$ defined by $f(x,y) = (x^2-y^2, 2xy)$ is injective. Unambiguous
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| 1663192 Given a linear map with an associated matrix, with respect to which basis is the matrix representation taken? Ambiguous
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| 291038 Let $A$ and $B$ be a toeplitz and symmetric positive definite $NxN$ matrices. If $\kappa (A) > \kappa (B)$, how to show that: $$\kappa (B^{-1}A) < \kappa (A)$$ where $\kappa $(X) is condition number of matrix $X$? Unambiguous
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| 4095882 I have some people each performing repeated trials. How many will get at least a certain number of successes? Ambiguous
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| 526574 I need to know if every element is either countable or co-countable. Ambiguous
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| 1403539 $\arctan (x) + \arctan(1/x) = \frac{\pi}{2}$ Ambiguous
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| 4628757 Prove $\frac{ab^2+2}{a+c} +\frac{bc^2+2}{b+a} +\frac{ca^2+2}{c+b} \geq \frac{9}{2}$ for $a,b,c\geq1$ Ambiguous
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| 546701 Find the number of positive integers whose digits add up to 42 Ambiguous
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| 1475726 Locating three sets of collinear points Ambiguous
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| 2431076 How do I show that if $\sigma^k$ is an $n$-cycle, then $\sigma$ is also an $n$-cycle? Ambiguous
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| 536735 Find all functions $f: \mathbb{Q} \to \mathbb{R}$ that satisfy the Cauchy functional equation $f(x+y) = f(x) + f(y)$ for all $x, y \in \mathbb{Q}$. Unambiguous
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| 1550929 Determine if a 4-tuple exists Ambiguous
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| 840522 Need explanation for simple differential equation Ambiguous
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| 2865778 Find $a$ such that $$f(x)=\left\lfloor \frac{1}{3}+2a\sin^3x\right\rfloor$$ satisfies a symmetry condition. Ambiguous
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| 1510422 How can I show $f(x)$ is zero if $\int_a^b f(x)g(x) dx=0$ for each continuous $g$? Ambiguous
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| 1601141 How to calculate the character of this series $\displaystyle{\sum _{n=0}^{\infty }\left(-1\right)^n\left(\frac{\ln n-1}{n^3+1}\right)}$? Ambiguous
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| 2885878 Distance between two stations Ambiguous
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| 2512671 I need to find a function in order to satisfy $f(f^{-1}(W)) \subseteq W$. Ambiguous
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| 1542105 For a four digit number using {2,3,5,7,9}, is the last digit choice 3 if the remainder is 2 when divided by 3 or 5? Should the answer be (4)(3)(2)(3)? Ambiguous
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| 970872 Provide a mathematical proof that the standard solution to the 'Burning Ropes' brain teaser is correct or incorrect, specifically regarding the method of measuring 45 minutes using two non-uniform ropes. Unambiguous
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| 1900241 How to find the expected value of a discrete random variable using its probability generating function? Unambiguous
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| 254347 Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$ Ambiguous
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| 2775319 For a polynomial $f(x)$, is the root of $f''$ always equal to $\frac13$ of the sum of the roots of $f$? Ambiguous
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| 2865778 Find the range of real values for $a$ such that the function $f(x) = \lfloor \frac{1}{3}+2a \sin ^3 x \rfloor$ is an even function. Unambiguous
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| 351359 How do I prove my metric space problem using sequential criteria? Ambiguous
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| 2093269 Formulas to find bisector coordinates from 3 points without using matrices or vectors? Ambiguous
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| 646238 How can I prove to my students that the value of a definite integral is independent of the dummy variable of integration? Unambiguous
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| 2634909 How to prove that $e^x > x$ for all real numbers $x$? Unambiguous
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| 2619473 Suppose a power series converges at its radius of convergence $R=1$. Does the derivative exist at 1? If not, are there counter-examples? Ambiguous
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| 264371 Fun but serious mathematics books to gift advanced undergraduates. Ambiguous
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| 2387841 Are the remainders $\beta \mathbb{N} \setminus \mathbb{N}$ and $\beta K_0 \setminus K_0$ homeomorphic? Ambiguous
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| 672529 Verify that $-3x+5y-6z=-8$ is the correct equation of the plane consisting of all points equidistant from $(4,3,-2)$ and $(7,-2,4)$. Unambiguous
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| 5877 What is an efficient algorithm to find two integers $x$ and $y$ such that $x^2 + y^2 = p$ for a given prime $p \equiv 1 \pmod 4$? Unambiguous
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| 772475 Is it true that for a differentiable function $f(x)$, $\lim_{x\to\infty} f(x)=0$ implies $\lim_{x\to\infty} f'(x)=0$? If not, provide a counterexample. Unambiguous
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| 4401632 This is a surface on a sphere. What are the equations of the surface in yellow? Ambiguous
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| 3348703 How to perform bivariate interpolation to find the function $y(x,z)$ from a given set of scattered data points? Unambiguous
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| 4008509 Find the critical points of the multivariable function $f(x,y) = (x-2)(y-2)(x+y-2)$. Unambiguous
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| 1822028 Is the closed convex hull of a compact set in a dual space compact? Ambiguous
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| 2361362 How is this a bijection? Ambiguous
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| 2396015 What is the probability that the sum of three fair six-sided dice is eleven? Unambiguous
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| 4253329 For what values of p is the series $\sum_{n=2}^\infty \frac{1}{n(\log n)^p}$ convergent or divergent, and how do I prove it? Unambiguous
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| 1779361 How to prove that the trigonometric identity $\cos^4x - \sin^4x - \cos^2x + \sin^2x = 0$ holds for all real numbers $x$? Unambiguous
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| 614812 How do you derive the formula $2\cdot(2\cdot(n/4) + \min(n\%4, 2))$? Ambiguous
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| 2768349 Evaluate the limit as $n$ approaches infinity of $\left(1 + \frac{a}{n^2}\right)^{n/b}$, assuming $a$ and $b$ are constants with $b \neq 0$. Unambiguous
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| 2591017 What is the definition and formula for the nth roots of unity in the complex plane? Unambiguous
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| 1987713 If a continuous function $f: \mathbb{R} \to \mathbb{R}$ has a square $f^2$ that is uniformly continuous, must $f$ itself be uniformly continuous? Unambiguous
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| 119307 Cauchy Sequence that Does Not Converge Ambiguous
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| 1295010 What are statements about the natural numbers where induction is impossible or unnecessary to prove? Ambiguous
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| 3178788 How do I determine the type of stationary point without calculating second derivative? Ambiguous
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| 2346308 What are the parts of a number in a given base called? Ambiguous
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| 2298323 How to merge $C_1, C_2, \dots, C_k$ to form $C_m = C(D)$ for my vertically divided dataset? Ambiguous
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| 916805 Prove that for a subset $X$ of a metric space, the distance function $d(a, X) = \inf\{d(x, a) : x \in X\}$ equals $0$ if and only if $a$ is in the closure of $X$. Unambiguous
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| 2138866 $\int_{0}^{\frac{\pi}{4}}\frac{\tan^2 x}{1+x^2}\text{d}x$ on 2015 MIT Integration Bee Ambiguous
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| 2492396 How do I transform the first-order differential equation $(\sin^2y + x \arctan y)y' = 1$ into the form $M(x,y)dx + N(x,y)dy = 0$ to apply Lagrange's method for finding an integrating factor? Unambiguous
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| 218977 For $\Omega = (-1,1)\times(-1,1)$ and the Dirac delta $\delta_0$ defined by $\langle \delta_0, \phi\rangle = \phi(0)$ for all $\phi \in C_0^\infty(\Omega)$, determine the smallest distribution space containing $\delta_0$. Unambiguous
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| 2769775 Let $Z=X/(X+Y),$ find the pdf of $Z$. Ambiguous
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| 2121133 Given $N$ numbers, how many arrangements are strictly increasing or decreasing? Ambiguous
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| 2278214 Let $Y$ be a discrete random variable. What is $H(Y)$? Ambiguous
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| 2309119 Prove that the polynomial equation $r^3-7r+1=0$ has no rational roots. Unambiguous
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| 2934174 Find all pairs of prime numbers $(p, q)$ that satisfy the equation $pq = 3p + 7q$. Unambiguous
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| 1694294 Show that $\pi(p_x^2) \geq 2p_x -2$ Ambiguous
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| 2093269 What is the formula to find the length of the internal angle bisector segment between two sides of a triangle given the lengths of those two sides and the included angle? Unambiguous
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| 249834 If a continuous function goes from $5$ to $7$, why does it have to hit $2x+3$ somewhere? Ambiguous
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| 2775319 What is the general formula for the second derivative of a third degree polynomial function? Unambiguous
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| 681124 Find all $x$ satisfying $\frac{\tan x}{x}=2$, arising from setting $f'(x)=0$ for $f(x)=\frac{\sin^2x}{x}$. Unambiguous
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| 599095 How do I calculate the required sample size to achieve a specific margin of error for a confidence interval of a population mean? Unambiguous
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| 963503 If the sum of n vectors in a Euclidean space is zero and all their norms are equal, what can be said about their geometric arrangement? Unambiguous
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| 1310890 Compute $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$ Unambiguous
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| 889570 Prove the trigonometric identity $\cot(\theta) \sec(\theta) = \frac{1}{\sin(\theta)}$. Unambiguous
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| 291038 Let $A$, $B$ be matrices with $\kappa(A) > \kappa(B)$. Show $\kappa(B^{-1}A) < \kappa(A)$. Ambiguous
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| 1592652 Provide an example of a binary relation on a non-empty set that is symmetric and transitive, but not reflexive. Unambiguous
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| 385679 What are the properties of matrices $A$ and $B$ that satisfy the commutation relation $AB-BA=B$? Unambiguous
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| 1982237 What is the general solution to the Bessel differential equation of order n? Unambiguous
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| 269798 How do you calculate the expected value of a continuous random variable? Unambiguous
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| 2175735 For non-negative integers $n, p, k$, find a closed-form expression for $A(p,n,k) = \frac{(pn)!}{(p!)^k(p(n-k))!}$ and for $A(p,n) = \sum_{k=1}^n A(p,n,k)$. Unambiguous
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| 2237243 What are effective study habits and problem-solving strategies for improving one's mathematical practice and proficiency? Unambiguous
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| 2146495 What are the basic steps for finding the convolution of $(f*f)(t)$ for a fraction? Ambiguous
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| 754268 What is the formal statement of the Continuum Hypothesis and its status in ZFC set theory? Unambiguous
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| 639890 Prove that the minimum value of $\cos(A-B)+\cos(B-C) +\cos(C-A)$ for any real numbers $A, B, C$ is $-3/2$. Unambiguous
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