| MathSE ID Math Question Tag
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| 137352 What are the domain and range of the map f in Devaney's definition of chaos on a metric space? Unambiguous
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| 2561078 How does the triangle inequality apply to the proof for f-g using epsilon and delta? Ambiguous
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| 735461 For a completely positive map $f: M_n \to M_m$ with $f(a) = I_m$ for some $a \in M_n$, prove or disprove that there exists a positive element $b \in M_n$ such that $f(b) = I_m$. Unambiguous
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| 2461048 What is the cyclic subgroup generated by -1? Ambiguous
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| 578647 What is an intuitive explanation of the Fourier transform and how is it used to analyze signals in the frequency domain? Unambiguous
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| 2430945 "Decide if the statement "" $n^2-1$ is multiple of $4$ if and only if $n-1$ is multiple of $4$"" is true or false." Unambiguous
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| 1403539 Prove that $\arctan (x) + \arctan(1/x) = \frac{\pi}{2}$ for $x >0$. Unambiguous
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| 510991 Prove that every continuous function defined on a compact metric space is uniformly continuous. Unambiguous
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| 2904744 Prove that $\lim_{x\to 1} f(x) = 3$ where $f(x) = \frac{x^3-1}{x-1}$ for $x \neq 1$. Unambiguous
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| 982186 Decompose the expression $\frac{1}{4n^2-1}$ into partial fractions. Unambiguous
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| 4087621 Between which two consecutive integers does the value of $\sqrt{12}$ lie? Unambiguous
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| 697675 How do you multiply a matrix by a row vector from the left? Unambiguous
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| 1025321 Find the derivative $\frac{dy}{dx}$ using implicit differentiation for the equation $\ln(1+xy) = xy$. Unambiguous
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| 3313255 What is the definition and standard form of Sum of Products (SOP) in boolean algebra? Unambiguous
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| 578647 In the Fourier transform, what does the cross term mean? Ambiguous
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| 3843282 finding quotient group relationship Ambiguous
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| 3372191 Asymptotic behavior of $a_{n+1}=a_n + f(a_n)$ Ambiguous
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| 2694508 Find the range of values of $k$ such that both roots of $x^2 - 2kx + k^2 - 1 = 0$ lie in the interval $(-2, 4)$. Unambiguous
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| 3735022 What is the formula for the curvature of a Frenet curve constrained to lie on a sphere? Unambiguous
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| 4870757 If I know the dimension, depth, and codimension of $R$ and $I$, can I determine the depth of $I$? Ambiguous
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| 166794 Proof that the set of irrational numbers is uncountable Unambiguous
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| 4127695 Evaluate the sum $\sum_{r=0}^n 2^{n-r} \binom{n+r}{r}$ for non-negative integers $n$ and $r$. Unambiguous
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| 2949838 Can every basis of a finite dimensional vector space be orthogonal? Ambiguous
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| 7391 How do I evaluate the definite integral $\int_0^{\pi} \sin(2x)\sin(x) dx$? Unambiguous
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| 1315088 Evaluate the limit $\lim_{x \to 0} \left( \frac{1}{\sin(x)\arctan(x)} - \frac{1}{\tan(x)\arcsin(x)} \right)$ Unambiguous
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| 36134 Modern Equivalent of Carr's Synopsis? Ambiguous
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| 2526693 Evaluate the limit: $\lim_{x \to 0^+} x^{\sqrt{x}}$ Unambiguous
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| 432999 Prove that the limit of the sequence $\frac{n}{2^n}$ as $n$ approaches infinity is 0. Unambiguous
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| 1572032 Why is the CDF of $Y_n$ equal to $(\frac{t- \theta}{\theta})$ and what are the restrictions on $t$? Ambiguous
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| 2186358 What is the correct term for $I^n f(x)$ where $I$ is the integral operator? Ambiguous
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| 606172 If the sequence $(x_n)$ of real numbers converges and $\lim_{n \to \infty} (2x_{n+1} - x_n) = x$, is it true that $\lim_{n \to \infty} x_n = x$? Unambiguous
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| 4468673 If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the maximum value of the product $xy$? Unambiguous
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| 166794 I found a proof arguing that the irrationals are countable based on the density of the rationals. I know this is wrong, but where is the mistake in the logic? Ambiguous
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| 1191610 Prove that the composition of two group homomorphisms is also a group homomorphism. Unambiguous
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| 4437668 What are some interesting examples of elementary proofs by mathematical induction for students? Unambiguous
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| 1354331 Does there exist a function that is discontinuous at a point but has a continuous derivative on its domain? Unambiguous
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| 970133 Prove that the infinite series $\sum_{n=1}^\infty \frac{n^2(n-1)}{2^n}$ converges to 20. Unambiguous
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| 419859 Prove that the graph $y=x^{p/q}$ has a vertical tangent. Ambiguous
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| 105575 What is the difference between the soundness and completeness theorems in first-order logic? Unambiguous
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| 456595 Prove: $\frac{1}{1^2} +\frac{1}{2^2} + \cdots + \frac{1}{n^2} + \cdots = \sum_{n=1}^\infty \frac{1}{n^2} < 2$ Ambiguous
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| 3075859 What is the next step after showing $(c^k)^t = (id)$ for cycle orders? Ambiguous
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| 2538727 How to use Cantor's diagonal to prove my space is not sequentially compact? Ambiguous
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| 217966 What is the relationship between monomorphisms and pullbacks in category theory? Unambiguous
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| 3117992 Could different physical systems follow different underlying mathematics? Ambiguous
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| 181367 Provide a counterexample to show that a pseudocompact topological space is not necessarily a compact space. Unambiguous
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| 854380 How to distinguish between walking on a sphere and walking on a torus? Ambiguous
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| 3087356 Why is the number 2 included in the definition of prime numbers instead of being excluded as the only even prime? Unambiguous
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| 4468673 If $x$ and $y$ are positive integers such that $5x+3y=100$, what is the greatest possible value of $xy$? Ambiguous
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| 4060048 How do I solve integrals of the form integral of (polynomial * exponential) dx using integration by parts? Unambiguous
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| 1024830 What is the intuitive meaning of a compact set in the context of a metric space or topology? Unambiguous
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| 3172708 How to efficiently update the inverse of a lower triangular matrix after changing 4 individual elements? Unambiguous
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| 1133113 How do we define arc length? Ambiguous
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| 2490690 In how many ways can a payment of $107$ shekels be made using coins/bills of denominations $1$, $10$, and $50$ shekels, assuming an unlimited supply of each? Unambiguous
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| 1711154 Prove that f is differentiable at x=0 Ambiguous
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| 551148 Why is $2x^3 + x$, where $x \in \mathbb{N}$, always divisible by 3? Ambiguous
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| 2304892 Probability of rolling any set of size k on n dice with m sides Ambiguous
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| 1576678 Can my sine formula with $\pi/6$ be put into Excel somehow to plot the graph? Ambiguous
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| 2982578 Prove that every finitely generated module over a ring $R$ is a homomorphic image of a free module. Unambiguous
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| 1619762 What are the equivalent statements of the Generalized Riemann Hypothesis (GRH) expressed in terms of the summatory functions of the Möbius and Liouville functions? Unambiguous
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| 1882798 Is there a mathematical rule to check if positive numbers $a$ and $b$ satisfy my modulo $P$ equation? Ambiguous
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| 289779 I'm looking at the sequence $a_n = 3^n - 2^{n+100}$. How do I handle this? Ambiguous
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| 1320951 Prove that the intersection of any two cyclic subgroups of a group is also a cyclic subgroup. Unambiguous
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| 2449459 What's wrong with this fake proof that $2+2=5$? Ambiguous
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| 1017503 Prove by induction that $\sum_{k=0}^n k\cdot k! = (n+1)! - 1$ for all $n \in \mathbb{N}$. Unambiguous
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| 3490887 Question on existence of square root function! Ambiguous
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| 3791238 Why is a curve homeomorphic to a knot? Ambiguous
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| 2284995 "Expected count of ""double records""" Ambiguous
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| 3468876 Suppose $Y_1$ and $Y_2$ are independent and $X=Y_1+Y_2$. What is the distribution of $X$? Ambiguous
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| 243106 How to apply $\epsilon-\delta$ definition to a 2-valued function? Ambiguous
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| 2396246 One tank holds more than another by some amount. When the smaller one is about 2/3 full, it holds roughly as much as half the larger one. What is the capacity? Ambiguous
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| 303933 Evaluate the limit $\lim_{n \to \infty} \frac{(\log(n))^a}{n^b}$ for positive real constants $a$ and $b$. Unambiguous
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| 975836 How to solve linear recurrence relations using the method of repeated substitution? Unambiguous
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| 164244 Prove that if a subgroup of index p is the smallest prime dividing the order of a finite group, then it is a normal subgroup. Unambiguous
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| 2344993 What are some unexpected real-world applications or occurrences of the natural logarithm in mathematics and science? Unambiguous
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| 781320 Why does this curve cross the y-axis if $\cos(\sin x)$ is never zero? Ambiguous
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| 2834788 Is the EulerâMascheroni constant $\gamma$ known to be irrational? Unambiguous
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| 3247615 How do I evaluate the polynomial P(x) at x = -2? Unambiguous
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| 1329195 How to calculate a percentage increase when the result is above 100%? Unambiguous
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| 2449459 Where is the logical fallacy in the common fake proof that $2+2=5$? Unambiguous
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| 3017476 Interpreting an agreement function Ambiguous
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| 1169872 Is there a positional numeral system base $b$ such that every rational number has a terminating representation? Unambiguous
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| 2923438 How does the RSA cryptosystem work, and what are the steps for key generation, encryption, and decryption? Unambiguous
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| 3114691 How to find $\lim\limits_{n\to\infty} A^n$? Ambiguous
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| 1559640 How to find all natural numbers $n$ for quadratic permutations with a perfect square sum? Ambiguous
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| 3699937 The cyclic subgroups of $p^2$ order non-cyclic group are normal Ambiguous
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| 551148 Prove that for every natural number $x$, the expression $2x^3 + x$ is always divisible by 3. Unambiguous
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| 3537073 Help with proof by induction, please! I may not be understanding how to work with factorials. Ambiguous
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| 3537073 Can you provide a step-by-step example of how to use proof by induction to prove a summation formula involving factorials? Unambiguous
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| 1647675 A Quadrilateral and A Triangle in a Trapizium Ambiguous
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| 2999909 In an arbitrary category, is the hom-set $Hom(X,Y)$ always equipped with an Abelian group structure? Unambiguous
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| 1466540 Find the $\lim_{x\to \infty} (\ln(x)-x)$ Unambiguous
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| 4247524 Finding the probability that at least 8 houses in a row are of same colour. Ambiguous
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| 486600 Given that ai (where i is the imaginary unit) is a root of the polynomial $x^3-bx^2+a^2x-a^2b=0$, prove this fact and find the other two roots in terms of $a$ and $b$. Unambiguous
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| 308644 Do I need to include the definition of union in this proof? Ambiguous
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| 2396246 How do I calculate the volume of water a cylindrical tank can hold given its radius and height? Unambiguous
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| 3560940 If the weights of three different items are 10g, 25g, and 5g, how do I divide 1kg among them? Ambiguous
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| 2561078 Prove that if functions $f$ and $g$ are continuous at a point $x$, then their difference $f-g$ is also continuous at $x$. Unambiguous
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| 1568161 Evaluating $\lim\limits_{x \to \pi} \frac{(\pi -x)\sin x}{1 + \cos x}$ Ambiguous
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| 1074072 Is there a notion dual to that of a path in a topological space? Ambiguous
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| 2664926 Evaluate the complex power $(-\sqrt{3} + i)^9$ using De Moivre's theorem. Unambiguous
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| 365782 Prove that $-\int \frac{d^3p}{(2\pi)^3}\, p\,\frac{\partial f(p,t)}{\partial p} = 3F$, where $F = \frac{1}{(2\pi)^3}\int d^3p\, f(p,t)$, using integration by parts. Unambiguous
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| 1283817 Given data points $(x_1,y_1),\dots,(x_n,y_n)$ and the model $f(x)=ae^{2x}+be^x+c$, find the transformation of the points $(x_i,y_i)$ needed to fit $f(z)=az^2+bz+c$ via least squares under the substitution $z=e^x$. Unambiguous
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| 2539486 How do I solve for the min of $\int_{-1}^1| x^3-a-bx-cx^2|^2 dx$ and the max of $\int_{-1}^1 x^3 g(x) dx$ given the constraints on $g$? Ambiguous
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| 2961334 How to prove a solution to a functional equation is unique? Ambiguous
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| 574551 Evaluate $\oint_C P\,dx + Q\,dy$ where $P(x,y)=\frac{y+x}{x^2+y^2}$ and $Q(x,y)=\frac{y-x}{x^2+y^2}$, and $C$ is the circle $x^2+y^2=a$ oriented clockwise, given that $P_y=Q_x$ but $(0,0)$ is a discontinuity. Unambiguous
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| 1941590 How do you use Cramer's rule to solve a system of linear equations using determinants? Unambiguous
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| 2158739 True or False: Every 3-dimensional linear subspace of the vector space of $2 \times 2$ real matrices $\mathbb{R}^{2 \times 2}$ contains at least one invertible matrix? Unambiguous
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| 258546 How to find the parabolic curve equation from length $L$ and area $S$ based on my picture? Ambiguous
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| 3328473 How to find the numerical solutions for $2x - \tan(x) = 0$ in the interval $[0, 2\pi]$? Unambiguous
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| 4268142 A coin is tossed three times, defining two related random variables from the outcomes. Find their joint pmf and show they're dependent. Ambiguous
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| 2881207 How does the irreducibility of a polynomial over a finite field depend on the size of the field? Unambiguous
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| 1037122 Prove that for any real number $\lambda$, the integral $\int_0^\infty e^{-x} \sin(\lambda x) \, dx = \frac{\lambda}{1+\lambda^2}$. Unambiguous
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| 2166855 How to find the maximum value of the objective function $x + y$ subject to a set of linear constraints? Unambiguous
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| 2049971 Prove that the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ cannot be transformed into the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ by any real coordinate transformation, without substituting $b \to ib$. Unambiguous
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| 3786586 How to solve an inequality involving the sum of two absolute value expressions, such as $|ax + b| + |cx + d| < k$? Unambiguous
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| 41706 What are some practical applications of matrix multiplication in computer science and engineering? Unambiguous
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| 3111111 If $X$ is a topological space, does the property still hold for the product of two continuous functions? Ambiguous
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| 2022771 In mathematical learning, does the complexity of notation generally decrease as one advances to more abstract levels of study? Unambiguous
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| 1980947 Which value is greater, $2^{\sqrt{2}}$ or the mathematical constant $e$? Unambiguous
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| 609404 Find all values of $c \in \mathbb{Z}_5$ such that the quotient ring $\mathbb{Z}_5[x]/\langle x^3+2x+c\rangle$ is a field. Unambiguous
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| 2539486 (a) Using the best approximation theorem, compute $\min_{a,b,c} \int_{-1}^1 |x^3 - a - bx - cx^2|^2\, dx$. (b) Find $\max \int_{-1}^1 x^3 g(x)\, dx$ subject to $\int_{-1}^1 g(x)\,dx = \int_{-1}^1 xg(x)\,dx = \int_{-1}^1 x^2 g(x)\,dx = 0$ and $\int_{-1}^1 |g(x)|^2\,dx = 1$. Unambiguous
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| 3087356 Why is the definition of prime numbers written to include 2 Ambiguous
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| 3399461 A polynomial defined by two squared terms is divided by two linear factors, giving known remainders. Find the coefficients. Ambiguous
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| 4107862 How should I think about the concept of location for a point? Ambiguous
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| 744139 Prove by induction that $2\cdot 8^n + 3\cdot 15^n + 2$ is divisible by $7$ for all $n \in \mathbb{N}$. Unambiguous
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| 4749159 Equation exercise involving nth-roots in Serge Lang's Basic Mathematics. Ambiguous
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| 795 How to prove the theorem of Riemann asked by Kenny? Ambiguous
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| 942204 Looking for the logic of a sequence from convolution of probability distributions Ambiguous
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| 4835425 Revisiting: Adding an optimizer to a nonlinear set of equations Ambiguous
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| 2237243 "What are good ""math habits"" that have improved your mathematical practice?" Ambiguous
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| 1406770 Iterated square roots over finite field. When do we hit a nonresidue? Ambiguous
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| 3472866 Are $\sigma^2$ and $\mu$ random variables? Ambiguous
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| 3806534 If $\lim_{x\to 0}(f(x) + \frac{1}{f(x)}) = 2$ and $\lim_{x\to 0} f(x)$ exists, prove that $\lim_{x\to 0} f(x) = 1$. Unambiguous
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| 4325846 How do I formally show that the Zariski tangent space of the intersection of two closed subschemes is the intersection of the tangent spaces? Ambiguous
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| 2530549 What are some mental math techniques for performing complex calculations without a calculator? Unambiguous
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| 164588 How to find the general coefficient of the Cauchy product of two power series? Unambiguous
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| 1838743 In the figure, two circles intersect at $P$ and $Q$... Ambiguous
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| 788217 A hammer and a nail cost $1.10, and the hammer costs one dollar more than the nail. How much does the nail cost? Ambiguous
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| 216344 Does the equation $ax + by = ab$ have any solutions for $\gcd(a,b)=1$? Ambiguous
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| 385679 A matrix satisfying $AB-BA=B$ Ambiguous
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| 925677 I need the coordinates for an octagon. Ambiguous
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| 2159465 Are two polygons homeomorphic? Ambiguous
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| 582557 Determine whether $\sum_{n=2}^\infty \frac{1}{n\ln(n^3)}$ converges or diverges. Unambiguous
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| 4336 If eigenvalues are positive, is the matrix positive definite? Ambiguous
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| 531128 Dimension of a subspace of finite-dimensional product space $V$ equals $\dim V - 1$ Ambiguous
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| 2388784 What is the intuitive explanation for the formula of variance in probability theory? Unambiguous
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| 1165928 What is the general formula for the k-th derivative of $G \circ F$? Ambiguous
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| 4768 every permutation is either even or odd,but not both Ambiguous
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| 1997424 What is the rigorous definition of the differential of a function in multivariable calculus? Unambiguous
|
| 2239918 Can someone help me with this: 2^(log(2x,x+2))+3^(log(2,x+3))=sqrt(-1-x) Ambiguous
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| 354134 "What is the logical negation of the statement ""$A\subseteq B$"" in set theory?" Unambiguous
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| 1871195 Given a function $a(x)$, is $$\max\left(\frac{1}{2}a'(x)\right) > \max\left(\frac{1}{3!}a''(x)\right) > \cdots$$ always true? Ambiguous
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| 422707 Finding eigen values of a binary matrix with diagonal elements are all 0s and non-diagonals are 1s Ambiguous
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| 747433 What are the standard tests for determining the absolute convergence of an infinite series? Unambiguous
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| 3300982 I proved that if a symmetric real matrix commutes with all orthogonal matrices, it is a scalar multiple of the identity. Now how do I do this for orthogonal matrices? Ambiguous
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| 1674072 How do you find the greatest integer whose square root differs from another integer's square root by at least one? Ambiguous
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| 188703 For $f(x,y,z) = e^{\sqrt{xy}+\sqrt{xz}+\sqrt{zy}}$, determine whether a Taylor series expansion exists at $(0,0,0)$, given that the partial derivatives there take the indeterminate form $0/0$. Unambiguous
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| 2072845 Why do different methods of factoring a quadratic trinomial, such as the AC method and trial and error, always yield the same linear factors? Unambiguous
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| 730358 Sketch $\tan x$, solve $\cot x=0.15$, and evaluate $\csc x$ given $\cot x=0.15$. Ambiguous
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| 853164 Provide an example of a binary relation on a set that is not reflexive, not symmetric, and not transitive. Unambiguous
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| 3934173 Can any permutation of elements be represented as a series of rotations in some n-dimensional space? Ambiguous
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| 265703 Under what conditions does every element of a monoid occur exactly once in its Cayley table? Unambiguous
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| 4067963 What is the sum of $\sum_{n\in M(P)} \frac{1}{n}$ where $M(P)$ contains numbers with prime divisors in $P$? Ambiguous
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| 2540359 What is the formal definition of an undecidable problem in computability theory? Unambiguous
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| 3519278 $6$ persons enter the train during the journey with $6$ different tickets of the same class. How many different sets of ticket may they have had? Ambiguous
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| 3310472 Is the P versus NP problem classified as a topic within the field of Operations Research? Unambiguous
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| 1072836 Is every symmetric matrix diagonalizable, and what are the possible eigenvalues of an orthogonal matrix? Ambiguous
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| 2096678 Suppose $A^2 + B^2 = AB$ and $AB - BA$ is invertible. What can be said about $n$? Ambiguous
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| 1798274 Least value of $a$ for which $4ax^2 + \frac{1}{x} \geq 1$ Ambiguous
|
| 488020 Prove that the set of signed circuits of an oriented matroid is invariant under reorientation of its elements. Unambiguous
|
| 110579 In how many ways can a batsman score exactly 100 runs using only 6s and 4s, where the order of scoring matters? Unambiguous
|
| 1249731 Let $X=(X_1,\dotsc,X_n)$ be a random vector with mean $0$. What is $\mathbb{E}[X_1\cdots X_n]$? Ambiguous
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| 646238 How do I convince my students that the choice of variable of integration is irrelevant? Ambiguous
|
| 3125432 Trouble with telescoping algorithm question Ambiguous
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| 3285074 Are there other functions that satisfy $|f(x)-f(y)|=|x-y|$? Ambiguous
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| 664657 I'm trying to connect $\epsilon$ and $\delta$ for $|f(x) - f(c)| < \epsilon$. How do I do this? Ambiguous
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| 2360710 Formula for Natural logarithm of $\pi$ Ambiguous
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| 1731822 Given some unlabeled 2D data points, how do I construct a k-nearest-neighbour graph and its Laplacian? Ambiguous
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| 2146495 For $f(t)=\frac{2}{1+t^2}$, compute the convolution $(f*f)(t) = \int_0^t f(u)f(t-u)\,du$. Unambiguous
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| 4341781 The integral of a function along any circle is zero. What does this mean, and what follows from it? Ambiguous
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| 227317 Explaining $\cos^\infty$ Ambiguous
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| 1067717 How do you get $\frac{2\sum_{k=0}^n2^n}{n+1}=2^{n+1}$? Ambiguous
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| 108308 Apostol proof divides by zero? Ambiguous
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| 2062239 Numerical algorithms for approximating the polar decomposition of a matrix Unambiguous
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| 687510 A shape is cut into 3 equal parts. Show one part contains 2 points at distance at least one. Ambiguous
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| 330556 $a^{n}$: is it arithmetic or geometric, or neither? Ambiguous
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| 3791855 How does $x^2-8x+17=0$ have nonreal solutions? Ambiguous
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| 988784 Why is it a common misconception that non-real numbers consist only of square roots of negative numbers? Unambiguous
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| 2394502 Under what conditions does a complex number $z=x+iy$ in the third quadrant imply that the ratio $\frac{\bar{z}}{z}$ also lies in the third quadrant? Unambiguous
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| 3098928 For a fixed real number $x > 0$, does the sequence $x^{1/n}$ converge as $n$ approaches infinity, where $n$ is a natural number? Unambiguous
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| 2823907 Prove that $\sum_{n=2}^\infty \frac{1}{n\ln(n^3)}$ diverges using the comparison test. Unambiguous
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| 3059714 How does one evaluate the multiplication $f(2)\cdot f(3)\cdot f(4)\cdots f(15)$ by formulating? Ambiguous
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| 2594206 Prove that there is no $2 \times 2$ real matrix $A$ such that $A^2 = \begin{pmatrix} 0 & 1 \ 0 & 0 \end{pmatrix}$. Unambiguous
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| 639890 Minimum value of $\cos(A-B)+\cos(B-C)+\cos(C-A)$? Ambiguous
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| 225922 An example for a calculation where imaginary numbers are used but don't occur in the question or the solution. Ambiguous
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| 983405 Prove the inequality $\|\nabla f\|_p \le C (\|\nabla \times f\|_p + \|\nabla \cdot f\|_p)$ for vector fields $f$ in $L^p$ spaces on $\mathbb{R}^3$. Unambiguous
|
| 4693000 Prove that $\frac{1}{\zeta(3)} < 2\gamma - 1$, where $\zeta(s)$ is the Riemann zeta function and $\gamma$ is the Euler-Mascheroni constant. Unambiguous
|
| 724075 Where can I find the book 'Here's a Cool Problem: A Collection of Short Questions with Clever Solutions'? Unambiguous
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| 1302479 I'm having trouble with this function: $$f(x)=\begin{cases}1, & \text{if } x\in \Bbb Q\\ -1, & \text{if } x\in \Bbb R\backslash \Bbb Q. \end{cases}$$ Ambiguous
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| 26918 Why is the mathematical constant $\pi$ defined as the ratio of a circle's circumference to its diameter rather than its ratio to the radius? Unambiguous
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| 361118 Prove that $4x-x^4 \leq 3, x \in \Bbb R$ Ambiguous
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| 2006621 How do I calculate the number of subsets of a finite set given its cardinality? Unambiguous
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| 62748 What is the difference between two related set-builder notations? Ambiguous
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| 2054106 Is it true that pointwise convergence with a uniform bound implies convergence of the integrals? Ambiguous
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| 742532 Why is the right endpoint given as $3\frac{i^2}{n^2}$ for the limit $\lim_{n \to \infty} \sum_{i=1}^{n} f(c_{i}) \Delta x_{i}$? Ambiguous
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| 105575 What is the difference between Completeness and Soundness in first order logic? Ambiguous
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| 1978354 Distribution of $\frac{X+Y}{X-Y}$ Ambiguous
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| 788217 A hammer and a nail together cost $1.10, and the hammer costs $1.00 more than the nail. What is the cost of the nail? Unambiguous
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| 1788328 Find the numerical value of $\sin 10^\circ \sin 50^\circ \sin 70^\circ$. Ambiguous
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| 3944628 In the definition of a stopping time, how important are the filtration conditions mentioned earlier? Ambiguous
|
| 1079395 Inclusion Exclusion Principle (Probability) Problem: What is P(Rain)? Ambiguous
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| 1783734 Can you explain the logical basis and validity of the principle of mathematical induction for proving statements over natural numbers? Unambiguous
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| 1896418 For a set of $n$ points in the plane where no four are collinear, what is $f(n)$ for the case where no three are collinear? Ambiguous
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| 1214106 Find all polynomials $P(X)$ such that $P(x^2-y^2) = P(x-y)P(x+y)$ for all complex numbers $x, y$. Unambiguous
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| 700216 Different solutions of $x+y+z=10$ where $x$, $y$, $z$ are all positive integers and $x, y, z \leq 10$ Ambiguous
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| 3086320 Evaluate $\lim_{x\to 2}\frac{2x-4}{x^2+2x-6}$ and explain why direct substitution giving $0$ differs from the result obtained via L'Hôpital's rule. Unambiguous
|
| 3289735 Is the arc length of a circle always irrational between two points with rational coordinates? Unambiguous
|
| 1762325 Is $\sim (\sim p) \rightarrow p$ always true? Ambiguous
|
| 227317 What is the limit of the sequence defined by the iterated cosine function $x_{n+1} = \cos(x_n)$ as $n$ approaches infinity? Unambiguous
|
| 4256389 Alternating sum involving reciprocals of powers of primes equals $\ln(\frac{\pi}{4})$ Ambiguous
|
| 1319618 An inequality, comprising of liminf and Sup of a set Ambiguous
|
| 2498847 Is 1/x a surjective function when the domain and the range are all real numbers? Ambiguous
|
| 1894173 Does the sum of the reciprocals of all prime numbers converge or diverge? Unambiguous
|
| 3247615 How to find $P(-2)$ here? Ambiguous
|
| 602860 How to calculate which point is furthest from the origin in the direction of a normalized vector? Ambiguous
|
| 3502297 How to show $\log(x)$ loses to powers? Ambiguous
|
| 1347 How can Euclidean geometry be axiomatized or derived using criteria from hyperbolic geometry? Unambiguous
|
| 11194 How to solve a linear recurrence relation where the nth term depends on the sum of all previous terms? Unambiguous
|
| 290435 Find five distinct positive integers whose reciprocals sum to 1. Unambiguous
|
| 4019674 Prove that the value of $\frac{\arcsin(3/5)}{\pi}$ is an irrational number. Unambiguous
|
| 2353213 Are there any other Lie subgroups of $\textrm{Gl}(n, \mathbb{R})$ and is there a classification for them? Ambiguous
|
| 1347 Studying Euclidean geometry using hyperbolic criteria Ambiguous
|
| 4255331 If $ \lim_{x\to \infty} (f(x+1)-f(x))=1$, then $ \lim_{x\to \infty} \frac{f(x)}{x}=1$? Ambiguous
|
| 3395798 Definition of a matrix by matching two vectors Ambiguous
|
| 984271 How does the isomorphism between $\mathbb{K} \otimes M_n(\mathbb{C})$ and $\mathbb{K}$ work? Ambiguous
|
| 1249731 What is the formula for the first order moment (mean vector) of a multivariate Gaussian random vector? Unambiguous
|
| 1251548 Provide an example of a set in a metric space that is bounded but not totally bounded. Unambiguous
|
| 4488057 Can a function be represented by a Laurent series expansion in a neighborhood of a non-isolated singularity? Unambiguous
|
| 217335 In how many ways can a total of $1.50 be formed using exactly 50 US coins? Unambiguous
|
| 329838 How to simplify a square root of a number by extracting perfect square factors? Unambiguous
|
| 1376320 Proving that if $a+b$ and $ab$ are of the same parity, then $a$ and $b$ are even. Ambiguous
|
| 4383384 How to extract the vector from a rank-$1$ matrix? Ambiguous
|
| 1895699 I'm stuck on this part of the proof: $\cot C \frac{\sin(A-B)}{\cos A \cos B}$. How do I get to the other side? Ambiguous
|
| 71874 Can I use my powers for good? Ambiguous
|
| 395543 What are the formulas for generating all primitive Pythagorean triples? Unambiguous
|
| 872256 What is the geometric interpretation of finding the $n^{ ext{th}}$ roots of a complex number in the complex plane? Unambiguous
|
| 2837226 Show that a subset of a complete metric space is complete. Ambiguous
|
| 538941 If $xy$ and $x+y$ are both even integers (with $x,y$ integers), then $x$ and $y$ are both even integers Ambiguous
|
| 884228 How do you calculate the reliability function for a continuous uniform distribution given its lower and upper bounds? Unambiguous
|
| 3035983 How can I find all pairs of integers $(n, m)$ that satisfy the equation $\frac{150 + n}{15 + n} = m$? Unambiguous
|
| 2880747 Product of Summation for a single table of values. Ambiguous
|
| 1002480 How to go from talking about line segments to points to prove $X(A)$ is compact? Ambiguous
|
| 488020 Let $M$ be a matrix, and define $V(M)$ from the signs of vectors in $\ker(M)$. Prove that $V$ is invariant under change of coordinates. Ambiguous
|
| 859968 Is $X/R$ homeomorphic to $Y$ for the broom spaces? Ambiguous
|
| 2520461 How to minimize $AP/PB$? It doesn't seem doable for some locations. Ambiguous
|
| 1496959 What are the necessary and sufficient conditions for a sequence of continuous functions to converge uniformly on a compact set? Unambiguous
|
| 1279205 Can an irrational number be classified as odd or even under the standard definition of parity for integers? Unambiguous
|
| 4437668 What are some good, elementary and maybe also interesting proofs by induction? Ambiguous
|
| 2576976 How do I find the inverse of a $2\times2$ matrix if the determinant is zero? Unambiguous
|
| 1626298 Prove that $2^{\log_4 n} = n^{\log_4 2}$ using logarithmic identities. Unambiguous
|
| 3811446 What is the value of the infinite series $\sum_{n=1}^{\infty}\frac{1+2+\cdots +n}{n!}$? Unambiguous
|
| 1891318 "Number of bit strings of length 8 that do not contain ""$100$""?" Ambiguous
|
| 1311558 What is the formal definition of a set in Zermelo-Fraenkel set theory and how is it intuitively conceptualized? Unambiguous
|
| 3960592 Finding the equation of hyperbola that passes through $(2,0)$ and has foci points $(2,3)$ and $(1,0)$ Ambiguous
|
| 3791855 Why does the quadratic equation $x^2-8x+17=0$ have non-real complex solutions? Unambiguous
|
| 1668681 Provide an example of a 2D planar shape whose center of mass lies on its boundary. Unambiguous
|
| 219343 How can I prove that the propositional logic formula $[(p \to \neg q) \wedge q] \to \neg p$ is a tautology using a truth table or natural deduction? Unambiguous
|
| 1141210 I am trying to do a set proof and I don't understand where the part highlighted in green comes from. Ambiguous
|
| 344268 How do I solve a rational inequality where the variable $x$ appears in the denominator? Unambiguous
|
| 1501369 How to prove a function is one to one given $f(f(m)+f(n))=m+n$? Ambiguous
|
| 2207598 Prove or disprove: if $A\times A = B\times B$ then $A=B$. Ambiguous
|
| 738236 How to calculate the area of a triangle ABC when given three position vectors $a, b$, and $ c$ in 3D? Ambiguous
|
| 4285591 Does the expression $\frac{1}{1-hL}$ have an upper bound for $h > 0$ and $L > 0$ such that $hL < 1$? Unambiguous
|
| 4080901 Using a block matrix to show that $A$ and $B$ commute Ambiguous
|
| 3582088 Solving for polynomial $f(x)$ satisfying $f(x)f(y)=f(x)+f(y)+f(xy)-2 \forall x\in \mathbb{R}, f(1)\ne 1, f(3)=10$ Ambiguous
|
| 3729349 If a series $\sum a_n$ converges and the sequence of its terms $(a_n)$ is monotonically increasing, why must the terms be non-positive? Unambiguous
|
| 2494260 List mathematical theorems, conjectures, or concepts that are named after geographic locations. Unambiguous
|
| 3265216 How to perform horizontal and vertical rescaling of a function $f(x)$ in algebra? Unambiguous
|
| 114560 Sum of normal bundle and tangent bundle. Ambiguous
|
| 1001101 Let $f:\mathbb{R}\to\mathbb{R}$ be an arbitrary function (not necessarily continuous). Prove there exists an interval $(a,b)$ and $c>0$ such that for every $x\in(a,b)$, there is a sequence $x_n\to x$ with $|f(x_n)|\le c$. Unambiguous
|
| 4564068 What is the formula for 0 + 1 + 3 + 6 + 10 + 15 ... ? Ambiguous
|
| 227211 Is there a real-valued function $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(x)) = f(x)$ for all $x$ and $f(0) = 1$? Unambiguous
|
| 1381335 How to tell which function fits my series to make it a Riemann Sum? Ambiguous
|
| 217315 How do you tell the difference between the minus signs? Ambiguous
|
| 1432379 What is the minimum of $F(x,y,z)=\frac{1}{x+y}+\frac{1}{x+z}-\frac{1}{x+y+z}$? Ambiguous
|
| 217315 In algebra, what is the difference between the unary minus operator used to indicate a negative number and the binary minus operator used for subtraction? Unambiguous
|
| 3711681 How to compute the matrix derivative of the scalar function $f(X) = \operatorname{tr}(B X X^T A)$ with respect to the matrix $X$? Unambiguous
|
| 1435003 How to find $P(X_i=1)$ to get the expected number of empty boxes? Ambiguous
|
| 1562459 Prove that the sequence $(1 + n^{-2})^n$ converges to 1 as $n$ approaches infinity. Unambiguous
|
| 1304823 Can someone explain the parts of this equation? Ambiguous
|
| 2657952 "What's the relationship between mathematical logic and just plain old ""logic""? The notation differs, do the concepts? The rules?" Ambiguous
|
| 982093 Proof for $\lim_{n \to \infty}\left(1+\frac{a_n}{n}\right)^n = e^a$? Ambiguous
|
| 251033 What are the search terms for the largest subset with no 3 element progressions? Ambiguous
|
| 2766082 How do you simplify the algebraic expression $\frac{10x\Delta x + 5(\Delta x)^2}{\Delta x}$ to get $10x + 5\Delta x$, assuming $\Delta x \neq 0$? Unambiguous
|
| 608477 What can you tell me about $4^{n+1}+5^{2n-1}$ and 21? Ambiguous
|
| 1329254 Solve the ODE $\frac{d^2y}{dt^2}+10\frac{dy}{dt} = -5t^2+t^4\cosh(t)$ using the Fast Fourier Transform method. Unambiguous
|
| 3422194 Compute the sum of the infinite series $\sum_{k=1}^{\infty} \frac{1}{k(k+2)}$ using partial fraction decomposition. Unambiguous
|
| 244424 If rank x < rank y, does it follow that x is an element of y? Ambiguous
|
| 687510 Provide an example of a Pigeonhole Principle problem involving points placed inside a square area. Unambiguous
|
| 2863657 Simple Ratios Shortcut - Why does it work? Ambiguous
|
| 721784 What is the absolute value of the complex exponential function $e^{iz}$ where $z$ is a real number? Unambiguous
|
| 2581976 How do I find the limit of a function as x approaches a specific value? Unambiguous
|
| 1645747 Compute the derivative of $x$ with respect to $\frac{1}{x}$. Unambiguous
|
| 997152 Why does the General Leibniz Rule for the nth derivative of a product have the same binomial coefficient structure as the Binomial Theorem for raising a sum to the nth power? Unambiguous
|
| 1475726 How to find three sets of three collinear points in a given 2D point set? Unambiguous
|
| 981781 $$f(x)=x^3-x^2-14x+24$$ Ambiguous
|
| 1040128 How do I evaluate the improper integral $\int_1^\infty \frac{dx}{x^2\sqrt{x^2-1}}$ using trigonometric substitution? Unambiguous
|
| 2278214 Calculate the Shannon entropy of the random variable representing the number of heads obtained when flipping a fair coin ten times. Unambiguous
|
| 2751401 If $a\mid b$ and $a>0$ then $(a,b)=a$ Ambiguous
|
| 4057665 Are these topologies the same? Ambiguous
|
| 1466559 How to find the angle between two vectors using the dot product formula derived from the law of cosines? Unambiguous
|
| 1602977 What's an example of an infinitesimal? Ambiguous
|
| 1899905 How can physical quantities that are modeled by irrational numbers be realized or measured in the physical world? Unambiguous
|
| 2604608 Prove that the constant function $f(x) = 2a + 3b$ is continuous for all x in its domain, where a and b are real constants. Unambiguous
|
| 1761660 Find the value of $a$ such that the range of the function $f(x) = ax(1-x)$ contains the interval $[0,1]$. Unambiguous
|
| 1695878 Let $A$ and $B$ be square matrices of order n so that $AB = BA$. Prove $\mathrm{rank}(A+B) \leq \mathrm{rank}(A) + \rm{rank}(B) - \mathrm{rank}(AB)$. Ambiguous
|
| 4269673 Is there a notation to indicate that a variable in this equation is constant? Ambiguous
|
| 127376 In the context of the extended real number system, why is the limit of $\frac{1}{x}$ as $x$ approaches $0$ from the right defined as $\infty$, while the limit from the left is $-\infty$? Unambiguous
|
| 3905420 Would a certain cyclic or dihedral group be an example? How do we find its subgroups? Ambiguous
|
| 2138866 What is the value of the definite integral $\int_{0}^{\pi/4} \frac{\tan^2 x}{1+x^2} \text{d}x$ from the 2015 MIT Integration Bee? Unambiguous
|
| 1688323 How to find the coefficients of a quadratic polynomial given three coordinate points using the method of undetermined coefficients or differentiation? Unambiguous
|
| 13582 Prove that every continuous function from a closed interval $[a, b]$ to itself has a fixed point. Unambiguous
|
| 254561 Provide a proof that $\arctan(x) = \arcsin(x/\sqrt{1+x^2})$ for all real numbers $x$. Unambiguous
|
| 1222768 Why are vector valued functions 'well-defined' when multivalued functions aren't? Ambiguous
|
| 738236 How do I calculate the area of a triangle with vertices defined by the position vectors $a$, $b$, and $c$ in 3D space using the cross product? Unambiguous
|
| 2597743 Can a certain type of integral be solved using the gamma function method? Ambiguous
|
| 2152735 What is the definition of an open set in the context of a general topological space? Unambiguous
|
| 2820510 How to find the rotation quaternion from the angles between coordinate axes $x_1, y_1, z_1$ and $x_2, y_2, z_2$? Ambiguous
|
| 2365371 Prove $ \frac{1}{x^{2n}}+x^{2n}$ is an integer for all $n$. Ambiguous
|
| 401477 Let $A$ be a commutative free algebra of rank $2$ over a ring. Is $A$ isomorphic to a quotient of a polynomial ring by an irreducible element? Ambiguous
|
| 2717459 What is the formula for the expected value of a weighted sum of positive random variables? Unambiguous
|
| 2639179 Am I wrong about the Monty Hall Problem? Ambiguous
|
| 1176215 Prove by induction that $3^{3n+1} + 2^{n+1}$ is divisible by 5 for all non-negative integers $n$. Unambiguous
|
| 1271168 What is the difference between the square of a logarithm, $(\log x)^2$, and the logarithm of a square, $\log(x^2)$? Unambiguous
|
| 1376320 Prove that for integers $a$ and $b$, if $a+b$ and $ab$ have the same parity, then both $a$ and $b$ must be even. Unambiguous
|
| 620187 What do these symbols mean? Ambiguous
|
| 2401656 Compute the value of ${34}^{429} \mod 431$. Unambiguous
|
| 1290374 Can you provide an intuitive explanation and a proof for both parts of the Fundamental Theorem of Calculus? Unambiguous
|
| 19236 Efficient numerical algorithms to compute the Euler gamma function for real and complex arguments Unambiguous
|
| 1194644 Is every integral extension of commutative rings a finite extension? Unambiguous
|
| 2619473 Does the one-sided derivative of a real power series always exist at the boundary of its interval of convergence if the series converges there? Unambiguous
|
| 846706 What strategies can I use to find a conformal map from a lens shape to the first quadrant? Ambiguous
|
| 547928 What is the minimum value of $a+b+\frac{1}{ab}$ if $a^2 + b^2 = 1$? Ambiguous
|
| 2273478 "Translate ""There is exactly one book that no students read"" into first-order predicate logic using predicates $\text{book}(y)$, $\text{student}(x)$, and $\text{reads}(x,y)$." Unambiguous
|
| 1435003 How do I calculate the total number of empty bins in the balls and bins problem given n balls and m bins? Unambiguous
|
| 973713 What are the common notation styles and conventions for the second-derivative symbol in calculus? Unambiguous
|
| 2489152 Why is the bracket always zero? Ambiguous
|
| 3005021 Proof Verification: Differentiability implies continuity. Ambiguous
|
| 2096678 Provide a set of practice exercises on basic matrix arithmetic, including addition, subtraction, and multiplication. Unambiguous
|
| 2618534 Compute the indefinite integral of $\int \frac {1+\sin (x)}{1+\cos (x)} dx$ with respect to $x$. Unambiguous
|
| 159505 Find the value of $x$ that solves the linear congruence $3x + 7 \equiv 6 \pmod{13}$. Unambiguous
|
| 12139 Number of relations that are both symmetric and reflexive Ambiguous
|
| 114107 Determine the rotation necessary to transform one point on a sphere to another. Ambiguous
|
| 1899905 How irrational quantities physically exist in nature? Ambiguous
|
| 1894173 Sum of reciprocal of primes Ambiguous
|
| 3628 Find a general formula for the n-th derivative of the function $f(x)=\frac {x} {x^2-1}$. Unambiguous
|
| 1314138 How do I prove my integral limit is $0$ using the substitution $xt=u$? Ambiguous
|
| 332632 What is the probability that a person which has a positive test result in AIDS, is indeed infected with AIDS? Ambiguous
|
| 1383373 Provide the solution and explanation for Question 55 from the GRE Mathematics Subject Test form 1268. Unambiguous
|
| 2452316 Evaluating a contour integral using Cauchy's generalised integral formula Ambiguous
|
| 2705618 Evaluate $\lim_{n\to\infty} \frac{e^{1/n} + e^{2/n} + \cdots + e^{n/n}}{n}$. Unambiguous
|
| 3021170 Provide an example of a sequence of Lebesgue integrable functions on $R$ that converges pointwise to a limit function, but where the integral of the limit is not equal to the limit of the integrals. Unambiguous
|
| 4569632 In $\triangle ABC$, $BD$ is a median, $\angle DAB=15$ and $\angle ABD=30$. Find $\angle ACB$. Unambiguous
|
| 3303672 Line intersecting circle from origin Ambiguous
|
| 92765 Find all complex roots of the polynomial equation $z^4 + 2z^3 + 6z - 9 = 0$ Unambiguous
|
| 2138847 If $f$ is a holomorphic function on the unit disk $\mathbb{D}$ such that $|f(z)| \le 1$ for all $z \in \mathbb{D}$ and $f(1/2) + f(-1/2) = 0$, prove that $|f(0)| \le 1/4$ and specify if a Möbius transformation is required for the proof. Unambiguous
|
| 685435 Trying to get a bound on the tail of the series for $\zeta(2)$ Ambiguous
|
| 820424 What are the standard methods and laws for simplifying Boolean functions in digital logic? Unambiguous
|
| 3117241 Complex function to Taylor and Laurent series Ambiguous
|
| 1516096 When does $A^TA=0$ imply $A=0$? Ambiguous
|
| 1950367 Does equality of the complexifications imply equality of the algebras? Ambiguous
|
| 551350 Find all complex solutions to the equation $x^4+24x^3+18x^2-27=0$. Unambiguous
|
| 1735792 Prove that for a homogeneous polynomial $P$ of degree $k$ in $n$ complex variables, $$P(z_1,\dots,z_n)=\frac{1}{k!}\sum_{\epsilon_1,\dots,\epsilon_k\in\{0,1\}}(-1)^{k-\sum_{j=1}^k \epsilon_j}P\left(a+\left(\sum_{j=1}^k\epsilon_j\right)z\right)$$ for any $a\in\mathbb{C}^n$. Unambiguous
|
| 1145215 Consider a matrix $A$ that is full rank. Is $A(A^\top A)^{-1}A^\top = I$? Ambiguous
|
| 2987994 Provide a list of examples of definite integrals solvable using the Feynman trick (Leibniz integral rule). Unambiguous
|
| 462723 What are some examples of mathematical games suitable for undergraduate students that can be used for teaching discrete mathematics or game theory? Unambiguous
|
| 184593 Is it necessary for the angle $\theta$ to be measured in radians for the limit $\lim_{\theta \to 0} \frac{\sin \theta}{\theta} = 1$ to hold? Unambiguous
|
| 2186187 How do you calculate the first Fourier coefficient $a_0$ for a periodic function in its Fourier series representation? Unambiguous
|
| 574465 How do you find the complex roots of the polynomial equation $x^4 - 16 = 0$ to show they are $2$, $-2$, $2i$, and $-2i$? Unambiguous
|
| 2289082 Compute the definite integral $\int_1^3\frac{\ln x}{x^2+3}\ dx$ Unambiguous
|
| 269798 Is it true that $E(X^a) = \int x^a g(x)\,dx$? Ambiguous
|
| 4683394 What is the category-theoretic concept that unifies affine hull, convex hull, closure, and interior as intersections of all sets with a given property containing a set? Unambiguous
|
| 4398943 What does 'abstract' mean in this context? Ambiguous
|
| 4367689 Does there exist an ordered field extension of the rational numbers $\mathbb{Q}$ in which $\mathbb{Q}$ is not a dense subset? Unambiguous
|
| 1867732 Gradient and Hessian of function on matrix domain Ambiguous
|
| 791508 Let $A, B, X$ be subgroups of $G$ with $A \subset X \subset AB$. Prove that $A(B\cap X) = X$. Unambiguous
|
| 1950039 What is the identity property of multiplication by one in arithmetic? Unambiguous
|
| 4073406 Infinite subset of natural numbers Ambiguous
|
| 823613 What is the time complexity in $\Theta$-notation in terms of $n$ for the Merge Sort algorithm? Unambiguous
|
| 1896195 Let $M$ be a module over a ring. If $\operatorname{Hom}(M,M)$ is free, what can we conclude about $M$? Ambiguous
|
| 3300982 Prove that if a real orthogonal matrix A commutes with all real orthogonal matrices of the same dimension, then A must be a scalar multiple of the identity matrix. Unambiguous
|
| 3178788 What are the methods to determine the type of stationary point of a single-variable function without calculating the second derivative? Unambiguous
|
| 1587079 How do I prove the map $(i,j) \mapsto (i+j, ij_0 - i_0 j)$ is surjective? Ambiguous
|
| 3764582 Is there a convenient implementation in R to compute my incomplete gamma function integral? Ambiguous
|
| 2918597 Find angle of which a cannon of fixed length has to fire Ambiguous
|
| 1651728 Prove that the union and intersection of two recursively enumerable sets are also recursively enumerable. Unambiguous
|
| 3487811 Evaluate the limit $\lim_{x \to 0} {1-x\cot x\over x^2}$ Unambiguous
|
| 1302479 Prove that the limit of the Dirichlet function does not exist at any point in its domain. Unambiguous
|
| 3493088 $\mathbb{C} \cup \{ \infty \}$ and $\mathbb{R} \cup \{ -\infty, +\infty \}$ Ambiguous
|
| 2520262 Show that $a_{n+1}= 1 + \frac{1}{a_n}$ converges. Ambiguous
|
| 377705 How many repetitions do I need to find a prime between n and 2n? Ambiguous
|
| 726827 Showing a Mapping Between $\left\langle a,b \mid abab^{-1}\right\rangle$ and $\left\langle c,d \mid c^2 d^2 \right\rangle$ is Surjective Ambiguous
|
| 3564289 What is the expected number of returns to the origin for a random walk? Ambiguous
|
| 1232385 How do I prove $\mathbb{Z}[w]/(a)$ is isomorphic to $\mathbb{Z}_{N(a)}$ using the norm? Ambiguous
|
| 700216 How many distinct integer solutions are there for the equation $x + y + z = 10$, where $x$, $y$, and $z$ are all positive integers such that $x, y, z \leq 10$? Unambiguous
|
| 3533343 Counter examples in measures Ambiguous
|
| 1612241 What is the logarithmic identity for the sum of logarithms of multiple terms? Unambiguous
|
| 3743564 Another coins weighing puzzle Ambiguous
|
| 4336 If all eigenvalues of a Hermitian matrix are positive, is the matrix positive definite? Unambiguous
|
| 166553 Can you provide a proof for the definite integral identity $\int_a^b f(x) dx = \int_a^b f(a+b-x) dx$? Unambiguous
|
| 532830 How can I get more intuition about the complex numbers (C) and their multiplication and exponentiation? Unambiguous
|
| 2054106 What are some common generalizations or variations of the Lebesgue Dominated Convergence Theorem in measure theory? Unambiguous
|
| 29758 Prove that every injective entire function from the complex plane to itself is a linear polynomial. Unambiguous
|
| 20813 How does a number system without irrational numbers handle circles? Ambiguous
|
| 2730855 Water is poured into a container at a given rate. How fast does the level rise at a certain height? Ambiguous
|
| 4194118 Area between square and circumscribed circle is less than half the area of the circle. Ambiguous
|
| 2614579 How do I evaluate the limit $\lim_{x\to1} \frac{\sqrt{2x-1} -1}{x^2-1}$ step-by-step? Unambiguous
|
| 1483533 How do I solve a linear equation for a real variable $x$? Unambiguous
|
| 1145215 What is the definition of a matrix inverse in linear algebra and how does it relate to the identity matrix? Unambiguous
|
| 218977 Let $\Omega$ be a rectangle. What is the smallest space to which $\delta_0$ belongs? Ambiguous
|
| 2361340 What is the limit as $x$ approaches infinity of $\frac{1}{x^{n-1}}$ for $n > 1$? Unambiguous
|
| 2770657 Find the Maclaurin series for $\ln(1-x)$ and state its interval of convergence using sigma notation. Unambiguous
|
| 2344095 Find coefficient of $x^2$ in a complicated expansion Ambiguous
|
| 1725118 What are the axioms needed to state the Fixed Point Theorem? Does it apply to ZF, Robinson arithmetic, or PA? Ambiguous
|
| 2732822 How do I solve a system of two equations with two variables where one equation is additive $(x + y = a)$ and the other is multiplicative $(xy = b)$? Unambiguous
|
| 2805228 Let $X_1,\dots,X_{20}$ be independent Poisson random variables with mean $1$. Using Markov's Inequality, find and verify the bound for $P(X_1+\cdots+X_{20} > 15)$. Unambiguous
|
| 20096 Basic addition and subtraction word problems for preschool and kindergarten children. Unambiguous
|
| 2824634 Prove that $\sin(x/2) + 2\sin(x/4) \leq 3\sqrt{3}/2$ for all $x \in [0, 2\pi]$. Unambiguous
|
| 292425 How do I solve a piecewise function if it's not defined on $(-4,-1)$? Ambiguous
|
| 2059626 choose 1 song to be played 3 times and the rest only once Ambiguous
|
| 494832 What is the definition of a ring that is complete with respect to the I-adic topology defined by an ideal $I$? Unambiguous
|
| 1613067 subtracting the eigenvalue matrix from the original transformation of a 2x2 hit's the other eigenvalue proof Ambiguous
|
| 546701 Find the number of positive integers with exactly 5 digits whose digits add up to 42 Unambiguous
|
| 3440597 What is the maximum order of an element in the symmetric group $S_n$ if all elements of the permutation's cycle decomposition must have odd lengths? Unambiguous
|
| 2512671 Find an example of a function $f$ and a set $W$ such that $f(f^{-1}(W)) \neq W$, where $f^{-1}(W)$ denotes the preimage of $W$. Unambiguous
|
| 62621 Is there at least one irrational number with the property that it cannot be defined by a finite string of information? Ambiguous
|
| 4494965 How many ways I can make \$5 in 50c, \$1 and \$2 coins? Ambiguous
|
| 2112893 How to calculate the 100th term of an arithmetic and a geometric series? Unambiguous
|
| 2108420 How to prove that the definite integral $\int_{0}^{\pi}(1+2x)\frac{\sin^3(x)}{1+\cos^2(x)} dx = (\pi+1)(\pi-2)$? Unambiguous
|
| 2806957 Under what conditions does a line intersect a circle in a 2D plane? Unambiguous
|
| 311580 Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$? Ambiguous
|
| 1726540 How to differentiate $x^{\frac1x}$? Ambiguous
|
| 1432379 Find the minimum value of the expression $\frac{1}{x+y} + \frac{1}{x+z} - \frac{1}{x+y+z}$ for positive real numbers $x, y, z$ subject to a fixed sum $x+y+z=S$. Unambiguous
|
| 2999909 Does Hom(X, Y) always form an abelian group? Ambiguous
|
| 1891318 How many binary strings of length 8 do not contain the substring '100'? Unambiguous
|
| 11194 Solving the recurrence relation that contains summation of nth term Ambiguous
|
| 942204 How to derive the general term of a sequence formed by the repeated convolution of a probability distribution with itself? Unambiguous
|
| 3254331 Prove that the definite integral $\int_0^\infty(\arctan(1/x))^2 \mathrm{d}x$ converges to $\pi\ln 2$. Unambiguous
|
| 2326677 What is the signifigance of a saddle point? Ambiguous
|
| 2732822 What do you call a system where $a+b=1$ and $ab=-1$? Ambiguous
|
| 451799 How to prove that $\lim_{x \to 1} \frac{(\sum_{k=1}^n x^k) - n}{x - 1} = \frac{n(n + 1)}{2}$ for a fixed positive integer $n$? Unambiguous
|
| 1258718 "The ""Smooth Factor"" in a number sequence" Ambiguous
|
| 846706 Find a conformal mapping from the lens-shaped intersection of the unit disks centered at $0$ and $1$ in $\mathbb{C}$ to the first quadrant. Unambiguous
|
| 3103052 Compute the limit as $n$ approaches infinity of $n^2\left(\left(1 + \frac{1}{n+1}\right)^{n+1} - \left(1 + \frac{1}{n}\right)^n\right)$ Unambiguous
|
| 1491490 What is the group generated by $M_\pi$? Ambiguous
|
| 720688 What is the average power of this signal? Ambiguous
|
| 2932046 Is this formula correct: $\frac{|(p-a) \times d|}{|d|}$? Ambiguous
|
| 2675393 How to find the derivative of a power series? Unambiguous
|
| 1075740 What happens to the angles of an isosceles triangle if one vertex is at infinity? Ambiguous
|
| 808565 What is the standard mathematical notation for the dimension of a vector space $V$? Unambiguous
|
| 1194644 I'm having trouble coming up with a concrete example of an integral infinite ring extension where $R$ is infinitely generated but $S[R]$ is finitely generated. Ambiguous
|
| 973713 Problem in the second-derivative symbol. Ambiguous
|
| 3328149 Tangents to parabola $y^2=-4(x-1)$ with slopes in a certain range determine chords, bisected by $x=1$, of a circle. Find the equation of the circle. Ambiguous
|
| 3481798 Prove that $\int_0^t\frac{(B^1_s)^2}{\big((B_s^1)^2+(B_s^2)^2+(B_s^3)^2\big)^3}ds<\infty $ a.s. Ambiguous
|
| 3472866 Are the sample mean and sample variance considered random variables? Unambiguous
|
| 345024 What are the applications of Catalan numbers in computer programming and algorithm design? Unambiguous
|
| 553280 What is the number of banded $(0,1)$-matrices with exactly $k$ ones and prescribed row/column sums? Ambiguous
|
| 1531029 If an abelian group $G$ has property $N$, then $G$ is finitely generated Ambiguous
|
| 2901457 Determine for which values of $k$ and $a$ the series $\sum_{n=1}^\infty \frac{\ln^k(n)}{n^a}$ converges. Unambiguous
|
| 3255482 Evaluate $\lim_{x \to 0} \frac{1}{x} \int_{x}^{2x} e^{-t^{2}}\,dt$ Unambiguous
|
| 3002761 How do I find the maximum value of a variable $x$ when it is subject to a given equality constraint? Unambiguous
|
| 298648 Is there a common symbol for concatenating two (finite) sequences? Ambiguous
|
| 1720548 Given a vector $v$, is it possible to find another vector $w$ such that $v$ is the result of the cross product of $w$ and some third vector $u$? Unambiguous
|
| 4768 Prove that every permutation of a finite set is either even or odd, but not both. Unambiguous
|
| 314408 What are the conditional probabilities for my simple OR-gate where $P(A)=0$ and $P(B)=0$? Ambiguous
|
| 4221432 What are the general integer solutions to the Diophantine equation $a^2+b^2=c^2-1$ for positive integers $a, b, c$? Unambiguous
|
| 744139 I'm having trouble with the expression 2*8^n + 3*15^n + 2. I tried using k+1 but I can't find a solution. Ambiguous
|
| 2368762 Given that $\frac{\sin(x)}{a}=\frac{\cos(x)}{b}$ for some constants $a$ and $b$, what is the value of $a\sin(2x)+b\cos(2x)$ in terms of $a$ and $b$? Unambiguous
|
| 1673403 A function is never zero, takes both signs, and is continuous. How is that possible? Ambiguous
|
| 378970 For a right triangle with a hypotenuse of 12 cm, what measures of the acute angles would produce the maximum area? Unambiguous
|
| 736346 What are the geometric methods to fold a rectangular piece of A4 paper into three equal parallel strips? Unambiguous
|
| 3673715 I need help with the heat equation in a 3D ball. Ambiguous
|
| 1494248 Evaluate the indefinite integral $\int \frac{\sin(4x)}{\sin(x)} \, dx$. Unambiguous
|
| 185267 How do I prove that a subset of a set with Lebesgue outer measure zero also has outer measure zero? Unambiguous
|
| 2492396 An equation is first-order nonlinear. How do I transform it into standard linear form? Ambiguous
|
| 289779 Determine whether the sequence $a_n = 3^n - 2^{n+100}$ for $n \in \mathbb{N}$ converges or diverges. Unambiguous
|
| 330556 Is the sequence defined by $a_n = 3^{2n}$ a geometric progression? If so, find its common ratio and the sum of the first n terms. Unambiguous
|
| 3487811 $\lim_{x \to 0} {1-x\cot x\over x^2}$ Ambiguous
|
| 366529 Is it valid to define $\int_{-a}^a f(x)\,dx = \int_{-a}^0 f(t)\,dt + \int_0^a f(x)\,dx$ for a real-valued function $f$? Unambiguous
|
| 387437 How can you prove that a number is an algebraic integer? Ambiguous
|
| 2030790 3 variable diophantine equation word problem: coins Ambiguous
|
| 464426 Evaluate the limit $\lim_{x \to 1} \frac{x^{1/5}-1}{x^{1/3}-1}$ for real-valued $x$. Unambiguous
|
| 3601099 For a symmetric matrix and a unit vector, why does a certain quartic inequality involving inner products hold? Ambiguous
|
| 1455761 What is the relationship between the determinant of a square matrix and its inverse? Unambiguous
|
| 2887105 Express $\frac{1}{1-i-z}$ as a power series in $z$ valid for $|-z-i|<1$. Unambiguous
|
| 2614579 How to solve $\lim_\limits{x\to1} \frac{\sqrt{2x-1} -1}{x^2-1}$? Ambiguous
|
| 531128 What are the subspaces of a finite-dimensional vector space $V$ that have dimension $\dim V - 1$, and what are they called? Unambiguous
|
| 735461 Suppose $f\colon M_n \to M_m$ with $f(a) = I_m$. Is there a positive element $b\in M_n$ such that $f(b)=I_m$? Ambiguous
|
| 1861189 $PC$ bisects $\angle APB$. Prove $XY \parallel AB$. Ambiguous
|
| 2369950 Is the statement $|x|=\pm x$ for $x>0$ a correct definition of absolute value, and why is it confusing? Unambiguous
|
| 736044 A number divided by $q$ leaves remainder $r$. Find $r+q$. Ambiguous
|
| 2339487 rove that whenever there exists an $[N,K,D]$-linear code over $\mathbb{F}_{q^{n-1}}$, there exists an $[nN,(n-1)K,2D]$-linear code over $\mathbb{F}_q$. Unambiguous
|
| 4044721 Find the limit of $\lim_{x\to 0}\left(\frac{\cos x}{\cos 2x}\right)^\frac{1}{x^2}$ Ambiguous
|
| 2666204 How do I optimize $(\pi R_1 R_2)h$ when I don't know what the surface area should be? Ambiguous
|
| 1071811 Why is the Zariski topology on an algebraic variety over an algebraically closed field not Hausdorff? Unambiguous
|
| 2260 Prove by mathematical induction that the sum of the first $n$ positive integers is $1+2+3+4+\cdots+n = \frac{n\times(n+1)}2$. Unambiguous
|
| 128823 limit of integral $n\int_{0}^{1} x^n f(x) \text{d}x$ as $n\rightarrow \infty$ Ambiguous
|
| 2006377 Average integral increasing Ambiguous
|
| 20813 What is the intuitionistic construction of the unit circle in constructive mathematics? Unambiguous
|
| 3367250 For this equation, does it matter which variable we treat as independent? Ambiguous
|
| 4236641 What is the best way to find the closest vector in a set to a given one? Ambiguous
|
| 721784 Absolute value of complex exponential Ambiguous
|
| 2844637 I need to calculate $\cos(\pi/20)$ with an error less than $10^{-5}$ using a series. Is my answer correct? Ambiguous
|
| 835454 $f: SL_2(\mathbb{R}) \to GL_4(\mathbb{R})$ show that $Im(f)=SL_4(\mathbb{R})$ Ambiguous
|
| 568493 How do you find the number of common codes for [1,5], [4,8] and [3,7], [2,6]? Ambiguous
|
| 1768578 How to find the relation between $a$, $c$ and $b$ to make my density function integral $1$? Ambiguous
|
| 3815586 If a function is differentiable almost everywhere, what is its regularity? Ambiguous
|
| 2931443 If $\sum c_n x^n = (\sum a_n x^n)(\sum b_n x^n)$, does it follow that $\sum c_n = (\sum a_n)(\sum b_n)$? Ambiguous
|
| 1283678 Prove $||\lambda x_1 + (1-\lambda) x_2 - y|| \leq ||x_1 - y||$ Ambiguous
|
| 1942246 I need to prove trigonometric equation Ambiguous
|
| 2620801 Proof Group Homomorphism: $\varphi(e)= e'$ & $\varphi(\hat{a})= \widehat{\varphi(a)}$ Ambiguous
|
| 960632 Evaluating product of exponent and polynomial Ambiguous
|
| 697675 multiplying a matrix by a row vector Ambiguous
|
| 2360710 What is the numerical value or a series expansion formula for the natural logarithm of $\pi$, $\ln(\pi)$? Unambiguous
|
| 587560 What is the purpose of the base case in a proof by mathematical induction? Unambiguous
|
| 2038540 Permutations with men and women alternating Ambiguous
|
| 1663674 Does my genome exist in the digits of pi? Ambiguous
|
| 2315737 Is checking a norm on a function space just the triangle inequality and the other two rules? Ambiguous
|
| 3969765 Evaluate the integral $\int_0^\infty \frac{e^{-tx^2}-e^{-x^2}}{x}dx$ for $t > 0$. Unambiguous
|
| 2205890 In what mathematical context or under what non-standard ordering could the inequality $\frac{1}{2} < \frac{1}{4}$ be true? Unambiguous
|
| 1072741 Is an open $n$-ball homeomorphic to $\mathbb{R}^{n}$? Ambiguous
|
| 62473 What is the definition of a quasifinite morphism of schemes? Unambiguous
|
| 824000 If a function $f: X \to X$ satisfies $f(f(x)) = x$ for all $x \in X$, does it follow that $f$ is bijective? Unambiguous
|
| 2165873 For $f(x)=\begin{cases}2,&x>2\\3,&x<2\end{cases}$ and $g(x)=\begin{cases}-2,&x\ge2\\2,&x<2\end{cases}$, find $g(x)-f(x)$, addressing whether the result is defined at $x=2$. Unambiguous
|
| 264371 Recommend challenging but engaging mathematics books suitable for advanced undergraduate students that cover topics beyond the standard curriculum. Unambiguous
|
| 3111260 Error evaluating $ \lim_{x\to 0}\frac{x-\tan x}{x^3} $ Ambiguous
|
| 1176875 Find all integer solutions $(a, b, c)$ to the equation $a + b + c = abc$. Unambiguous
|
| 4094225 Given point $K$ in a triangle, is it possible to construct a line through $K$ that bisects the area of the triangle? Ambiguous
|
| 13582 Show that a continuous function has a fixed point Ambiguous
|
| 3735022 Does knowing the Gauss curvature is $1/R^2$ help prove the curve's curvature is $\geq 1/R$? Ambiguous
|
| 587560 What is the purpose of the first test in an inductive proof? Ambiguous
|
| 1108298 Why is the canonical map $M \otimes_A N \to M \otimes_{A/I} N$ an isomorphism? Ambiguous
|
| 3979952 Are $\sum_{i=1}^{n} \xi_i / i$ and $\max\xi_n$ equally distributed? Ambiguous
|
| 665341 Using only a compass fixed at a radius of $5$ inches and a straightedge, construct a circle of radius $4$ inches. Unambiguous
|
| 4067963 Prove that the sum of the reciprocals of the integers in the set $M(P)$, where $M(P)$ consists of all positive integers whose prime factors are in the set $P$, converges and find its sum in terms of the prime zeta function. Unambiguous
|
| 1048 Compare the different definitions of trigonometric functions using right triangles, the unit circle, and power series. Unambiguous
|
| 675332 On the set $S = \mathbb{R}\setminus\{-1\}$ with operation $a * b = a+b+ab$, solve $2*x*3 = 7$ for $x$. Unambiguous
|
| 2605427 Prove that for any connected graph $G$, there exists a partition of the vertex set into two sets $V_1$ and $V_2$ such that the induced subgraphs $G[V_1]$ and $G[V_2]$ are both connected. Unambiguous
|
| 3729113 What is the definition and region of convergence for a Dirichlet series of a complex variable? Unambiguous
|
| 290435 Find five positive integers whose reciprocals sum to $1$ Ambiguous
|
| 261680 Find integer values of $a,b$ such that $k=a^3-b^2$ is a perfect square. Ambiguous
|
| 2042807 Construct a homeomorphism between the unit circle $S^1$ and the boundary of a square in $R^2$. Unambiguous
|
| 288432 Let a power series have radius of convergence 1 and diverge at $x=1$. Does it diverge as $x\to 1$? Ambiguous
|
| 4812185 How to prove what the Wikipedia page says about the entry wise norm limit being the maximum norm? Ambiguous
|
| 1490059 What is the definition of the curl of a 3D vector field in vector calculus? Unambiguous
|
| 3468876 Calculate the mean, variance, and marginal distribution of the random variable X = Y1 + Y2, where Y1 and Y2 are independent standard normal random variables. Unambiguous
|
| 331345 How do I find the solutions for the equation $2x^2 - 5x + 3 = 0$? Unambiguous
|
| 295318 Are all algebraic vector bundles on the affine line over a principal ideal domain (PID) trivial? Unambiguous
|
| 219774 Finding the periods of functions... Ambiguous
|
| 172468 Why does MatLab generate polynomials for cyclic codes for all $n,k$ I try dividing $x^n-1$? Ambiguous
|
| 4117494 Volume of tetrahedron Solid Ambiguous
|
| 2007373 What are the fundamental geometric intuitions used to understand concepts in undergraduate linear algebra and multivariable calculus? Unambiguous
|
| 2897989 Prove that the dilation operator on $L^2(\mathbb{R})$ is a bounded linear operator. Unambiguous
|
| 4567071 How can you show the results from substituting $x=a\cos{\theta}$ and $x=a\sin{\theta}$ are the same when finding $\int{\frac{16}{\sqrt{9-x^2}}}$? Ambiguous
|
| 730358 How do I graph a general sine function of the form y = a sin(bx - c) + d? Unambiguous
|
| 2394582 Show that $f(x) = x^3 - x$ is an odd function. Unambiguous
|
| 3839814 Probability that $\text{det}(A)$ is an even number. Ambiguous
|
| 2160552 Do elementary row operations change the eigenvalues of a square matrix? Unambiguous
|
| 4016729 Find all real values of theta such that $(\sin(\theta) - \cos(\theta))(2+\sin(\theta) \cos(\theta)) \leq 2$. Unambiguous
|
| 315869 Sequence of sets and neighborhoods Ambiguous
|
| 742878 Modeling with Exponential and Logarithmic Functions Ambiguous
|
| 1496959 How to show $f_n$ converges uniformly to $f'$ if the derivative is bounded by $3|x-y|$? Ambiguous
|
| 1745083 How do you find the shortest path between two fixed points in a 2D plane that avoids a given linear obstacle? Unambiguous
|
| 124287 Is the map $f(a+bi)=a$ a homomorphism of rings? Ambiguous
|
| 4221432 Near-Pythagorean triplets: What are the general solutions to $a^2+b^2=c^2-1$? Ambiguous
|
| 2540002 Let $$S=\sum_{i=0}^N \frac{1}{\sqrt{2\pi\sigma^2}}e^{-(i+0.5)^2/(2\sigma^2)}$$. Any ideas? Ambiguous
|
| 765044 Challenge: Demonstrate a Contradiction in Leibniz' differential notation Ambiguous
|
| 1896195 Under what conditions is the endomorphism ring of a module free as a module over the base ring? Unambiguous
|
| 1882798 Given constants $X, Y, P$, determine whether there exist positive integers $a, b$ such that $(aX+bY) \bmod P = 0$. Unambiguous
|
| 2540359 Does the fact that both examples and counterexamples exist mean a property is undecidable from the axioms? Ambiguous
|
| 3516041 Third order Taylor polynomial of $f:(0, \infty) \times \mathbb{R} \to \mathbb{R}$ given by $f(x,y) = x^y$ Ambiguous
|
| 2128278 How do I compute the indefinite integral of the hyperbolic sine function $\sinh(x)$? Unambiguous
|
| 4087621 In which of the intervals is $\sqrt{12}$ Ambiguous
|
| 458261 How do I rewrite a triple integral with different limits for $x+y-2z=2$? Ambiguous
|
| 4044721 Find the limit of $\lim_{x\to 0}\left(\frac{\cos x}{\cos 2x}\right)^\frac{1}{x^2}$ Unambiguous
|
| 1310890 What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$? Ambiguous
|
| 195504 Prove that for a linear functional, the kernel has codimension one. Ambiguous
|
| 1438319 Prove that $\lim_{x\to 0} \frac{e^x-1}{x}=1$ using the definition of the exponential function or power series, without using L'Hôpital's rule or derivatives. Unambiguous
|
| 2597743 How do I compute the indefinite integral of a function of the form $f(x) = x^n e^{-ax}$? Unambiguous
|
| 2093882 Problem in solving a question related to finite difference. Ambiguous
|
| 2555463 How do I find the coordinates of a point in a 2D plane that is equidistant from two given points and a given line? Unambiguous
|
| 2339487 Does putting $n-1$ copies of a codeword after itself prove there is a linear code? Ambiguous
|
| 12139 How many binary relations on a set of size n are both symmetric and reflexive? Unambiguous
|
| 3084662 How to convert a complex number $z = a + bi$ to polar form (calculate the magnitude r and the argument theta). Unambiguous
|
| 1007952 For a random variable $X$ with pdf $f(x)=\frac12 e^{-|x|}$, what can we say about it? Ambiguous
|
| 608477 What is the general method for a proof by mathematical induction, and can you provide a step-by-step example? Unambiguous
|
| 4569632 In $\triangle ABC$, $BD$ is a median, $\angle DAB=15$ and $\angle ABD=30$. Find $\angle ACB$. Ambiguous
|
| 1002480 Is the Minkowski sum of a finite collection of compact line segments in Euclidean space compact? Unambiguous
|
| 2782880 Proof check: AB not invertible Ambiguous
|
| 25648 Prove that if two integers $a$ and $b$ are congruent modulo $n$, then $\gcd(a, n) = \gcd(b, n)$. Unambiguous
|
| 2548701 Find the integer part of the value of the infinite nested radical $x = \sqrt[3]{24+\sqrt[3]{24+\sqrt[3]{24+\cdots}}}$ Unambiguous
|
| 3017595 Dimension of subspace 10x10 Ambiguous
|
| 2932095 Find $a$ so that a line is tangent, secant or external from a sphere Ambiguous
|
| 176625 Prove that there do not exist positive integers $x$ and $y$ with $x^2 - y^2 = n$ Ambiguous
|
| 2035929 How to prove bounds of area integral? Ambiguous
|
| 1024146 Is a group divisible if and only if it has no maximal subgroup? Ambiguous
|
| 2140493 What are some classic counterintuitive examples or paradoxes in probability theory, such as the Monty Hall problem or the Birthday paradox? Unambiguous
|
| 2657826 How to find values of $a$ and $b$ if the rest is $15$ when $P(x)$ is divided by $(x-2)$? Ambiguous
|
| 2604608 How do I prove $f(x)$ is continuous when it only has constants $a$ and $b$? Ambiguous
|
| 795652 How to find nth moment? Ambiguous
|
| 1391080 Can I express the theorem about $\sqrt{2}$ as $p\Rightarrow q$? Ambiguous
|
| 83035 How to prove $(1+1/x)^x$ is increasing when $x>0$? Ambiguous
|
| 36545 What are some examples of mathematically simple puzzles or conjectures that remained unsolved or were counterintuitive to professional mathematicians for a long time? Unambiguous
|
| 2044396 Can this be proven for all groups? Ambiguous
|
| 184593 Is it necessary to have $\theta$ in radians to obtain $\frac{\sin{\theta}}{\theta} \to 1$ as $\theta\to 0$? Ambiguous
|
| 3083195 How to solve a linear first-order ODE for various initial conditions? Unambiguous
|
| 3219211 Can a first-order homogeneous ordinary differential equation have a singular solution that is not a member of the general solution family? Unambiguous
|
| 225922 Provide an example of a problem in real-variable calculus or algebra where the solution is real, but the most efficient method of calculation requires the use of complex numbers as an intermediate step. Unambiguous
|
| 3172708 I have the inverse of a sparse matrix, and only 4 entries change. I need a quick way to get the new inverse. Ambiguous
|
| 2457906 Evaluate the double integral in polar coordinates $\int_{0}^{3\pi/2}\int_{1}^{4}(4-r)(2+\sin\theta)r dr d\theta$. Unambiguous
|
| 289461 Is the set of midpoints of the open intervals that make up the complement of the Cantor ternary set countable? Unambiguous
|
| 3123246 What is the closed-form value of the definite integral $\int_0^\pi \ln(1+\sin^2 t) dt$? Unambiguous
|
| 19236 Algorithm to compute Gamma function Ambiguous
|
| 3415231 How do I prove the universal generalization theorem in my discrete math image? Ambiguous
|
| 262629 What is the probability of a specific set of group stage pairings occurring in a UEFA Champions League draw, assuming all valid permutations are equally likely? Unambiguous
|
| 1386774 What is the definition and convergence criteria for a power series representation of a function? Unambiguous
|
| 1890614 Mathematical definition of infinity Ambiguous
|
| 3762261 What is the geometric intuition behind the spectral theorem for Hermitian operators on a finite-dimensional complex Hilbert space? Unambiguous
|
| 314809 Super or subscript notation on the left hand side of a symbol? Ambiguous
|
| 4814 Is there a name for graphs with 2 connections per node? Ambiguous
|
| 1824176 Why is the graph of the function $f(x) = \sin(\arccos(x))$ a semicircle with radius $1$ centered at the origin? Unambiguous
|
| 262371 How do you solve the area of a trapezoid using diagonals Ambiguous
|
| 3524864 Solve the first-order linear partial differential equation $-x^2u_x+u_y=1$ with the initial condition $u(e^y,y)=y$. Unambiguous
|
| 1291623 Direct Proof on Divisibilty Ambiguous
|
| 2445959 Find all natural numbers $n$ such that $n - 2$ divides $n^2 - 2$. Unambiguous
|
| 1176875 Find all integral solutions to $a+b+c=abc$. Ambiguous
|
| 67407 Prove that every group of order 15 is abelian. Unambiguous
|
| 457969 What is the definition and property of the minimum of a function on a closed interval? Unambiguous
|
| 125846 L'Hopital's rule, why is this incorrect? Ambiguous
|
| 2344095 How do I find the coefficient of $x^2$ in the binomial expansion of $(1 + 2x + 3x^2)^10$? Unambiguous
|
| 71874 In the context of power sets in set theory, can I apply the properties of power sets to prove the existence of larger cardinalities? Unambiguous
|
| 2338603 What is the formula and definition for the binomial coefficient ${n\choose k}$? Unambiguous
|
| 1327420 Solve the system of equations $x + xy + y = 11$ and $yx^2 + xy^2 = 30$ for real numbers $x$ and $y$. Unambiguous
|
| 1831188 How to compute the 2006th power of a given square matrix $M$? Unambiguous
|
| 1067717 How do I prove that the summation $\frac{2\sum_{k=0}^n 2^k}{n+1} = 2^{n+1}$ is false, or what is the correct simplification of $\frac{2\sum_{k=0}^n 2^k}{n+1}$? Unambiguous
|
| 3976203 What do I do with the extra variables in this equation: $$0 = -i+(iq-ix+1)\ln(1+i)-(1-d)^xln(1+i)-(1-d)^xln(1-d)+t (1-d)^xln(1+i)+t \ln(1-d)^x$$ Ambiguous
|
| 456595 Prove that the infinite series $\sum_{n=1}^\infty \frac{1}{n^2}$ converges and that its sum is less than 2. Unambiguous
|
| 3005021 Provide a formal proof that if a function $f: \mathbb{R} \to \mathbb{R}$ is differentiable at a point $x$, then it must also be continuous at that point. Unambiguous
|
| 1951021 Why in calculus the angles are measured in radians? Ambiguous
|
| 1831188 Calculating the matrix $M^{2006}$ Ambiguous
|
| 3832187 Distributing 3 objects in 5 boxes Ambiguous
|
| 2903468 Prove that the definite integral $\int_0^1\frac{\ln(x)}{\sqrt{1-x^2}}dx = -\frac{\pi}{2}\ln(2)$. Unambiguous
|
| 110579 In how many ways can a batsman score a century in all $6$'s and $4$'s? Ambiguous
|
| 2246596 What is the max function exactly and how do I examine its contour maps? Ambiguous
|
| 510991 If every continuous function on $X$ is uniformly continuous, is $X$ compact? Ambiguous
|
| 614812 What is the maximum number of knights that can be placed on a $2 \times n$ chessboard such that no two knights attack each other? Unambiguous
|
| 1290291 Identification of a quadrilateral as a trapezoid, rectangle, or square Ambiguous
|
| 3483693 Find the smallest integer $n > 1$ such that $n^2 \equiv n \pmod{1000}$. Unambiguous
|
| 1153474 Is the function $f(n) = 2^{\log_3(n) + 1}$ in $\Theta(n)$ for asymptotic running time analysis? Unambiguous
|
| 2206714 Evaluate the indefinite integral $\int \sin(2x) \frac{e^{\cos^2 x}}{e^{\sin^2 x}} dx$. Unambiguous
|
| 2470166 What are the conditions for the eigenvectors of this matrix to be to be real and orthogonal? Ambiguous
|
| 2307642 Proof of the spectral theorem for normal operators on a finite-dimensional complex inner product space Unambiguous
|
| 1054529 the purpose of induction Ambiguous
|
| 2669751 How do you count all unique groups that can be made with items Ambiguous
|
| 2049971 Is it possible to transform $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ into $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$? Ambiguous
|
| 1731227 Find he local maximum and minimum value and saddle points of the function? Ambiguous
|
| 4343109 For a graph $(G, V)$, $\
|
| 1271168 How do I square a logarithm? Ambiguous
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| 292425 For $f(x)=\begin{cases}\dfrac{x^2-1}{x+1},&x<-4\\[4pt] ax^2+2x+b,&-1\le x<0\\[4pt] |x+a+2|,&x\ge0\end{cases}$, find $a$ and $b$ such that $f$ is continuous everywhere it is defined, noting that $f$ has no definition on $(-4,-1)$. Unambiguous
|
| 2897989 Let $D$ be defined by $D(a)=f_a$ for $f\in L^2(\mathbb{R})$. Show that $D$ is continuous. Ambiguous
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| 241316 Does the infinite series $\sum_{k=1}^{\infty} \frac{\sqrt{k}}{(k+1)^2}$ converge? Unambiguous
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| 1961686 If $X$ is a topological space, is it true that for any two points $x, y \in X$, the subspaces $X \setminus \{x\}$ and $X \setminus \{y\}$ are homeomorphic? Unambiguous
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| 1438319 Prove that $\lim_\limits{x\to 0}{\frac{e^x-1}{x}}=1$ without derivatives Ambiguous
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| 33296 How do you prove that a differentiable function is monotonic given information about the sign of its derivative? Unambiguous
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| 4317139 Bianchi classification of solvable Lie groups and cocompact subgroups Ambiguous
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| 820492 Are there algorithms to simulate the continuous deformation of a cup into a donut? Ambiguous
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| 521814 I have this picture and I know a height. How do I find its other proportions using perspective projection? Ambiguous
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| 709004 Evaluate $\lim_{x\to\infty}\left(\frac{x^2+2x-1}{2x^3-3x-2}\right)^{1/x}$. Unambiguous
|
| 866327 Prove that $\lim_{x\to 1} \frac{x^n-1}{x-1} = n$ for all positive integers $n$ without using L'Hôpital's rule. Unambiguous
|
| 2296759 What is the relationship between a symmetric matrix and the inner product it defines on a vector space? Unambiguous
|
| 3538836 How is this inequality proved for the squeeze theorem if it doesn't hold for all $x$? Ambiguous
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| 1900241 What is the expected value of $X$, given its generating function? Ambiguous
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| 4595703 If parallel chords of a circle subtend central angles of $72^\circ$ and $144^\circ$, then the perpendicular distance between them is half the radius Ambiguous
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| 2537775 Evaluate $\prod_{r=1}^{10}(1+\tan r^\circ)\cdot\prod_{r=46}^{55}(1+\cot r^\circ)$. Unambiguous
|
| 2249320 Find a closed-form expression for $g(x) = \cos x + \cos 3x + \cos 5x + \cdots + \cos((2n-1)x)$. Unambiguous
|
| 972189 Provide a proof that the limit as $n$ approaches infinity of $\left(\frac{n - 1}{n}\right)^n$ is equal to $\frac{1}{e}$. Unambiguous
|
| 298648 What is the standard notation for the concatenation of two finite sequences in mathematics and computer science? Unambiguous
|
| 2820510 How are quaternions used to represent 3D rotations in geometry? Unambiguous
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| 1812294 How to find $P(B\cup C)$ when $A$ and $B$ are independent and the union of $A,B,C$ is $1$? Ambiguous
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| 1111222 Is a function that's unbounded near a boundary point still integrable if we redefine its value there? Ambiguous
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| 986013 What should I do with the fact that my Laurent series converges in $z=1+i$? Ambiguous
|
| 108308 Does Tom Apostol's proof of the Fundamental Theorem of Calculus involve a division by zero? Unambiguous
|
| 2697247 What are the standard integral representations of the Bessel function of the first kind $J_n(x)$? Unambiguous
|
| 2296602 Simplify the propositional logic expression $\neg ((P \to (Q \to R)) \to (Q \to (P \to R)))$ to its simplest form. Unambiguous
|
| 3944628 I'm reading a book and, in its section on the definition of a stopping time(continuous), the author declares at the start that for the whole section every filtration will be complete and right-continuous. So, in the definition of a Stopping Time, how important are these conditions? Why would they matter? Unambiguous
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| 548732 In set theory, is it true that $A\cup(B\triangle C)=(A\cup B)\triangle(A\cup C)$ for all sets A, B, and C? Unambiguous
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| 1045011 How to find the limit $\lim_{n\to \infty}\frac{n}{2^n-1}$? Ambiguous
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| 1258955 Convergence of the integral $\int_0^{\pi/2}\ln(\cos(x))dx$ Ambiguous
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| 2427685 Calculate the limit $\lim_{n \to \infty} \sum_{k=1}^{n} \frac{(-1)^{k-1}}{k^2 \binom{n}{k}}$. Unambiguous
|
| 124986 Is the function $\alpha : \mathbb{Z}_{11} \rightarrow \mathbb{Z}_{11}$ defined by $\alpha(x) = 4x^2 - 3x^7 \pmod{11}$ a permutation, and if so, is it a single cycle? Unambiguous
|
| 3289735 Is the arc length always irrational between two rational points? Ambiguous
|
| 3564289 What is the expected number of times a simple symmetric random walk on a 1D integer lattice returns to the origin? Unambiguous
|
| 2381284 For $f_{a,c}(x)=\int_0^\infty\left[t^a(1+t)^{c-a-1}e^{-xt}-e^{-t}+e^{-xt}\right]\frac{dt}{t}$ with $a>0,x>0,c\in\mathbb{R}$, determine the sign of $f_{a,c}(x)$, given that $f_{a,c}'(x)<0$. Unambiguous
|
| 1592652 Example of a relation that is symmetric and transitive, but not reflexive Ambiguous
|
| 984271 Provide an explicit isomorphism showing that $\mathbb{K} \otimes M_n(\mathbb{C})$ is isomorphic to $\mathbb{K}$, where $\mathbb{K}$ denotes the compact operators on a separable Hilbert space. Unambiguous
|
| 3762872 Zeno's Achilles & Tortoise - Where exactly is the proof wrong? Ambiguous
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| 1489146 How is the imaginary unit $i$ formally defined in the context of complex numbers, and why is $i$ not equal to $-i$? Unambiguous
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| 1987599 It's known that a certain function behaves like $1/u$ near $u=0$. Are there sharper inequalities describing this behavior? Ambiguous
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| 859968 Let $Y = \{(x, x/n) \in \mathbb{R}\times\mathbb{R} : x \in [0,1], n \in \mathbb{N}\}$ and $X = \bigcup_{n\in\mathbb{N}} [0,1]\times\{n\}$ with equivalence relation $(0,n) \sim (0,m)$ for all $n,m \in \mathbb{N}$. Prove or disprove that the quotient space $X/{\sim}$ is homeomorphic to $Y$. Unambiguous
|
| 1204425 Solve the nonlinear ODE $y' + y^2 = 0$ using a power series solution $y = \sum_{n=0}^\infty a_n x^n$, given that substitution leads to $\sum_{n=1}^\infty a_n n x^{n-1} + \sum_{n=0}^\infty\left(\sum_{k=0}^n a_k a_{n-k}\right)x^n = 0$. Unambiguous
|
| 1059293 Can someone explain how the proof for f(x) works? Ambiguous
|
| 956087 Provide an example problem and a step-by-step solution involving implicit differentiation of a curve defined by an equation in x and y. Unambiguous
|
| 3023583 Does the infinite series $\sum_{n=1}^\infty \frac{n^2(-1)^n}{1+n^2}$ converge or diverge? Unambiguous
|
| 759112 Given that $Y - X^2$ is an irreducible polynomial, prove that the variety $V(Y-X^2)$ is irreducible. Unambiguous
|
| 959137 Finding missing coordinates in a non-linear graph? Ambiguous
|
| 2715973 $$ \frac{n}{n+2}\sum_{k=1}^n\frac{k}{k+3}$$ Ambiguous
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| 801923 Prove that for all integers $x$ and $y$, if $x + y + xy = 0$, then $(x, y) = (0, 0)$ or $(x, y) = (-2, -2)$. Unambiguous
|
| 1503414 Why is the natural logarithm of 1 equal to 0? Unambiguous
|
| 3035983 How can I find integers which satisfy $\frac{150+n}{15+n}=m$? Ambiguous
|
| 476186 Is there a category whose internal logic is paraconsistent? Ambiguous
|
| 108191 Why won't sine functions work as a counter example for my infinite integral proof? Ambiguous
|
| 401477 What is the definition of a $\mathbb{Z}/N\mathbb{Z}$-algebra? Unambiguous
|
| 1135959 What is the standard way to represent a complex number as a $2 \times 2$ real matrix? Unambiguous
|
| 802940 How to calculate the numerical value of the sum from $k=1$ to $50$ of $k^{1/3}$? Unambiguous
|
| 1035200 Let $p:\mathbb{N}\to\mathbb{N}$. What is $\lim p(n)$? Ambiguous
|
| 685681 Prove that a finite-dimensional vector space has a finite basis. Unambiguous
|
| 1893124 If 16 players are divided into eight pairs, what is the probability that only one of S1 or S2 advances? Ambiguous
|
| 158469 Prove that if a linear endomorphism $\alpha$ on a finite-dimensional complex inner product space satisfies $\alpha^* = -\alpha$, then its eigenvalues are purely imaginary. Unambiguous
|
| 1564864 What does the symbol
|
| 2564222 Find the equations of the tangent lines drawn from the point $(11, 3)$ to the circle defined by $x^2 + y^2 = 65$. Unambiguous
|
| 1295010 What are examples of true statements about natural numbers that can be proven using non-inductive methods, or that are independent of Peano arithmetic and thus cannot be proven by induction? Unambiguous
|
| 3743564 Examples of classic coin weighing puzzles and their optimal solutions using a balance scale Unambiguous
|
| 783173 Evaluate the definite integral $\int_0^1 \frac{dx}{\sqrt{x(1-x)}}$ Unambiguous
|
| 4814 What are the names of directed graphs where every vertex has an in-degree of 2 and an out-degree of 2? Unambiguous
|
| 2448533 How to evaluate a limit with arctan(x) Ambiguous
|
| 2365371 If $x + frac{1}{x}$ is an integer, prove that $x^{2n} + frac{1}{x^{2n}}$ is an integer for all positive integers $n$. Unambiguous
|
| 1232385 Let $S=\{\sqrt{D}: D\equiv 2,3\pmod4\}$ and $T=\left\{\frac{1-\sqrt{D}}{2}: D\equiv 1\pmod 4\right\}$. For $w\in S\cup T$ and the norm map $N:\mathbb{Z}[w]\to\mathbb{Z}$, prove that $\mathbb{Z}[w]/(a) \cong \mathbb{Z}_{N(a)}$ for $a\in\mathbb{Z}[w]$. Unambiguous
|
| 1528935 How to prove a set is linearly independent without using a basis or FTA? Ambiguous
|
| 2274060 If $x$ and $y$ are positive numbers, what is the minimum possible value of $(x+y)\left(\frac1x + \frac1y\right)?$ Ambiguous
|
| 1788328 Calculate the numerical value of the product $\sin(10^\circ) \sin(50^\circ) \sin(70^\circ)$. Unambiguous
|
| 311665 Proof a graph is bipartite if and only if it contains no odd cycles Ambiguous
|
| 176625 For which positive integers $n$ is it true that there do not exist positive integers $x$ and $y$ such that $x^2 - y^2 = n$? Unambiguous
|
| 1883279 What are examples of continuous functions that cannot be uniformly approximated by polynomials on a given interval? Unambiguous
|
| 405972 A basis for a subspace of $\mathbb R^3$ Ambiguous
|
| 4734106 Is there an equation similar to square root, but faster for a computer to compute? Ambiguous
|
| 3226462 On an infinitely sided die, is it possible to roll and get the same number twice? Ambiguous
|
| 529215 Is it true that if a sequence {a_n} converges, then the set of its values has exactly one limit point? Ambiguous
|
| 2297557 Given three points $A, B, M$ in the plane, determine whether there is a unique point $R$ satisfying $d(R,A)\cdot d(R,B) = d(R,M)^2$, or find the curve formed by all such points $R$. Unambiguous
|
| 1796173 I tried to expand the bracket $[X,Y]=XY-YX=Y$, how do I proceed to find $[Y,Z]$? Ambiguous
|
| 3154407 Applying a function on any multiset of real numbers Ambiguous
|
| 2591017 Unity roots that sum to 1 Ambiguous
|
| 1382185 How many divisors of the combination of numbers? Ambiguous
|
| 151810 What is the probability of getting exactly 3 heads in 10 independent flips of a fair coin? Unambiguous
|
| 807589 For a pure tensor $v_1\otimes\cdots\otimes v_n \in V^{\otimes n}$, what is the standard terminology for the component vector $v_j$? Unambiguous
|
| 927248 Maximum value of $a+b$ given that $\frac{1}{a} + \frac{1}{b} = \frac{1}{20}$ Ambiguous
|
| 1286651 How do I compute the limit of a function of two variables as it approaches a point $(x, y)$? Unambiguous
|
| 2666326 For a square matrix $A$ over the complex numbers, is it true that if $A^4 = I$, then $A^2 = I$ or $A^2 = -I$? Unambiguous
|
| 2322481 Does the limit as $k$ approaches infinity of the ratio $\frac{\sum_{n=1}^{k} 2^{2 \cdot 3^n}}{2^{2 \cdot 3^k}}$ equal $1$? Unambiguous
|
| 4093371 Show that a graph that is connected but not complete has vertices u,v and w such that uv and vw are edges but not uw. Ambiguous
|
| 1565903 What are some simple-to-prove, counter-intuitive theorems in set theory that depend on the Axiom of Choice? Unambiguous
|
| 2893411 Evaluate the sum $\sum\limits_{k=1}^n {\binom{n}{k} f(k)}$. Ambiguous
|
| 2555463 Find the point equidistant from two points and a line Ambiguous
|
| 728599 How to evaluate the triple integral for region $E$ bounded by the spheres? Ambiguous
|
| 5877 Efficiently finding two squares which sum to a prime Ambiguous
|
| 3111260 How do I evaluate $\lim_{x\to 0}\frac{x-\tan x}{x^3} $? Unambiguous
|
| 2307642 How to find an orthonormal $T$ eigenbasis without matrices? Ambiguous
|
| 1774294 Explain why $y^2 = 2x^2 + C$ is not equivalent to $y = \sqrt{2x^2} + C$. Unambiguous
|
| 3322357 How is the matrix identity $\det\begin{pmatrix}A&B\\B&A\end{pmatrix}=\det(A+B)\det(A-B)$ proved for square matrices $A$ and $B$ of the same size? Unambiguous
|
| 449507 Compute the indefinite integral of $\frac{\sqrt{x^2-4}}{x^4}$ with respect to $x$. Unambiguous
|
| 1037426 Find $\lim\limits_{x \to \infty}{e^{-x}\sqrt{x}}$ Ambiguous
|
| 1822028 In a normed vector space, is the closed convex hull of a weak*-compact subset of the dual space also weak*-compact? Unambiguous
|
| 2959054 Can I use stars and bars for this? Ambiguous
|
| 398593 Calculate the length of curve $f(x)=\arcsin(e^x)$, check solution, please. Ambiguous
|
| 199447 Provide a proof that the derivative of the function $f(x) = e^x$ is $f'(x) = e^x$ using the limit definition of the derivative and without using the chain rule. Unambiguous
|
| 43118 How can I explain to a layperson why the 'staircase' proof that $\pi = 4$ is mathematically incorrect? Unambiguous
|
| 1562459 Prove that $( 1 + n^{-2}) ^n \to 1$. Ambiguous
|
| 2116037 Does $\sum_{n=1}^{\infty} \frac{\sin^2(nx)}{n}$ converge uniformly? Ambiguous
|
| 3258160 Calculate $\iint_\Omega \left(\sqrt{\frac xa}+\sqrt{\frac yb}\right)\,dxdy$ Ambiguous
|
| 4564068 Is there a closed-form formula for the sum of the first $n$ squares, $\sum_{k=1}^{n} k^2$? Unambiguous
|
| 1086318 I'm looking for an explanation regarding an exponential function and a Taylor series approximation. Could you elaborate on how these relate in the context of a measurement? Ambiguous
|
| 68897 Let $A$ be positive definite and $B$ be full rank. Show that $BAB'$ is positive definite. Ambiguous
|
| 611256 How do you convert a decimal number to 8-bit two's complement binary representation? Unambiguous
|
| 1410163 Show that $\lim_{(x,y)\to(0,0)} \frac{xy^2}{x^2+y^4}$ does not exist by evaluating the limit along the paths $y=x$ and $y=-x$. Unambiguous
|
| 1982170 Probability of an event in relationship with a certain geometrical representation Ambiguous
|
| 763272 Which is greater: the value of $\sqrt{1001} - \sqrt{1000}$ or the fraction $\frac{1}{10}$? Unambiguous
|
| 1372825 Evaluating numerically $\int_0^{\infty}e^{-t^2 /100} \sin \pi t $ Ambiguous
|
| 1117045 What are the standard methods and techniques for evaluating definite integrals given specific upper and lower limits of integration? Unambiguous
|
| 1762215 Diamond and Shurman page 73 says $j'(\tau)$ doesn't vanish, how do I prove this? Ambiguous
|
| 405972 How do I find a basis for a subspace of $\mathbb{R}^3$ defined by a system of linear equations? Unambiguous
|
| 2490690 In how many ways can you make 107 using 1, 10, and 50? Ambiguous
|
| 2247820 For some general variable $c$, why is the limit always positive infinity except when $c=1$? What happens if $c=0$ or $c=-1$? Ambiguous
|
| 1602977 What is an example of an infinitesimal in the context of non-standard analysis? Unambiguous
|
| 611256 What are the least and greatest decimal integers that can be stored in an 8-bit register? Ambiguous
|
| 1502938 How to prove the sum equals $n/(n+1)$ using induction? Ambiguous
|
| 811451 Evaluate $\sqrt{2+\sqrt[3]{3+\sqrt[4]{4+\cdots}}}$. Unambiguous
|
| 4566790 Can someone help me understand eigenvalues? Ambiguous
|
| 1008311 Prove that for a bounded linear operator $L$ on a Hilbert space $H$, the null space of $L^*$ is equal to the null space of $L L^*$. Unambiguous
|
| 262371 How do you calculate the area of a trapezoid given the lengths of its diagonals and the angle between them? Unambiguous
|
| 3248549 Let $f$ be a continuous map then which of the following is correct Ambiguous
|
| 119307 Give an example of a Cauchy sequence that does not converge in the space of rational numbers $Q$. Unambiguous
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