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deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\sqrt{x} \\left( \\sqrt[3]{x+1} - \\sqrt[3]{x-1} \\right) \\]" } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 0, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the auxiliary equation for the ordinary differential equation with constant coefficients: \\((x^2D^2 + xD + 1)y = \\sin(2\\log x)\\sin(\\log x)\\)." } ]
math
{ "style": "rule", "ground_truth": "m^2 + 1 = 0" }
{ "index": 1, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left(\\dfrac{1}{\\tan^2 x}-\\dfrac{1}{x^2} \\right) \\]" } ]
math
{ "style": "rule", "ground_truth": "-\\dfrac{2}{3}" }
{ "index": 2, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the minimum sample size required such that the probability of at least two people being a match at all six genetic markers exceeds 0.001, given that the probability of a match at each individual marker is 1/9." } ]
math
{ "style": "rule", "ground_truth": "34" }
{ "index": 3, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the limit: \\[ \\lim_{x \\to \\infty} (x!)^{1/x} \\]" } ]
math
{ "style": "rule", "ground_truth": "\\infty" }
{ "index": 4, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the length of the polar curve given by \\( r = \\sqrt{1 + \\cos(2\\theta)} \\) for \\( 0 \\leq \\theta \\leq \\frac{\\pi\\sqrt{2}}{4} \\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{\\pi}{2}" }
{ "index": 5, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $A$ be a proper infinite subset of a set $X$. If $x$ and $y$ are two distinct elements of $X$ that are not in $A$, and we define $B = \\{x, y\\} \\cup A$, what is the cardinality of $B$ in terms of the cardinality of $A$?" } ]
math
{ "style": "rule", "ground_truth": "|A|" }
{ "index": 6, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Consider a regular pentagon circumscribed in a circle. Connect each vertex of this pentagon to every other non-adjacent vertex with a straight line segment to form a pentagram, which contains a smaller pentagon. What is the ratio of the area of the original (large) pentagon to the smaller one in terms of the golden ratio?" } ]
math
{ "style": "rule", "ground_truth": "\\phi^4" }
{ "index": 7, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the longest geometric progression with a common ratio greater than 1 that can be formed from the set \\( \\{100, 101, 102, \\ldots, 1000\\} \\). What is the length of this progression?" } ]
math
{ "style": "rule", "ground_truth": "6" }
{ "index": 8, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the expectation \\( \\mathbb{E}[X_t] \\) where \\( X_t = \\sin(B_t) \\) and \\( B_t \\) is a standard Brownian motion for \\( t \\geq 0 \\)." } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 9, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the values of \\( k \\) for which the equation \\( x^3 - 3x^2 + 6x + k = 0 \\) has three real roots." } ]
math
{ "style": "rule", "ground_truth": "\\emptyset" }
{ "index": 10, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Verify that the distance from the function \\( f = x \\) to the set \\( Y = \\{ f \\in C[0,1] : \\int_0^1 f = 0 \\} \\) is 0.5, given that \\( Y \\) is a closed subset of \\( X = \\{ f \\in C[0,1] : f(0) = 0 \\} \\)." } ]
math
{ "style": "rule", "ground_truth": "0.5" }
{ "index": 11, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\frac{\\sum_{k=1}^n k^p}{n^{p+1}} \\]" } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{p+1}" }
{ "index": 12, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Provide an example of a field that properly contains the field of complex numbers \\( \\mathbb{C} \\)." } ]
math
{ "style": "rule", "ground_truth": "\\mathbb{C}(t)" }
{ "index": 13, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $T$ be a continuous linear operator. Suppose $(u_n)$ is a sequence that converges weakly to $u$, denoted as $(u_n) \\rightharpoonup u$. Additionally, assume $T(u_n) \\rightharpoonup T(u)$ and there exists a subsequence $(u_{n_k})$ such that $T(u_{n_k}) \\rightarrow T(u)$. Does it follow that $T(u_n) \\rightarrow T(u)$?" } ]
math
{ "style": "rule", "ground_truth": "No" }
{ "index": 14, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $a, b, c, d$ be a permutation of the numbers $1, 9, 8, 4$. Define $n = (10a + b)^{10c + d}$. Calculate the probability that $1984!$ is divisible by $n$. Use Fermat's Little Theorem to assist in your calculations." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{5}{6}" }
{ "index": 15, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let \\( A \\) be a C* algebra of operators on a Hilbert space \\( H \\). Determine if there exists an \\( x \\) in \\( H \\) such that the set \\( Ax \\) is dense in \\( H \\) but not equal to the whole \\( H \\)." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 16, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{t\\to 0}\\left(\\frac{1}{\\ln(1 + t)}+\\frac{1}{\\ln(1-t)}\\right). \\]" } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 17, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the limit of \\( \\frac{\\pi(x)}{x} \\) as \\( x \\to \\infty \\), where \\( \\pi(x) \\) is the prime counting function." } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 18, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Consider a sequence $(r_n)$ resulting from infinite coin flips, where $R_n=1$ if $r_n$ is a head and $R_n=-1$ if $r_n$ is a tail. Determine if $P\\left(\\sum \\frac{R_n}{n} < \\infty\\right) = 1$. Provide a justification for your answer." } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 19, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Consider a locally path connected space $X$. If every open subset $U \\subseteq X$ is semi-locally simply connected, does it follow that $X$ is locally simply connected?" } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 20, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find parametric equations for a unit circle with a speed of \\( e^t \\), starting from \\( x=1 \\), \\( y=0 \\). Determine when the circle is completed." } ]
math
{ "style": "rule", "ground_truth": "\\ln(2\\pi + 1)" }
{ "index": 21, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Using the generating function \\( \\sum_{n=0}^{\\infty}P_n(x)r^n=(1-2rx+r^2)^{-\\frac{1}{2}} \\), find the value of \\( P_n(1) \\)." } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 22, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the expression \\( \\log \\left| 1 + \\alpha + \\alpha^2 + \\alpha^3 - \\frac{1}{\\alpha} \\right| \\), where \\( \\alpha \\) is a fifth root of unity." } ]
math
{ "style": "rule", "ground_truth": "\\log 2" }
{ "index": 23, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Verify that for \\(n = 2^kN\\), where \\(N\\) is odd, the following identity holds:\n\\[ \\sum_{d\\mid n}(-1)^{n/d}\\phi(d) = \\sum_{d\\mid 2^{k-1}N}\\phi(d) - \\sum_{d\\mid N}\\phi(2^kd) = 0. \\]" } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 24, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the kernel of the Vandermonde matrix \\( A \\) given by\n\\[\nA = \\begin{pmatrix} x_1^0 & x_1^1 & \\ldots & x_1^n \\\\ x_2^0 & x_2^1 & \\ldots & x_2^n \\\\ \\vdots & \\vdots & \\ldots & \\vdots \\\\ x_m^0 & x_m^1 & \\ldots & x_m^n \\end{pmatrix}\n\\]\nwhere \\( n < m - 1 \\) and the \\( x_i \\) are pairwise distinct." } ]
math
{ "style": "rule", "ground_truth": "\\{\\mathbf{0}\\}" }
{ "index": 25, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the minimum value of the product \\(abc\\) if the quadratic equation \\(ax^2 - bx + c = 0\\) has two distinct roots in the interval \\((0, 1)\\), where \\(a\\), \\(b\\), and \\(c\\) are natural numbers." } ]
math
{ "style": "rule", "ground_truth": "25" }
{ "index": 26, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the maximum value of $x^2 + y^2$ given that $(x, y)$ satisfy the following equations:\n\\[ 2x^2 + 5xy + 3y^2 = 2 \\]\n\\[ 6x^2 + 8xy + 4y^2 = 3 \\]\nCalculus is not allowed." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{5}{2}" }
{ "index": 27, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine whether the following statement is true or false: \"Any bounded sequence in $L^4[0,1]$ has a convergent subsequence in $L^2[0,1]$.\"" } ]
math
{ "style": "rule", "ground_truth": "B" }
{ "index": 28, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the infinite series \\( \\sum_{n=1}^{\\infty} \\frac{2n+1}{(n^{2}+n)^{2}}. \\)" } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 29, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine whether the following inequality is true for all real numbers $0 < r < 1$ and $t \\geq 0$:\n\\[ \\int_t^{t+r} \\sin(x)\\, dx \\leq \\int_{\\frac{\\pi}{2}-\\frac{r}{2}}^{\\frac{\\pi}{2}+\\frac{r}{2}}\\sin(x)\\, dx. \\]" } ]
math
{ "style": "rule", "ground_truth": "True" }
{ "index": 30, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $E \\subset \\mathbb{C}$ be a set such that for any sequence of distinct elements $(e_n)_{n \\in \\mathbb{N}}$ from $E$, $e_n \\to 0$ in norm. Is $E$ necessarily countable? Provide a justification for your answer." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 31, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $S$ be an algebraic smooth surface over $\\\\mathbb{C}\\\\). Suppose there is a fibration $p: S \\rightarrow C$ onto a smooth curve, and let $f$ be a fiber of this fibration. Let $K$ be a canonical divisor on $S$ such that $K \\cdot f = 0$. Determine whether each $m$-canonical map $\\varphi_{mK}: S \\rightarrow \\mathbb{P}^N$, when defined, will contract $f$ to a point." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 32, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the number of ways to make change for a dollar using generating functions. Specifically, determine the coefficient of the \\(x^{100}\\) term in the expansion of the generating function \\(\\frac{1}{(x-1)(x^5-1)\\cdots(x^{50}-1)}\\)." } ]
math
{ "style": "rule", "ground_truth": "292" }
{ "index": 33, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $a$ and $b$ be positive integers such that the range of the function \\( y = \\frac{x^2 + ax + b}{x^2 + 2x + 3} \\) is the interval \\(-5 \\leq y \\leq 4\\) for all real numbers $x$. Find the value of $a + b$. \\( \\boxed{} \\)" } ]
math
{ "style": "rule", "ground_truth": "23" }
{ "index": 34, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim _{n\\to \\infty }n \\int_{-1}^0(x + e^x)^{n}dx. \\]" } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{2}" }
{ "index": 35, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Given the joint probability distribution of $X$ and $Y$:\n\\[ f(x,y) = \\begin{cases} \n e^{-(x+y)}, & x > 0, y > 0 \\\\\n 0, & \\text{otherwise} \n\\end{cases} \\]\ncompute the probability $P(Y > X+1)$." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{2e}" }
{ "index": 36, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{x\\to 0}\\left(\\log\\frac{1}{x}\\right)^x \\]" } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 37, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate \\(1234^{1234} \\pmod{5379}\\). Note that \\(5379 = 3 \\times 11 \\times 163\\)." } ]
math
{ "style": "rule", "ground_truth": "4603" }
{ "index": 38, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the derivative of the matrix product $\\mathbf{A}\\mathbf{B}\\mathbf{c}$ with respect to the matrix $\\mathbf{B}$, where $\\mathbf{A}$ is an $n\\times m$ matrix, $\\mathbf{B}$ is an $m\\times k$ matrix, and $\\mathbf{c}$ is a $k\\times 1$ vector." } ]
math
{ "style": "rule", "ground_truth": "\\mathbf{c}^\\top \\otimes \\mathbf{A}" }
{ "index": 39, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the maximum value of the function \\( f(x) = \\int^{x}_{0} \\sqrt{(x^2-x)^2+y^4}~dy \\) for \\( 0 \\leq x \\leq 1 \\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{3}" }
{ "index": 40, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Is the space \\(X = \\prod_{t \\in \\mathbb{Z}} \\mathbb{R}\\), with the product topology \\(T\\), completely metrizable by a metric \\(d\\) such that \\(d(\\tau x, \\tau y) = d(x, y)\\) for the shift map \\(\\tau\\) defined by \\(\\tau x = (\\ldots, x_0, x_1, x_2, \\ldots)\\)?" } ]
math
{ "style": "rule", "ground_truth": "No" }
{ "index": 41, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "A triangle is inscribed in a circle with radius 1. What is the maximum value of the sum of the squares of the sides of the triangle?" } ]
math
{ "style": "rule", "ground_truth": "9" }
{ "index": 42, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find a matrix $X \\in M_n(\\mathbb{C})$ such that the linear functional $f(A) = \\text{tr}(XA)$ on $M_n(\\mathbb{C})$ preserves matrix multiplication." } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 43, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the minimum natural number \\( n \\) such that the expression \\( f(n) = \\sqrt{100+\\sqrt{n}} + \\sqrt{100-\\sqrt{n}} \\) is an integer." } ]
math
{ "style": "rule", "ground_truth": "6156" }
{ "index": 44, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Compute the limit \\( \\lim_{n\\to\\infty}{(\\sqrt[n]{e}-\\frac{2}{n})^n} \\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{e}" }
{ "index": 45, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Calculate the integral: \\[ \\int_{0}^{2} \\sqrt{1+x^3} \\, dx \\]" } ]
math
{ "style": "rule", "ground_truth": "3.241" }
{ "index": 46, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "For the function \\( u(x, y) = \\sinh x \\cos y \\), find the conjugate harmonic function \\( v(x, y) \\)." } ]
math
{ "style": "rule", "ground_truth": "\\cosh x \\sin y" }
{ "index": 47, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "In a compact metric space $X$, consider a finite subset $F \\subset X$ that is $\\epsilon$-equidistant, meaning that the distance $d(x,y) = \\epsilon$ for all distinct $x,y \\in F$. For a given $\\epsilon > 0$, does there exist a maximum number $N$, depending on both $\\epsilon$ and $X$, such that the cardinality of any $\\epsilon$-equidistant set $F$ is at most $N$? Provide a proof or counterexample." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 48, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: $$\\lim_{x\\to\\infty}\\left(\\frac1{x^2\\sin^2\\frac 1x}\\right)^\\frac 1{x\\sin\\frac 1x-1}$$ without using L'Hospital's Rule or Series expansion." } ]
math
{ "style": "rule", "ground_truth": "e^{-2}" }
{ "index": 49, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the number of orientations of a smooth manifold with \\(n\\) maximal connected components." } ]
math
{ "style": "rule", "ground_truth": "2^n" }
{ "index": 50, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $X$ and $Y$ be orthogonal skew symmetric matrices. Determine if $X$ and $Y$ are orthogonally conjugate, i.e., if there exists an orthogonal matrix $U \\in O(n)$ such that $UX = YU$. Provide a justification for your answer." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 51, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the double integral \\( \\iint_\\Omega \\sqrt{x^2+y^2} \\,\\mathrm{d}x\\mathrm{d}y \\), where \\( \\Omega \\) is the region defined by \\((x-1)^2+y^2 \\leq 1\\) and \\(0 \\leq y\\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{16}{9}" }
{ "index": 52, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find all real harmonic functions $u$ on the unit disk $D$ centered at $0$ in the complex plane such that $u(0) = 0$ and $u^2$ is also harmonic on $D$." } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 54, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let \\( A \\) be an integral domain. For every maximal ideal \\( m \\) in \\( A \\), consider \\( A_m \\) as a subring of the quotient field \\( K \\) of \\( A \\). Prove that \\( \\bigcap_{m \\text{: maximal ideal}} A_m = A \\), where the intersection is taken over all maximal ideals \\( m \\) of \\( A \\)." } ]
math
{ "style": "rule", "ground_truth": "A" }
{ "index": 55, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the value of \\( \\lim_{x \\to 0} \\frac{4\\cos^2(f(x)) - 1}{1 - x^2} \\), given that the function \\( f(x) \\) satisfies \\( f(x) = f(2x) \\) for all \\( x \\in \\mathbb{R} \\) and \\( f(2017) = \\frac{\\pi}{4} \\)." } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 56, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the integral \\( \\int_{\\gamma} \\frac{e^{2 \\pi z}}{(z+i)^3}dz \\) using the Cauchy Integration Formula, where \\( \\gamma(t)=2e^{it}, t \\in [0,2 \\pi] \\). Determine if the calculation \\( \\int_{\\gamma} \\frac{f(z)}{z-0}dz = 2 \\pi i f(0) = 0 \\) is correct." } ]
math
{ "style": "rule", "ground_truth": "4\\pi^3 i" }
{ "index": 57, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "A stock market trader buys 100 shares of stock A and 200 shares of stock B. Let X and Y be the price changes of stock A and B, respectively, over a certain time period. Assume that the joint probability density function (PDF) of X and Y is uniform over the set of integers (x, y) satisfying βˆ’2 ≀ x ≀ 4 and βˆ’1 ≀ y βˆ’ x ≀ 1. Find the expected value of the trader's profit." } ]
math
{ "style": "rule", "ground_truth": "300" }
{ "index": 58, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Using the Fundamental Theorem of Line Integrals, evaluate \\( \\int_{C} e^x \\, dy + e^{x}y \\, dx, \\) where \\( C \\) is the parabola parameterized by \\( r(t)=\\langle t+1,t^2 \\rangle \\) for \\( t\\in[-1,3]. \\)" } ]
math
{ "style": "rule", "ground_truth": "9e^4 - 1" }
{ "index": 59, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the fundamental group of the space \\((S^1 \\times S^1)/(S^1 \\times \\{x\\})\\), where \\(x\\) is a point in \\(S^1\\)." } ]
math
{ "style": "rule", "ground_truth": "\\mathbb{Z}" }
{ "index": 60, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the radius of convergence for the function \\( \\frac{1}{z^2 + 2z + 2} \\)." } ]
math
{ "style": "rule", "ground_truth": "\\sqrt{2}" }
{ "index": 61, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the surface area of the solid of revolution obtained by rotating the function \\( x=\\frac{1}{15}(y^2+10)^{3/2} \\) from \\( y=2 \\) to \\( y=4 \\) about the \\( x \\)-axis." } ]
math
{ "style": "rule", "ground_truth": "36\\pi" }
{ "index": 62, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the minimum value of the function \\( f(x) = \\max_{t \\in [0,1]} |t^2 - tx| \\) for \\( x \\in (0,1) \\)." } ]
math
{ "style": "rule", "ground_truth": "3 - 2\\sqrt{2}" }
{ "index": 63, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Assume that \\( f \\) is a non-negative real function, and let \\( a > 0 \\) be a real number. Define \\( I_a(f) \\) as follows:\n\\[ I_a(f) = \\frac{1}{a}\\int_{0}^{a} f(x) \\, dx \\]\nSuppose \\( \\lim_{x \\rightarrow \\infty} f(x) = A \\) exists. Determine whether \\( \\lim_{a \\rightarrow \\infty} I_a(f) = A \\) is always true. Provide a proof or a counterexample to support your conclusion." } ]
math
{ "style": "rule", "ground_truth": "A" }
{ "index": 64, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Given a linear transformation \\( T: M^R_{2x2} \\rightarrow R_4[x] \\) defined by the following mappings: \\( T\\begin{pmatrix} 2 & 3 \\\\ 1 & 0 \\end{pmatrix} = x^2 \\), \\( T\\begin{pmatrix} 1 & 0 \\\\ 0 & 2 \\end{pmatrix} = 3x - 4 \\), and \\( T\\begin{pmatrix} 0 & 2 \\\\ 4 & 5 \\end{pmatrix} = 2x^2 - 7 \\), find \\( T\\begin{pmatrix} 5 & 0 \\\\ -10 & -13 \\end{pmatrix} \\). Assume the given matrices are linearly independent." } ]
math
{ "style": "rule", "ground_truth": "-4x^2 + 3x + 17" }
{ "index": 65, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "A cube is to be colored using 6 distinct colors such that no two adjacent faces share the same color. How many distinct ways can this be done?" } ]
math
{ "style": "rule", "ground_truth": "30" }
{ "index": 66, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $k$ be a number field, and $F/k$ a finite extension. Is it possible to find a countable family of extensions $k_i/k$ of degree 2 and a place $v_i$ of $k_i$ such that if $v$ is the place of $k$ lying below $v_i$, then $[k_{v_i}:k_v] = 2$, where $k_{v_i}$ and $k_v$ are the completions of $k_i$ and $k$ at $v_i$ and $v$, respectively? Furthermore, for some place $w$ of $F$ lying above $v$, is it possible that $F_w = k_v$?" } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 67, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit \\( \\lim_{n\\to \\infty} \\int_{1}^{\\pi}\\frac{\\cos(\\frac{x}{n})}{1-e^{-xn}}dx \\)." } ]
math
{ "style": "rule", "ground_truth": "\\pi - 1" }
{ "index": 68, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the sum of all integer values of \\( a \\) such that \\( a(x^2+x-1) \\leq (x^2+x+1)^2 \\) for all real numbers \\( x \\)." } ]
math
{ "style": "rule", "ground_truth": "36" }
{ "index": 69, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "If a vector space over the complex numbers has dimension $n$, is it possible to redefine the operations of addition and scalar multiplication such that the dimension of the vector space changes?" } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 70, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Consider a connected undirected simple non-planar graph $G$ with 15 vertices. If removing any edge from $G$ results in a planar graph, how many edges does $G$ have?" } ]
math
{ "style": "rule", "ground_truth": "40" }
{ "index": 71, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit \\( \\lim_{n\\to\\infty} \\sum_{k=1}^{n} \\sin\\left(\\frac{(2k-1)a}{n^2}\\right) \\) by expressing it as a Riemann sum and finding the corresponding integral, where \\( a \\in \\mathbb{R} \\)." } ]
math
{ "style": "rule", "ground_truth": "a" }
{ "index": 72, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Calculate the first partial derivative with respect to $x$ of the function \\( f(x,y) \\) at the point \\((0,0)\\), where\n\\[\nf(x,y) =\n\\begin{cases}\n0 & (x,y)=(0,0)\\\\\n\\frac{xy}{|x|+|y|} & (x,y) \\neq (0,0)\n\\end{cases}\n\\]" } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 73, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the minimal possible order of a group $G$ that contains a subset $A \\subset G$ with $|A| = 2n$, such that for every $a \\in A$, there exists a unique $b \\in A$ with $[a, b] \\neq e$. Provide your answer as a single integer." } ]
math
{ "style": "rule", "ground_truth": "6^n" }
{ "index": 74, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find all strictly increasing functions \\( f : \\Bbb{Z} \\rightarrow \\Bbb{Z} \\) such that \\( f(f(x)) = x + 2 \\) for all integers \\( x \\)." } ]
math
{ "style": "rule", "ground_truth": "f(x) = x + 1" }
{ "index": 75, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Is the statement \"If $\\gcd(y,z)=1$, then $yz$ is perfect if and only if $D(y)D(z)=2s(y)s(z)$\" always true for odd perfect numbers $q^k n^2$? Here, $D(x) = 2x - \\sigma(x)$ is the deficiency of $x$, $s(x) = \\sigma(x) - x$ is the sum of the aliquot divisors of $x$, and $\\sigma(x)$ is the sum of divisors of $x \\in \\mathbb{N}$, the set of positive integers." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 76, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Given that \\( f(\\phi) = \\Delta \\phi \\), where \\( \\Delta \\phi = \\nabla \\cdot \\nabla \\phi \\), find the expression for \\( \\frac{df(\\phi)}{d\\phi} \\)." } ]
math
{ "style": "rule", "ground_truth": "\\Delta" }
{ "index": 77, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Calculate the minimum distance from the curve \\( f(x) = \\begin{pmatrix} \\cos(\\pi x) \\\\ \\sin(\\pi x) \\\\ 1-x^2 \\end{pmatrix} \\) to the origin in \\( \\mathbb{R}^3 \\)." } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 78, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine whether the sequence \\( \\frac{2^n - 3n^3}{1-4^n} \\) converges or diverges using the ratio test." } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 79, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Compute \\( \\lim\\limits_{n\\to \\infty} \\int\\limits_0^1 x^{2019} \\{nx\\} \\, dx \\), where \\( \\{a\\} \\) denotes the fractional part of the real number \\( a \\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{4040}" }
{ "index": 80, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Use Logarithmic Differentiation to find \\(\\frac{d}{dx} (x^{{x}^{x}})\\) at \\(x=1\\)." } ]
math
{ "style": "rule", "ground_truth": "1" }
{ "index": 81, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the number of integers in the range from 1 to \\(10^9\\) that are not perfect squares, perfect cubes, or perfect fifth powers." } ]
math
{ "style": "rule", "ground_truth": "999967355" }
{ "index": 82, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine whether the hyperoctahedral group, defined as the wreath product of $S_2$ and $S_n$ or equivalently $G = S_2^n \\rtimes S_n$, has only 3 maximal normal subgroups. Consider $G$ as a subgroup of $S_{2n}$ with its natural action on $[2] \\times [n]$. The group $G$ has two known normal subgroups of index two: $N_1$, the preimage of $A_n$ under the quotient map $G \\to S_n$, and $N_2$, the intersection in $S_{2n}$ of $G$ and $A_{2n}$. A third normal subgroup of index two arises from the diagonal in the Klein group $G/(N_1 \\cap N_2)$. Are there any additional maximal normal subgroups in $G$?" } ]
math
{ "style": "rule", "ground_truth": "3" }
{ "index": 83, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let $F$ be a finite Galois extension of the rational function field $\\mathbb{Q}(x)$. Let $k$ be the field of constants of $F$, defined as the algebraic closure of $\\mathbb{Q}$ in $F$. Is $k$ necessarily a Galois extension of $\\mathbb{Q}$? Provide a justification for your answer." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 84, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the 9th derivative of \\( \\frac{\\cos(5 x^2)-1}{x^3} \\) and evaluate it at \\( x=0 \\) using the Maclaurin Series." } ]
math
{ "style": "rule", "ground_truth": "-7875000" }
{ "index": 85, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Consider the upper half-plane \\( \\mathbb{H} = \\{ x \\in \\mathbb{R}^n : x_n > 0 \\} \\). Let \\( u \\in C^2(\\mathbb{H}) \\cap C(\\bar{\\mathbb{H}}) \\) be a bounded harmonic function such that \\( u \\leq 0 \\) on \\( \\partial\\mathbb{H} = \\{ x_n = 0 \\} \\). Determine if it is possible to conclude that \\( u \\leq 0 \\) in all of \\( \\mathbb{H} \\) for \\( n \\geq 3 \\)." } ]
math
{ "style": "rule", "ground_truth": "Yes" }
{ "index": 86, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "A ladder is being moved through a corridor in the first quadrant of the $x$-$y$ plane. The ladder is represented by the line $y = mx + c$, where $m < 0$ and $c > 0$. The length of the ladder is $L$. The goal is to find the maximum length $L$ such that the ladder just touches the corner of the corridor as it clears it. Given the coordinates of the corner are $(a, b)$, find the maximum length of the ladder when $a = 8$ and $b = 6$. Express your answer to the nearest whole number." } ]
math
{ "style": "rule", "ground_truth": "20" }
{ "index": 87, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the sign of the map induced by the covering map \\( p: S^n \\to \\mathbb{R}P^n \\) on homology, specifically \\( p_{*}: H_n(S^n, R) \\to H_n(\\mathbb{R}P^n, R) \\), where \\( R \\) is an arbitrary ring. Given that \\( H_n(S^n, R) \\cong R \\) is generated by the class \\([\\sigma_n^{(1)} + \\sigma_n^{(2)}]\\) and \\( H_n(\\mathbb{R}P^n, R) \\cong R \\) is generated by the class \\([\\tau_n]\\), find the sign in the expression \\( p_{*} [\\sigma_n^{(1)} + \\sigma_n^{(2)}] = \\tau_n \\pm \\tau_n \\)." } ]
math
{ "style": "rule", "ground_truth": "+" }
{ "index": 88, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Given the fixed point iteration \\( p_n = \\frac{p_{n - 1}^2 + 3}{5} \\), which converges for any initial \\( p_0 \\in [0, 1] \\), estimate an expression for the number of iterations \\( n \\) required to achieve an absolute error \\( \\left| p_n - p \\right| < 10^{-4} \\) when \\( p_0 = 1 \\). Use the error bound \\( \\left| p_n - p \\right| \\leq k^n\\max\\{ p_0 - a, b - p_0 \\} \\), where \\([a, b]\\) is the interval of convergence and \\( k \\) is the bound on the derivative of the function within this interval." } ]
math
{ "style": "rule", "ground_truth": "11" }
{ "index": 89, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the unique polynomial \\( r(x) \\) such that for all \\( p(x) \\in \\mathbb{P}^2 \\), the functional \\( f(p(x)) = p'(-15) + 8p(-1) \\) can be expressed as \\( \\langle p, r \\rangle = \\int_0^1 p(x)r(x)dx \\). Here, \\( \\mathbb{P}^2 \\) is the space of polynomials of degree less than two." } ]
math
{ "style": "rule", "ground_truth": "-132x + 74" }
{ "index": 90, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the limit: \\[ \\lim_{x \\to \\infty} \\frac{\\left(\\int_0^x e^{t^2} \\, dt\\right)^2}{\\int_0^x e^{2t^2} \\, dt} \\]" } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 91, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Let \\( A \\in M_{5\\times 6}(\\mathbb{R}) \\) be a matrix with rank 4. Consider the block matrix \\( D = \\begin{pmatrix} I_5 & A \\\\ A^T & 0 \\end{pmatrix} \\). Determine the rank of \\( D \\)." } ]
math
{ "style": "rule", "ground_truth": "9" }
{ "index": 92, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "A consumer is searching for 1 unit of a product across stores with prices 1, 2, 3, ..., each occurring with probabilities 1/2, 1/4, 1/8, ..., 1/2^n respectively. The consumer incurs a search cost of 1 for each store visited. Determine the price at which the consumer should stop searching." } ]
math
{ "style": "rule", "ground_truth": "2" }
{ "index": 93, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Determine the intervals where the function \\(f(x) = (x+\\frac{1}{x})^{x}\\) is increasing and where it is decreasing." } ]
math
{ "style": "rule", "ground_truth": "(0, \\infty)" }
{ "index": 94, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate \\( \\lim_{n \\rightarrow \\infty} \\int_0^1 \\frac{nx^{n-1}}{2+x} \\, dx \\)." } ]
math
{ "style": "rule", "ground_truth": "\\dfrac{1}{3}" }
{ "index": 95, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Calculate the unconditional variance of the random variable $N$, where $N|\\Lambda$ follows a binomial distribution with parameters $\\Lambda$ and $q = 0.4$, and $\\Lambda$ has a probability function defined by $p(1) = p(2) = p(3) = p(4) = 0.25$. Provide your answer as a numerical value." } ]
math
{ "style": "rule", "ground_truth": "0.8" }
{ "index": 96, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Is it true that for all Sylow subgroups $P$ of a nonabelian simple group $G$, the inequality $|P|^2 < |G|$ holds?" } ]
math
{ "style": "rule", "ground_truth": "True" }
{ "index": 97, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Calculate the limit: $$ \\lim_{n\\rightarrow\\infty}\\frac{2^n + n\\sin{n}}{\\log_2{n} + e^n} $$" } ]
math
{ "style": "rule", "ground_truth": "0" }
{ "index": 98, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Find the minimum value of the perimeter of a triangle whose area is 3 cmΒ²." } ]
math
{ "style": "rule", "ground_truth": "6\\sqrt[4]{3}" }
{ "index": 99, "original_dataset": "deepmath-103k", "split": "train" }
deepmath-103k
[ { "role": "user", "content": "Evaluate the surface integral \\( \\int \\int_S z \\, dS \\) where \\( S \\) is the surface of the hemisphere defined by \\( x^2 + y^2 + z^2 = a^2 \\) with \\( z \\geq 0 \\)." } ]
math
{ "style": "rule", "ground_truth": "\\pi a^3" }
{ "index": 100, "original_dataset": "deepmath-103k", "split": "train" }
End of preview. Expand in Data Studio

DeepMath-103K VERL

Dataset Size Format License

πŸ“Š Dataset Summary

This dataset contains 95,496 mathematical reasoning problems in VERL format, processed from zwhe99/DeepMath-103K.

Key Features:

  • 95,496 high-quality math problems
  • Converted to VERL format for reward modeling
  • Verified ground truth answers
  • Ready for reinforcement learning training

πŸ”— Source Dataset

Original Repository

Dataset Description

DeepMath-103K is a curated collection of 103,000 mathematical problems covering various difficulty levels and mathematical domains. The dataset emphasizes step-by-step reasoning and verification.


πŸ”„ Preprocessing Pipeline

This dataset has been preprocessed and converted to the VERL (Verification and Reinforcement Learning) format for use in mathematical reasoning tasks with reward modeling.

Cleaning Methodology

Standard Processing:

  • URL filtering (samples containing URLs removed)
  • Format normalization to VERL schema
  • Basic text cleaning and validation

Deduplication

Intra-dataset Deduplication:

  • Method: SHA-256 hash-based with text normalization
  • Before deduplication: 103,000 samples
  • After deduplication: 95,496 samples
  • Reduction: 7.3%

Inter-dataset Deduplication (v3.0):

  • Priority level: 4
  • Cross-dataset duplicates removed: 5,000

πŸ’‘ Preprocessing Examples

Example 1: Standard Processing (No Cleaning Preset)

Before Cleaning:

Calculate the derivative of $f(x) = x^2 + 3x + 2$ with respect to $x$.

After Cleaning:

Calculate the derivative of $f(x) = x^2 + 3x + 2$ with respect to $x$.

Changes Applied:

  • βœ“ Format normalization to VERL schema
  • βœ“ URL filtering (samples with URLs removed)
  • βœ“ Basic text validation
  • βœ“ No artifact removal applied

πŸ“ VERL Schema

This dataset follows the standardized VERL (Verification and Reinforcement Learning) format:

{
  "data_source": "openai/gsm8k",
  "prompt": [
    {
      "content": "Calculate the sum of all odd numbers from 1 to 99.",
      "role": "user"
    }
  ],
  "ability": "math",
  "reward_model": {
    "style": "rule",
    "ground_truth": "\boxed{2500}",
    "hash": "sha256:abc123..."
  },
  "extra_info": {
    "split": "train"
  }
}

Field Descriptions

Field Type Description
data_source string Original dataset identifier (e.g., openai/gsm8k, numina_aime)
prompt list[dict] User query in chat format with role and content
ability string Task type (always "math" for this dataset)
reward_model.style string Reward computation method ("rule" for rule-based verification)
reward_model.ground_truth string Expected answer for verification (often in \boxed{} format)
reward_model.hash string SHA-256 hash of prompt content for deduplication
extra_info.split string Original split identifier ("train", "test", etc.)

πŸ“ˆ Dataset Statistics

Sample Distribution

  • Total Samples: 95,496
  • Dataset Size: 10.5 MB
  • Average Problem Length: N/A characters

Data Sources

Distribution of problems by original data source:

Source Count Percentage
Mixed Sources 95,496 100%

Note: Detailed source distribution statistics will be added in future updates.


πŸš€ Usage

Loading the Dataset

from datasets import load_dataset

# Load the full dataset
dataset = load_dataset("sungyub/deepmath-103k-verl")

# Load with streaming (recommended for large datasets)
dataset = load_dataset("sungyub/deepmath-103k-verl", streaming=True)

# Preview first few examples
for example in dataset['train'].take(5):
    print(example['prompt'][0]['content'])  # User question
    print(example['reward_model']['ground_truth'])  # Answer
    print("---")

Using with VERL

from datatrove.utils.reward_score import compute_score

# Compute reward score for a generated solution
score = compute_score(
    data_source=example['data_source'],
    solution_str=generated_solution,
    ground_truth=example['reward_model']['ground_truth'],
    format_type="auto"  # Auto-detect XML or GPT OSS format
)

print(f"Reward score: {score}")

Integration with DataTrove

from datatrove.pipeline.readers import ParquetReader
from datatrove.pipeline.filters import LambdaFilter
from datatrove.executor import LocalPipelineExecutor

pipeline = [
    ParquetReader("sungyub/deepmath-103k-verl", text_key="prompt"),
    LambdaFilter(lambda doc: len(doc.text) > 100),  # Filter short problems
    # Add more processing steps...
]

executor = LocalPipelineExecutor(pipeline=pipeline, tasks=4)
executor.run()

πŸ“š Citation

Original Dataset

@article{he2025deepmath,
  title = {DeepMath: Deep Learning for Mathematical Reasoning},
  author = {He, Zhenwen and others},
  journal = {arXiv preprint arXiv:2504.11456},
  year = {2025},
  url = {https://arxiv.org/abs/2504.11456}
}

This Processed Version

@dataset{sungyub_math_verl_deepmath-103k-verl,
  author = {Sungyub Kim},
  title = DeepMath-103K VERL,
  year = {2025},
  publisher = {Hugging Face},
  howpublished = {\url{https://huggingface.co/datasets/sungyub/deepmath-103k-verl}}
}

βš–οΈ License

  • This processed dataset: mit
  • Original dataset: MIT

πŸ™ Acknowledgments

This dataset was processed using the DataTrove library.

Credits:

  • Original dataset authors: Zhenwen He et al.
  • Processing and VERL conversion: Sungyub Kim
  • MathDatasetCleaner implementation: DataTrove contributors

Special thanks to: Zhenwen He and collaborators for the DeepMath dataset


πŸ“ Version History

v1.0.0 (Initial Release)

  • Processed 95,496 samples from zwhe99/DeepMath-103K
  • Converted to VERL format
  • Standard processing applied
  • Ready for reinforcement learning training

πŸ”— Related Resources


Questions or issues? Open an issue on the DataTrove GitHub repository

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