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[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a polynomial $\\\\phi \\\\in K[X_1, X_2, \\\\ldots, X_n]$ whose only zero is $(0,0,\\\\ldots,0)$, given that $K$ is not algebraically closed.\"}", "{\"role\":\"assistant\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven that the probability of a child being a boy or a girl is equal, and a student picked at random from a large class is a boy, determine whether the probability that this boy...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the minimal polynomial of the matrix \\\\( A = \\\\begin{bmatrix} 0 & 4 & 1 & -2 \\\\\\\\ -1 & 4 & 0 & -1 \\\\\\\\ 0 & 0 & 1 & 0 \\\\\\\\ -1 & 3 & 0 & 0 \\\\end{bmatrix} \\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the correct dual formulation for the given integer program:\\n\\\\[\\n\\\\begin{align}\\n\\\\max & \\\\sum_{i \\\\in N} w_i x_i \\\\\\\\[4pt]\\n\\\\text{s.t. } & x_i \...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nEvaluate the integral $$\\\\int e^{-1\\/x^2} \\\\, dx.$$\"}", "{\"role\":\"assistant\",\"content\":\"The integral can be evaluated by using the substitution \\\\(y = \\\\frac{...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nExpress $\\\\sum_{j=1}^{n}\\\\sum_{i=1}^{n} \\\\frac{1}{i(i+j)}$ in terms of harmonic numbers $H_n$.\"}", "{\"role\":\"assistant\",\"content\":\"We have the double sum\\n\\n\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nIn triangle $ABC$, given the lengths of sides $AB = 10$, $BC = 6$, and the angle $\\\\angle ABC = 120^\\\\circ$, find the measure of angle $\\\\angle BCA$.\"}", "{\"role\":\"a...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the density distribution of $\\\\xi$ defined by:\\n\\\\[ P_{\\\\xi}(x)= \\\\begin{cases} Cx^{-3\\/2} & \\\\text{if } 1\\\\leq x, \\\\\\\\ 0 & \\\\text{if } x<1 \\\\end{cas...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow many different timetables can be compiled for a train schedule where two trains depart twice a day for three days, one train departs once a day for two days, and three train...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nA fly is trapped inside a hollow cube and moves from point A to point C along the edges of the cube, taking the shortest possible route. It then returns to point A along the edg...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the general equation \\\\(Ax^2 + Cy^2 + Dx + Ey + F = 0\\\\), what constraints on the set \\\\(\\\\{A, C, D, E, F\\\\}\\\\) will apply if the equation represents a hyperbo...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the ratios $r_i = \\\\frac{d_{i+1}}{d_i}$ for the leading coefficients of the degree-$2j$ polynomials, given by:\\n\\\\[\\nr_1 = \\\\frac{(1109 - 497 n) n}{3468},\\n\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDefine a variable \\\\( x \\\\) using linear equations based on the following conditions for \\\\( n \\\\) binary variables \\\\( a, b, c, \\\\ldots \\\\):\\n\\n- \\\\( x = 0 \\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nProvide a recursive definition for the set \\\\( S = \\\\left\\\\{{(a,b) \\\\mid a \\\\in \\\\mathbb{Z}^+, b \\\\in \\\\mathbb{Z}^+ \\\\text{ and } a + b \\\\text{ is odd}}\\\\r...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine whether the polynomials \\\\( p_1(x) = x^2 + 1 \\\\), \\\\( p_2(x) = x^2 + x \\\\), \\\\( p_3(x) = x + 2 \\\\), and \\\\( p_4(x) = x^2 + 3 \\\\) are linearly dependent...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the asymptotic behavior of the real positive root of the polynomial \\\\(x^{k\\/2} - x - 1\\\\) as \\\\(k\\\\) becomes a large even integer.\"}", "{\"role\":\"assist...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nStarting at 4, how many ways can you add or subtract 1 forty times to reach 0 without dropping below 0?\"}", "{\"role\":\"assistant\",\"content\":\"We need to count the number...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nConsider the conservation law \\\\( u_t + (u^4)_x = 0 \\\\). Find the solution at \\\\( t=1 \\\\) with the initial condition:\\n\\\\[ u(x,0) = \\\\left\\\\lbrace\\\\begin{align...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind an explicit upper bound for the Legendre function of the second kind of degree $1\\/2$, $Q_{1\\/2}(u)$, of the form $c u^{-3\\/2}$, where $c$ is an explicit real number.\"}...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the family of confocal ellipses defined by\\n\\\\[ \\\\frac{x^2}{a^2} + \\\\frac{y^2}{a^2 - c^2} = 1, \\\\]\\nwhere \\\\( c \\\\) is constant and \\\\( a \\\\) varies, fin...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nSolve the following system of linear equations using Gaussian elimination and find the general solutions for \\\\(x\\\\) and \\\\(y\\\\) in terms of the parameter \\\\(t\\\\):\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the determinant of the matrix \\\\( A_{n \\\\times n} \\\\) defined as:\\n\\\\[ \\\\det(A_{n \\\\times n}) = \\\\begin{vmatrix}\\n0 & a_{1} + a_{2} & a_{1} + a_{3} & \\\\cd...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the limit of the sum of sine products as \\\\( n \\\\) approaches infinity:\\n\\\\[ \\\\lim_{n \\\\to \\\\infty} \\\\sum_{k=1}^{n-1} \\\\sin{\\\\frac{k}{n^2}} \\\\sin{\\\\f...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the general solution for the equation \\\\( \\\\tan(2x + 1.426) = -2.156 \\\\).\"}", "{\"role\":\"assistant\",\"content\":\"The general solution is obtained by solving th...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a conformal mapping from $\\\\{|z-8|<16\\\\}\\\\setminus\\\\{|z-3|<9\\\\}$ onto $\\\\{t<|z|<1\\\\}$. Find $t$.\"}", "{\"role\":\"assistant\",\"content\":\"We are to find ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat is the probability that Alex applies for his first sick leave on the fifth day, given that the probability of applying for sick leave on any particular day is the same and ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow can one approximate the value of the function \\\\( f(n) = \\\\sum_{i=1}^{n} \\\\frac{1}{2i-1} \\\\) for specific values of \\\\( n \\\\), such as \\\\( f(20) \\\\) or \\\\(...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat is the probability that a sequence of 12 zeros and ones has exactly five ones but begins and ends in zero?\"}", "{\"role\":\"assistant\",\"content\":\"The total number of...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven a set \\\\( C = \\\\{ p_0, p_1, \\\\ldots, p_n \\\\} \\\\) where each \\\\( p_i \\\\geq 0 \\\\) and \\\\( \\\\sum_{i=0}^n p_i = 1 \\\\), what is the expected number of ele...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven that the power series $\\\\sum a_nx^n$ is convergent at $x=-3$ and divergent at $x=5$, determine the convergence at $x=3$.\"}", "{\"role\":\"assistant\",\"content\":\"We...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nUse linear approximation to approximate $\\\\sqrt{81.3}$ as follows: Let $f(x) = \\\\sqrt{x}$. The equation of the tangent line to $f(x)$ at $x=81$ can be written in the form $y...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nConsider the set \\\\( W \\\\) which consists of \\\\( 2 \\\\times 2 \\\\) matrices of the form\\n\\\\[\\n\\\\begin{bmatrix} 2a & b \\\\\\\\ 3a + b & 3b \\\\end{bmatrix}.\\n\\\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat is the antiderivative of $(2x^2+9)^{3\\/4}$?\"}", "{\"role\":\"assistant\",\"content\":\"We seek the antiderivative \\\\(\\\\int (2x^2+9)^{3\\/4}\\\\,dx\\\\). \\nBecause...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDecompose a matrix \\\\( A \\\\) expressed as the tensor \\\\( A = \\\\sum_{m=1}^M x^{(m)} A^{(m)} \\\\) (where \\\\( A \\\\) and \\\\( A^{(i)} \\\\) are \\\\( N \\\\times P \\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat is the value of the series $\\\\sum_{n=0}^\\\\infty \\\\beta(4n+1) - \\\\beta(4n+3)$, where $\\\\beta(s)$ is the Dirichlet beta function?\"}", "{\"role\":\"assistant\",\"...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nSolve the differential equation $\\\\frac{dT}{dt} = cT - cT_{\\\\text{end}}$ and identify the error in the particular solution approach.\"}", "{\"role\":\"assistant\",\"conten...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the asymptotic expansion of $\\\\int_{-\\\\infty}^{y} \\\\frac{e^{-x^2\\/2}}{\\\\sqrt{2\\\\pi}} dx$ where $x \\\\sim N(0,1)$.\"}", "{\"role\":\"assistant\",\"content\":\"...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nA car moves from point $A$ to $B$ in $t_{\\\\text{total}} = 10.0\\\\ \\\\text{s}$ with initial velocity $v_i = 0\\\\ \\\\text{m\\/s}$, acceleration $a = 0.65\\\\ \\\\text{m\\/s}...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nLet \\\\( f(x) \\\\) be a four-times differentiable function such that \\\\( f(2x^2 - 1) = 2xf(x) \\\\). What is the value of \\\\( f''''(0) \\\\)?\"}", "{\"role\":\"assistant...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the stereographic projection formulas for the unit circle \\\\( S^1 \\\\):\\n\\\\[\\n\\\\varphi_N(x^1, x^2) = \\\\frac{x^1}{1 - x^2} \\\\quad \\\\text{for} \\\\quad S^1 \\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDerive the conjugate of the negative geometric mean function \\\\( f(x) = - \\\\left( \\\\prod_{i=1}^n x_i \\\\right)^{\\\\frac{1}{n}} \\\\).\"}", "{\"role\":\"assistant\",\"c...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow many edge deletions are required to make a $4$-regular graph on $7$ vertices planar?\"}", "{\"role\":\"assistant\",\"content\":\"The two non-isomorphic $4$-regular graphs ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat is the maximum number of unique Tambola tickets possible, given the following constraints:\\n- Each ticket has 3 rows and 9 columns.\\n- Each ticket contains exactly 15 num...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFactorize the expression \\\\(a^3(b+c) + b^3(a+c) + c^3(a+b)\\\\).\"}", "{\"role\":\"assistant\",\"content\":\"We start with the expression\\n\\n\\\\[\\nE = a^3(b+c) + b^3(a+c...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a representation of $\\\\Bbb Z_2$ on $\\\\Bbb R^2$.\"}", "{\"role\":\"assistant\",\"content\":\"A representation of a group $G$ on a vector space $V$ is a group homomorph...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a bijective function \\\\( f \\\\) defined for positive integers \\\\( n \\\\) such that \\\\( f(n) = f(f(n-1)) = f^n(1) \\\\) and for every integer \\\\( k \\\\), the equa...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the determinant of the matrix \\\\( M_{n \\\\times n} \\\\) depending on \\\\( x, y, n \\\\in \\\\mathbb{R} \\\\), where the matrix is given by:\\n\\\\[ y^{n} \\\\cdot \\\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFormulate a function \\\\( f(s, j, b) \\\\) such that:\\n- \\\\( f(1,1,1) = 1 \\\\)\\n- \\\\( f(2,1,1) = 2 \\\\)\\n- \\\\( f(1,1,2) = 3 \\\\)\\n- \\\\( f(2,1,2) = 4 \\\\)\\n- \\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the number of computational steps required for the multiplication $56 \\\\times 2$ and $11 \\\\times 12$ based on the given rules:\\n- Multiplication between any two n...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nIf there are 8 possible outcomes, what is the probability that in 8 \\\"rolls\\\" I get a different outcome each time?\"}", "{\"role\":\"assistant\",\"content\":\"The total nu...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nCompute $\\\\int_0^\\\\infty \\\\frac{dx}{x^5+1}$ using a contour in the upper half complex plane that encloses one of the roots of $z^5+1=0$. The contour should consist of the ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nOrthogonally diagonalize the matrix \\\\( A \\\\), where\\n\\n\\\\[\\nA = \\\\begin{bmatrix}\\n1 & 1 & 1 \\\\\\\\\\n1 & 1 & 1 \\\\\\\\\\n1 & 1 & 1 \\n\\\\end{bmatrix}\\n\\\\]\"}...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven two matrices \\\\( M \\\\) and \\\\( N \\\\) such that \\\\( u = Mv \\\\) and \\\\( u = Nv \\\\) for some non-zero vector \\\\( v \\\\), can we conclude anything stronger ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine whether the function $g(x) = -e^{-x}$ represents exponential growth, decay, or neither.\"}", "{\"role\":\"assistant\",\"content\":\"The function \\\\(g(x) = -e^{-x}\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the double integral of the function \\\\( F(x,y) = 3y \\\\) over the triangle with vertices \\\\((-1,1)\\\\), \\\\((0,0)\\\\), and \\\\((1,1)\\\\). Determine the correct bo...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow slowly can a function $f \\\\in C^{\\\\infty}(\\\\mathbb{R}^+, \\\\mathbb{R})$ with $f'(x) > 0$ and $\\\\lim_{x \\\\to +\\\\infty} f(x) = +\\\\infty$ grow to ensure that\\n$...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the joint cumulative distribution function (CDF) $F(x,y)$ for the probability density function $f(x,y)=2(x+y)$ over the region $0\\\\leq x\\\\leq y\\\\leq 1$.\"}", "{\"ro...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the system of congruence equations:\\n\\\\[\\n\\\\alpha x_1 + \\\\beta \\\\equiv 0 \\\\pmod{26}\\n\\\\]\\n\\\\[\\n\\\\alpha x_2 + \\\\beta \\\\equiv 1 \\\\pmod{26}\\n\\\\]...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind all polynomials with coefficients in $\\\\mathbb{Q}$ and roots given by $r^{1\\/2}(\\\\omega^2, -\\\\omega^2,\\\\omega,-\\\\omega)$, where $\\\\omega = \\\\exp(2 \\\\pi i\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the eigenvalues and eigenfunctions for the operator \\\\( A \\\\) defined by\\n\\\\[ Au = -\\\\frac{d^2u}{dx^2} - 6\\\\frac{du}{dx} \\\\]\\nwith boundary conditions \\\\( 0...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the parametric equations \\\\(x = t^2 - 2t\\\\) and \\\\(y = \\\\sqrt{t}\\\\), calculate the areas \\\\(B\\\\) and \\\\(C\\\\) where \\\\(B\\\\) is the region enclosed bet...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the locus of points \\\\( Z \\\\) that satisfy the equation \\\\( Z = a + bt + ct^2 \\\\), where \\\\( a, b, c \\\\in \\\\mathbb{C} \\\\), \\\\( t \\\\in \\\\mathbb{R}...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nEvaluate the summation $\\\\sum_{n=0}^{\\\\infty} \\\\frac{P_n(\\\\cos \\\\theta)}{n+1}$, where $P_n$ is the Legendre polynomial of degree $n$.\"}", "{\"role\":\"assistant\",\...
StackExchange-Math
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cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nSolve the differential equation \\\\( y^{(4)} - \\\\lambda y = 0 \\\\) with the boundary conditions \\\\( y'(0)=0 \\\\), \\\\( y'''(0)=0 \\\\), \\\\( y(\\\\pi)=0 \\\\), and \\\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind all intervals containing solutions to the equation $4x^2 - e^x = 0$ without using a graph.\"}", "{\"role\":\"assistant\",\"content\":\"The function \\\\(f(x) = 4x^2 - e^x...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a non-trivial solution \\\\( y \\\\) of the boundary value problem (BVP) given by\\n\\\\[ y'' + xy = 0, \\\\quad x \\\\in [a, b], \\\\]\\nwith boundary conditions\\n\\\\[ y...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nDetermine the lowest value of $n$ such that for any division of the set ${1,2,3,...,n}$ into two groups $A$ and $B$, at least one of the groups contains three numbers $a$, $b$, ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nWhat are the elements \\\\( x \\\\in H_K \\\\) that satisfy a polynomial equation \\\\( f(x) = 0 \\\\) where \\\\( f(x) \\\\) is monic and has integer coefficients? Call such el...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow many solutions exist for each row of matrix $A$ given the constraints that each row contains exactly 16 entries of $+1$, 16 entries of $-1$, and the rest are $0$?\"}", "{\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the equations \\\\(a + 2b + 3c = 4\\\\), \\\\(a^2 + 4b^2 + 9c^2 = 6\\\\), and \\\\(2ab + 6bc + 3ac = 5\\\\), find the maximum value of \\\\(\\\\lfloor a \\\\rfloor^2 + \\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the probability mass function of a random variable \\\\( Y \\\\) as\\n\\\\[ f(y) = \\\\frac{a^{(y-3)}}{(e^a)(y-3)!} \\\\quad \\\\text{for } y = 3,4,\\\\dots \\\\text{ and ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nCalculate the total cost of an investment at level 45, given that the cost increases by 5000 for each level. The cost at level 1 is 5000, at level 2 is 10000, at level 3 is 1500...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nConsider a matrix \\\\( A \\\\in \\\\mathbb{R}^{n \\\\times m} \\\\) with \\\\( n > m \\\\), independent columns, and non-negative entries. For a matrix \\\\( B \\\\in \\\\mathb...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nEvaluate the line integral \\\\(\\\\int_C \\\\sqrt{1+4x^2 z^2} \\\\, ds\\\\), where \\\\(C\\\\) is the curve of intersection of the surfaces \\\\(x^2 + z^2 = 1\\\\) and \\\\(y =...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nEvaluate the infinite product $\\\\prod_{n=1}^{\\\\infty}(1+e^{-n})$.\"}", "{\"role\":\"assistant\",\"content\":\"We start with the product\\n\\n\\\\[\\nP = \\\\prod_{n=1}^{\\...
StackExchange-Math
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cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nConsider the Lebesgue probability space on the interval $[0,1)$. Define the random variable $X$ as:\\n$$X(w)=\\\\begin{cases} 2w &, 0\\\\leq w < 1\\/2 \\\\\\\\ 2w\\u22121 &, 1\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nHow can the value of the integral $$\\\\int_0^\\\\infty\\\\left(\\\\dfrac{\\\\sin x}{x}\\\\right)^5dx$$ be found using contour integrals?\"}", "{\"role\":\"assistant\",\"conte...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nSimplify the expression \\\\(4 - (X \\\\mod (Y \\\\mod (X - 4)))\\\\) such that the last 4 rows of the expression yield the values 4, 3, 2, 1 respectively.\"}", "{\"role\":\"a...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind the area of the figure that is bound by the lines $y=|x^2-1|$ and $y=3|x|-3$.\"}", "{\"role\":\"assistant\",\"content\":\"The area bounded by the curves \\\\(y=|x^2-1|\\\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a basis for the set of polynomials \\\\( p(x) \\\\) such that \\\\( p(x) = 0 \\\\) or \\\\( p(x) \\\\) is a polynomial of degree at most 4 with real coefficients and \\\\( ...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nEvaluate the integral \\\\(\\\\int_{-\\\\infty}^{\\\\infty}\\\\frac{\\\\text{sinc}^2(t\\/2)}{\\\\sqrt{1-t^2}}dt\\\\), considering the infinite discontinuities at \\\\(t = \\\\pm...
StackExchange-Math
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without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nLet \\\\(a_1, a_2, \\\\ldots, a_{2n}\\\\) be complex numbers. Construct a \\\\(2n \\\\times 2n\\\\) skew-symmetric matrix \\\\(A\\\\) where the entries are given by \\\\(\\\\alp...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nIf \\\\( f(x) = \\\\mu x - \\\\sin x \\\\) for \\\\( x > 0 \\\\) is a monotonically increasing function, find the value of \\\\( \\\\mu \\\\).\"}", "{\"role\":\"assistant\",\"...
StackExchange-Math
[]
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without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nFind a vector \\\\( w \\\\in (0,1)^5 \\\\) that minimizes \\\\( w'd \\\\) where \\\\( d \\\\in (0,10)^5 \\\\), subject to the constraints \\\\( \\\\sum_{i=1}^5 w_i = \\\\frac{2}...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
[ "{\"role\":\"user\",\"content\":\"Solve the following math problem. Make sure to put the answer (and only answer) inside \\\\boxed{}.\\n\\nGiven the elliptic curve \\\\( E: y^2 = x^3 + x + 1 \\\\) modulo 11, calculate the order of the elliptic curve using the Hasse bound. Assume there is a point \\\\( P \\\\) on \\...
StackExchange-Math
[]
cc-by-sa-4.0
without Python TIR
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AMALIA Paper Data Main Repo Eval Repo

AMALIA Nemotron-SFT-Math-v3

Version of the nvidia/Nemotron-SFT-Math-v3 dataset used in the AMALIA's Supervised Fine-Tuning stage.

This dataset went through a processing pipeline to:

  • Remove entries with tool usage;
  • Remove entries that reference other LLMs or research labs;
  • Removed the reasoning_content field;
  • Drop extra unnecessary columns;

Original Dataset: https://huggingface.co/datasets/nvidia/Nemotron-SFT-Math-v3

This dataset is provided as part of the AMALIA project and is included in the data mix used to post-train the AMALIA model.


Citation

If you use this dataset or AMALIA in your work, please cite:

@inproceedings{simplicio-etal-2026-amalia,
    title = "{AMALIA}: A Fully Open Large Language Model for {E}uropean {P}ortuguese",
    author = "Simpl{{\'i}}cio, Afonso and Vinagre, Gon{{\c{{c}}}}alo and Ramos, Miguel Moura and Tavares, Diogo and Ferreira, Rafael and Attanasio, Giuseppe and Alves, Duarte M. and Calvo, In{{\^e}}s and Vieira, In{{\^e}}s and Guerra, Rui and Furtado, James and Canaverde, Beatriz and Paulo, Iago and Ramos, Vasco and Gl{{\'o}}ria-Silva, Diogo and Faria, Miguel and Treviso, Marcos and Gomes, Daniel and Gomes, Pedro and Semedo, David and Martins, Andr{{\'e}} and Magalh{{\~a}}es, Jo{{\~a}}o",
    booktitle = "Proceedings of the 17th International Conference on Computational Processing of {{P}}ortuguese ({{PROPOR}} 2026) - Vol. 1",
    month = apr,
    year = "2026",
    address = "Salvador, Brazil",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2026.propor-1.38/",
    pages = "380--391",
    isbn = "979-8-89176-387-6"
}

@misc{simplicio2026amaliatechnicalreportfully,
    title = {AMALIA Technical Report: A Fully Open Source Large Language Model for European Portuguese},
    author = {Afonso Simplício and Gonçalo Vinagre and Miguel Moura Ramos and Diogo Tavares and Rafael Ferreira and Giuseppe Attanasio and Duarte M. Alves and Inês Calvo and Inês Vieira and Rui Guerra and James Furtado and Beatriz Canaverde and Iago Paulo and Vasco Ramos and Diogo Glória-Silva and Miguel Faria and Marcos Treviso and Daniel Gomes and Pedro Gomes and David Semedo and André Martins and João Magalhães},
    year = {2026},
    eprint = {2603.26511},
    archivePrefix = {arXiv},
    primaryClass = {cs.CL},
    url = {https://arxiv.org/abs/2603.26511}
}
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