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dm000661
[ { "role": "user", "content": "Find a quadratic polynomial that is orthogonal to both \\( p(x) = 1 \\) and \\( q(x) = x \\)." }, { "role": "assistant", "content": "Okay, so I need to find a quadratic polynomial that's orthogonal to both p(x) = 1 and q(x) = x. Hmm, orthogonal in the context of pol...
{ "question": "Find a quadratic polynomial that is orthogonal to both \\( p(x) = 1 \\) and \\( q(x) = x \\).", "final_answer": "3x^2 - 1", "difficulty": 5, "topic": "Mathematics -> Algebra -> Algebra -> Polynomial Operations", "topic_bucket": "Algebra", "source": "zwhe99/DeepMath-103K", "solution_field": ...
dm000787
[ { "role": "user", "content": "Can every hyperplane in \\( \\mathbb{F}^n \\) be described as \\( \\{(x_1, \\dots, x_n) \\in \\mathbb{F}^n \\mid a_1x_1 + \\dots + a_nx_n = 0\\} \\) for some coefficients \\( a_1, \\dots, a_n \\) where at least one \\( a_i \\neq 0 \\)? Assume a hyperplane is defined as a subspa...
{ "question": "Can every hyperplane in \\( \\mathbb{F}^n \\) be described as \\( \\{(x_1, \\dots, x_n) \\in \\mathbb{F}^n \\mid a_1x_1 + \\dots + a_nx_n = 0\\} \\) for some coefficients \\( a_1, \\dots, a_n \\) where at least one \\( a_i \\neq 0 \\)? Assume a hyperplane is defined as a subspace with dimension one les...
dm000831
[ { "role": "user", "content": "Find the sum of all the digits of the smallest positive integer \\( n \\) such that the product \\( P_2 \\times P_3 \\times \\ldots \\times P_n \\) exceeds 2010, where \\( P_k = 1 + \\frac{1}{k} - \\frac{1}{k^2} - \\frac{1}{k^3} \\) for a positive integer \\( k \\)." }, { ...
{ "question": "Find the sum of all the digits of the smallest positive integer \\( n \\) such that the product \\( P_2 \\times P_3 \\times \\ldots \\times P_n \\) exceeds 2010, where \\( P_k = 1 + \\frac{1}{k} - \\frac{1}{k^2} - \\frac{1}{k^3} \\) for a positive integer \\( k \\).", "final_answer": "19", "difficu...
dm001151
[ { "role": "user", "content": "Given that \\(x+y+z=3\\), \\(x^2 + y^2 + z^2 = 5\\), and \\(x^3+y^3+z^3=7\\), find the value of \\(x^4+y^4+z^4\\)." }, { "role": "assistant", "content": "Okay, so I need to find the value of \\(x^4 + y^4 + z^4\\) given the equations \\(x + y + z = 3\\), \\(x^2 + y^2...
{ "question": "Given that \\(x+y+z=3\\), \\(x^2 + y^2 + z^2 = 5\\), and \\(x^3+y^3+z^3=7\\), find the value of \\(x^4+y^4+z^4\\).", "final_answer": "9", "difficulty": 4.5, "topic": "Mathematics -> Algebra -> Algebra -> Equations and Inequalities", "topic_bucket": "Algebra", "source": "zwhe99/DeepMath-103K",...
dm001606
[ { "role": "user", "content": "Real numbers \\(x, y\\) satisfy \\(x^2 + y^2 = 1\\). If the minimum and maximum values of the expression \\(z = \\frac{4-y}{7-x}\\) are \\(m\\) and \\(M\\) respectively, find \\(2M + 6m\\)." }, { "role": "assistant", "content": "Okay, so I need to find the minimum a...
{ "question": "Real numbers \\(x, y\\) satisfy \\(x^2 + y^2 = 1\\). If the minimum and maximum values of the expression \\(z = \\frac{4-y}{7-x}\\) are \\(m\\) and \\(M\\) respectively, find \\(2M + 6m\\).", "final_answer": "4", "difficulty": 5, "topic": "Mathematics -> Algebra -> Algebra -> Equations and Inequa...
dm002083
[ { "role": "user", "content": "Given the quadratic function \\( f(x) = ax^2 + bx + c \\) with \\( a < b \\) and \\( f(x) \\ge 0 \\) for all \\( x \\in \\mathbb{R} \\), find the minimum value of \\( \\frac{a+b+c}{b-a} \\)." }, { "role": "assistant", "content": "Okay, let's tackle this problem step...
{ "question": "Given the quadratic function \\( f(x) = ax^2 + bx + c \\) with \\( a < b \\) and \\( f(x) \\ge 0 \\) for all \\( x \\in \\mathbb{R} \\), find the minimum value of \\( \\frac{a+b+c}{b-a} \\).", "final_answer": "3", "difficulty": 5, "topic": "Mathematics -> Algebra -> Intermediate Algebra -> Quadra...
dm002125
[ { "role": "user", "content": "Consider the vector \\((1\\ 2\\ 2\\ 3\\ 3\\ 3)^T\\) in the vector space \\(\\mathbb{R}^6\\). The symmetric group \\(S_6\\) acts on \\(\\mathbb{R}^6\\) by permuting the coordinates. Determine the order of the stabilizer of this vector under the given action of \\(S_6\\)." }, ...
{ "question": "Consider the vector \\((1\\ 2\\ 2\\ 3\\ 3\\ 3)^T\\) in the vector space \\(\\mathbb{R}^6\\). The symmetric group \\(S_6\\) acts on \\(\\mathbb{R}^6\\) by permuting the coordinates. Determine the order of the stabilizer of this vector under the given action of \\(S_6\\).", "final_answer": "12", "dif...
dm002323
[ { "role": "user", "content": "Which of the following sets form an ideal in the ring \\(C(\\mathbb{R})\\) of all continuous real-valued functions on \\(\\mathbb{R}\\)?\n\n(a) The set of all \\(C^\\infty\\) functions with compact support.\n(b) The set of all continuous functions with compact support.\n(c) The...
{ "question": "Which of the following sets form an ideal in the ring \\(C(\\mathbb{R})\\) of all continuous real-valued functions on \\(\\mathbb{R}\\)?\n\n(a) The set of all \\(C^\\infty\\) functions with compact support.\n(b) The set of all continuous functions with compact support.\n(c) The set of all continuous fu...
dm002646
[ { "role": "user", "content": "Determine if 28 is the only integer that can be expressed both as the sum of a positive cube plus one and as \\(2^n - 4\\)." }, { "role": "assistant", "content": "Okay, so I need to figure out if 28 is the only integer that can be written both as the sum of a positi...
{ "question": "Determine if 28 is the only integer that can be expressed both as the sum of a positive cube plus one and as \\(2^n - 4\\).", "final_answer": "28", "difficulty": 4.5, "topic": "Mathematics -> Algebra -> Algebra -> Equations and Inequalities", "topic_bucket": "Algebra", "source": "zwhe99/DeepM...
dm002796
[ { "role": "user", "content": "Determine the set of cluster points of the set \\( \\left\\{\\frac{m}{10^n} : m \\in \\mathbb{Z}, n \\in \\mathbb{N}\\right\\} \\)." }, { "role": "assistant", "content": "Okay, so I need to figure out the set of cluster points for the set \\( S = \\left\\{\\frac{m}{...
{ "question": "Determine the set of cluster points of the set \\( \\left\\{\\frac{m}{10^n} : m \\in \\mathbb{Z}, n \\in \\mathbb{N}\\right\\} \\).", "final_answer": "\\mathbb{R}", "difficulty": 5, "topic": "Mathematics -> Algebra -> Abstract Algebra -> Field Theory", "topic_bucket": "Algebra", "source": "zw...
dm002802
[ { "role": "user", "content": "Consider a non-homogeneous linear system with $n+1$ equations and $n$ unknowns. If the row echelon form of the augmented matrix of this system has exactly one row of zeros, does the system have exactly one solution? Justify your answer." }, { "role": "assistant", "c...
{ "question": "Consider a non-homogeneous linear system with $n+1$ equations and $n$ unknowns. If the row echelon form of the augmented matrix of this system has exactly one row of zeros, does the system have exactly one solution? Justify your answer.", "final_answer": "Yes", "difficulty": 5, "topic": "Mathemat...
dm003302
[ { "role": "user", "content": "Find the smallest integer \\( n \\geq 2 \\) such that the equation \\( x^2 - x + \\hat{2} = \\hat{0} \\) has a unique solution in \\( \\mathbb{Z}_n \\)." }, { "role": "assistant", "content": "Okay, so I need to find the smallest integer \\( n \\geq 2 \\) such that t...
{ "question": "Find the smallest integer \\( n \\geq 2 \\) such that the equation \\( x^2 - x + \\hat{2} = \\hat{0} \\) has a unique solution in \\( \\mathbb{Z}_n \\).", "final_answer": "7", "difficulty": 4.5, "topic": "Mathematics -> Algebra -> Abstract Algebra -> Field Theory", "topic_bucket": "Algebra", ...
dm003341
[ { "role": "user", "content": "Is there a field with a characteristic that is a composite number, such as 4?" }, { "role": "assistant", "content": "Okay, so I need to figure out if there's a field with characteristic 4. Hmm, I remember that the characteristic of a field is the smallest positive i...
{ "question": "Is there a field with a characteristic that is a composite number, such as 4?", "final_answer": "No", "difficulty": 4.5, "topic": "Mathematics -> Algebra -> Abstract Algebra -> Field Theory", "topic_bucket": "Algebra", "source": "zwhe99/DeepMath-103K", "solution_field": "r1_solution_1", "...
dm003831
[ { "role": "user", "content": "If \\(a, b, c, d, e\\) are the roots of the polynomial \\(6x^5 + 5x^4 + 4x^3 + 3x^2 + 2x + 1\\), find the value of \\((a+1)(b+1)(c+1)(d+1)(e+1)\\)." }, { "role": "assistant", "content": "Okay, so I need to find the value of \\((a+1)(b+1)(c+1)(d+1)(e+1)\\) where \\(a...
{ "question": "If \\(a, b, c, d, e\\) are the roots of the polynomial \\(6x^5 + 5x^4 + 4x^3 + 3x^2 + 2x + 1\\), find the value of \\((a+1)(b+1)(c+1)(d+1)(e+1)\\).", "final_answer": "\\dfrac{1}{2}", "difficulty": 5, "topic": "Mathematics -> Algebra -> Algebra -> Polynomial Operations", "topic_bucket": "Algebra...
dm004114
[ { "role": "user", "content": "Solve the equation: \\( \\sqrt[4]{13x+1} + \\sqrt[4]{4x-1} = 3\\sqrt[4]{x} \\) for \\(x\\)." }, { "role": "assistant", "content": "Okay, so I need to solve the equation \\( \\sqrt[4]{13x+1} + \\sqrt[4]{4x-1} = 3\\sqrt[4]{x} \\). Hmm, fourth roots, that seems a bit t...
{ "question": "Solve the equation: \\( \\sqrt[4]{13x+1} + \\sqrt[4]{4x-1} = 3\\sqrt[4]{x} \\) for \\(x\\).", "final_answer": "\\dfrac{1}{3}", "difficulty": 5, "topic": "Mathematics -> Algebra -> Intermediate Algebra -> Exponential Functions", "topic_bucket": "Algebra", "source": "zwhe99/DeepMath-103K", "s...
dm004321
[ { "role": "user", "content": "Evaluate \\( \\det(aI_n + bJ_n) \\), where \\( a, b \\in \\mathbb{R} \\), \\( I_n \\) is the \\( n \\times n \\) identity matrix, and \\( J_n \\in M_n(\\mathbb{R}) \\) is the matrix with every entry equal to 1." }, { "role": "assistant", "content": "Okay, so I need ...
{ "question": "Evaluate \\( \\det(aI_n + bJ_n) \\), where \\( a, b \\in \\mathbb{R} \\), \\( I_n \\) is the \\( n \\times n \\) identity matrix, and \\( J_n \\in M_n(\\mathbb{R}) \\) is the matrix with every entry equal to 1.", "final_answer": "a^{n-1}(a + bn)", "difficulty": 5, "topic": "Mathematics -> Algebra...
dm004522
[ { "role": "user", "content": "Let \\( f = (1\\ 2\\ 3\\ 4\\ 5\\ 6) \\circ (7\\ 8\\ 9\\ 10) \\in S_{10} \\). Does there exist a positive integer \\( n \\) such that, when \\( f^n \\) is decomposed into disjoint cycles, one of the cycles has length 5? Justify your answer." }, { "role": "assistant", ...
{ "question": "Let \\( f = (1\\ 2\\ 3\\ 4\\ 5\\ 6) \\circ (7\\ 8\\ 9\\ 10) \\in S_{10} \\). Does there exist a positive integer \\( n \\) such that, when \\( f^n \\) is decomposed into disjoint cycles, one of the cycles has length 5? Justify your answer.", "final_answer": "No", "difficulty": 5, "topic": "Mathem...
dm004739
[ { "role": "user", "content": "Given the polynomial \\( P(x) = x^4 + ax^3 + bx^2 + cx + d \\) with the conditions \\( P(1) = 10 \\), \\( P(2) = 20 \\), and \\( P(3) = 30 \\), find the value of \\( P(12) + P(-8) \\)." }, { "role": "assistant", "content": "Okay, let's try to figure out how to solve...
{ "question": "Given the polynomial \\( P(x) = x^4 + ax^3 + bx^2 + cx + d \\) with the conditions \\( P(1) = 10 \\), \\( P(2) = 20 \\), and \\( P(3) = 30 \\), find the value of \\( P(12) + P(-8) \\).", "final_answer": "19840", "difficulty": 4.5, "topic": "Mathematics -> Algebra -> Algebra -> Polynomial Operatio...
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DeepMath-103K Β· 10K Non-Thinking SFT Subset

A 10,138-example stratified subset of zwhe99/DeepMath-103K, reformatted as ChatML for supervised fine-tuning of mathematical reasoning.

Each target is a single chain-of-thought ending in \boxed{answer}, with no <think> tags: the sample is meant to be rendered with enable_thinking=False, where the Qwen chat template supplies the empty thinking block itself.

Files

File Rows
train.jsonl 9,634
val.jsonl 504

One record:

{
  "id": "dm002083",
  "messages": [
    {"role": "user", "content": "..."},
    {"role": "assistant", "content": "... Therefore, the answer should be \\boxed{3}."}
  ],
  "meta": {
    "question": "...",
    "final_answer": "3",
    "difficulty": 6.5,
    "topic": "Mathematics -> Algebra -> Algebra -> Polynomial Operations",
    "topic_bucket": "Algebra",
    "source": "zwhe99/DeepMath-103K",
    "solution_field": "r1_solution_1",
    "target_format": "r1_cot_pre_think"
  }
}

meta.question duplicates the user turn for convenience; drop meta if your collator does not ignore unused columns.

How it was built

Starting from all 103,022 rows:

  1. Difficulty window 4.5 ≀ d < 8.5 β†’ 87,765 rows.
  2. Answer consistency: the last \boxed{} in r1_solution_1 must match final_answer (numeric tolerance, fractions and percentages normalized). Pass rate over the whole corpus: 98.97%.
  3. Not truncated: the solution must end with a boxed answer.
  4. Length 3,000–50,000 characters.
  5. Deduplicate by normalized question (punctuation, whitespace, case stripped) β†’ 82,749 rows.
  6. Stratified sampling over (topic, difficulty) cells with a 50% per-cell cap, seed 42.
  7. Split by question, 95/5, so no question appears in both splits.
  8. Target normalization: DeepSeek-R1 solutions carry a </think> boundary β€” a long CoT ending in \boxed{}, followed by a second, condensed restatement of the same solution. Everything from </think> onward was removed, keeping the long CoT. 45 rows where the model declared the problem statement incomplete were dropped, plus 25 rows whose target did not end in \boxed{}.

Difficulty quota was 20 / 30 / 30 / 20 over the four bins; realized exactly 20.0 / 30.0 / 30.0 / 20.0.

Topic quota was adjusted to what the corpus can actually supply:

Bucket Target Realized Available in window Sampling rate
Algebra 24% 24.5% 26,696 9.4%
Calculus 14% 14.7% 26,577 5.6%
Number Theory 14% 13.8% 4,940 28.6%
Geometry 14% 12.9% 6,042 21.8%
Stats 12% 12.0% 5,831 21.0%
Precalculus 8% 8.1% 8,285 9.9%
Discrete 8% 8.0% 4,817 17.0%
Other 4% 4.0% 3,158 13.1%
Differential Equations 2% 2.0% 1,419 14.4%

Number Theory was originally planned at 20%, but the corpus only has 4,940 rows in the window β€” 20% would have consumed 41% of the whole topic.

Realized distribution (train)

Bucket Rows
Algebra 2,360
Calculus 1,412
Number Theory 1,331
Geometry 1,249
Stats 1,151
Precalculus 777
Discrete Mathematics 772
Other 388
Differential Equations 194

Difficulty: 4.5 β†’ 415, 5.0 β†’ 1,509, 5.5 β†’ 1,325, 6.0 β†’ 1,565, 6.5 β†’ 1,423, 7.0 β†’ 1,465, 7.5 β†’ 689, 8.0 β†’ 1,243.

Target length (characters): p5 = 4,574, median = 12,021, p95 = 35,287, max = 48,375. About 43M tokens per epoch at ~3.5 characters per token.

Usage

from datasets import load_dataset
from transformers import AutoTokenizer

ds = load_dataset("HuggingMicah/deepmath-103k-10k-sft-nothink")
tok = AutoTokenizer.from_pretrained("Qwen/Qwen3-8B")

text = tok.apply_chat_template(
    ds["train"][0]["messages"],
    tokenize=False,
    enable_thinking=False,          # empty <think> block comes from the template
)

The trailing \boxed{} makes answer extraction a simple regex over the generated text.

Caveats

  • This is not ROSS. It is a plain full-sequence SFT set distilled from external R1 solutions, equivalent to a positive-rollout / rejection-sampling baseline. It contains no model-generated rollouts and no token-level supervision mask.
  • Roughly 15% of questions are phrased as proofs ("prove that ..."), but all of them were retained only when the solution carried a verifiable boxed answer. Expect the model to pick up some proof-style phrasing.
  • Targets are long relative to Qwen's usual no-thinking outputs. With a 16K output budget, a small fraction of generations may hit the cap.
  • Only r1_solution_1 is used. The other two solutions are not included, to avoid selection bias in this first version.

Attribution

  • Base corpus: zwhe99/DeepMath-103K (MIT), which is decontaminated against common benchmarks.
  • Solutions: generated by DeepSeek-R1, as distributed in DeepMath-103K.
  • Filtering, normalization, and sampling: this repository.

License

MIT, inherited from DeepMath-103K.

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