Datasets:
id stringlengths 8 8 | messages listlengths 2 2 | meta dict |
|---|---|---|
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... |
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:
- Difficulty window 4.5 β€ d < 8.5 β 87,765 rows.
- Answer consistency: the last
\boxed{}inr1_solution_1must matchfinal_answer(numeric tolerance, fractions and percentages normalized). Pass rate over the whole corpus: 98.97%. - Not truncated: the solution must end with a boxed answer.
- Length 3,000β50,000 characters.
- Deduplicate by normalized question (punctuation, whitespace, case stripped) β 82,749 rows.
- Stratified sampling over (topic, difficulty) cells with a 50% per-cell cap, seed 42.
- Split by question, 95/5, so no question appears in both splits.
- 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_1is 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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