BlueMO

The "Little Blue Book" (小蓝书) series, published by East China Normal University Press, is a cornerstone resource for students striving to master mathematical olympiads. Renowned for its depth, challenging problems, and elegant solutions, the series provides rigorous training for top-tier competitions.

BlueMO encompasses a total of 14 volumes from the third edition of the series, covering a wide range of mathematical topics for the high school level.

High School Collection

Potential Applications

This dataset is a valuable resource for AI researchers and developers, with key applications including:

• Training & Fine-Tuning: Enhancing large language models’ capabilities in advanced mathematical reasoning.
• AI Evaluation: Benchmarking the problem-solving proficiency and logical rigor of AI systems.
• Formal Verification: Formalizing problems into mathematical languages (e.g., LEAN) to evaluate AI's reasoning capability with formal methods.
• Comparative Analysis: Systematically assessing reasoning skills across different models and methodologies.

Data Structure

We provide the raw data (*.tex) and the processed dataset. Each entry in the JSON dataset contains the problem, a detailed solution, and metadata. Below is an example case for a `calculation` problem:

{
    "source_file": "./raw_volume-zh/volume1/chapter1.tex",
    "problem_type": "calculation",
    "problem": "例1. 设集合 $M=\\left\\{x |{\\frac{a x-5}{x^{2}-a}}<0,\\,x\\in\\mathbb{R}\\right\\}$ \n(1)当 $a=4$ 时,化简集合 $M$ ;\n(2)若 $3\\in M,$ ,且 $5\\notin M,$ 求实数a的取值范围.",
    "solution": "分析: 化简集合 $M$, 实际上就是解不等式 ${\\frac{a x-5}{x^{2}-a}}<0.$ \n解: (1) 当 $a=4$ 时,有\n$$\n{\\frac{4x-5}{x^{2}-4}}<0\\,, \n$$\n即\n$$\n\\left(x-\\frac{5}{4}\\right)(x+2)(x-2)<0. \n$$\n$x<-2$ 或 ${\\frac{5}{4}}9. \n$$\n由 $5\\notin M$ 得, ${\\frac{5a-5}{5^{2}-a}}\\geqslant0$ 或 $5^{2}-a=0$ ,所以\n$$\n1\\leq a\\leq25. \n$$\n可得 $a\\in\\left[1,{\\frac{5}{3}}\\right)\\cup\\left(9,25\\right]$.\n说明: $5\\notin M$ 隐含了条件 $5^{2}-a=0$,这是容易被忽视的.\n由概括原则我们知道,判断一个对象 $x$ 是否为集合 $S$ 的元素,等价于判断 $x$ 是否具有性质 $P$.",
    "remark": "",
    "figures": []
}

• source_file: Path to the original .tex source file containing this problem.
• problem_type: Problem category (e.g., "calculation", "proof", etc.).
• problem: Complete problem statement in LaTeX format, including sub-questions.
• solution: Step-by-step solution with mathematical derivations in LaTeX.
• remark: Additional notes or comments about the problem (empty if none).
• figures: Array containing any associated diagram files (empty if none).

Citation

If you use the BlueMO dataset in your research, please consider citing it as follows:

@misc{bluemo2024,
      title={BlueMO: A comprehensive collection of challenging mathematical olympiad problems from the little blue book series}, 
      author={Chen, Yizhou and Luo, Yifan and Zhang, Yifan and Yuan, Yang},
      year={2024},
}

License

The BlueMO dataset is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.