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This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty.

# deepmind/mathematics_dataset

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# Mathematics Dataset

This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.

Original paper: Analysing Mathematical Reasoning Abilities of Neural Models (Saxton, Grefenstette, Hill, Kohli).

## Example questions

``````Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.

Question: Calculate -841880142.544 + 411127.

Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).

Question: Let e(l) = l - 6. Is 2 a factor of both e(9) and 2?

Question: Let u(n) = -n**3 - n**2. Let e(c) = -2*c**3 + c. Let l(j) = -118*e(j) + 54*u(j). What is the derivative of l(a)?
Answer: 546*a**2 - 108*a - 118

Question: Three letters picked without replacement from qqqkkklkqkkk. Give prob of sequence qql.
``````

## Pre-generated data

Pre-generated files

### Version 1.0

This is the version released with the original paper. It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:

• algebra (linear equations, polynomial roots, sequences)
• arithmetic (pairwise operations and mixed expressions, surds)
• calculus (differentiation)
• comparison (closest numbers, pairwise comparisons, sorting)
• measurement (conversion, working with time)
• numbers (base conversion, remainders, common divisors and multiples, primality, place value, rounding numbers)
• polynomials (addition, simplification, composition, evaluating, expansion)
• probability (sampling without replacement)

## Getting the source

### PyPI

The easiest way to get the source is to use pip:

`\$ pip install mathematics_dataset`

### From GitHub

Alternately you can get the source by cloning the mathematics_dataset repository:

```\$ git clone https://github.com/deepmind/mathematics_dataset

## Generating examples

Generated examples can be printed to stdout via the `generate` script. For example:

`python -m mathematics_dataset.generate --filter=linear_1d`

will generate example (question, answer) pairs for solving linear equations in one variable.

We've also included `generate_to_file.py` as an example of how to write the generated examples to text files. You can use this directly, or adapt it for your generation and training needs.

The following table is necessary for this dataset to be indexed by search engines such as Google Dataset Search.

property value
name `Mathematics Dataset`
url
sameAs `https://github.com/deepmind/mathematics_dataset`
description ```This dataset consists of mathematical question and answer pairs, from a range of question types at roughly school-level difficulty. This is designed to test the mathematical learning and algebraic reasoning skills of learning models.\n \n ## Example questions\n \n ```\n Question: Solve -42*r + 27*c = -1167 and 130*r + 4*c = 372 for r.\n Answer: 4\n \n Question: Calculate -841880142.544 + 411127.\n Answer: -841469015.544\n \n Question: Let x(g) = 9*g + 1. Let q(c) = 2*c + 1. Let f(i) = 3*i - 39. Let w(j) = q(x(j)). Calculate f(w(a)).\n Answer: 54*a - 30\n ```\n \n It contains 2 million (question, answer) pairs per module, with questions limited to 160 characters in length, and answers to 30 characters in length. Note the training data for each question type is split into "train-easy", "train-medium", and "train-hard". This allows training models via a curriculum. The data can also be mixed together uniformly from these training datasets to obtain the results reported in the paper. Categories:\n \n * **algebra** (linear equations, polynomial roots, sequences)\n * **arithmetic** (pairwise operations and mixed expressions, surds)\n * **calculus** (differentiation)\n * **comparison** (closest numbers, pairwise comparisons, sorting)\n * **measurement** (conversion, working with time)\n * **numbers** (base conversion, remainders, common divisors and multiples,\n primality, place value, rounding numbers)\n * **polynomials** (addition, simplification, composition, evaluating, expansion)\n * **probability** (sampling without replacement)```
provider
property value
name `DeepMind`
sameAs `https://en.wikipedia.org/wiki/DeepMind`
citation `https://identifiers.org/arxiv:1904.01557`

This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty.

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