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https://github.com/google-deepmind/mathematics_dataset

This dataset code generates mathematical question and answer pairs, from a range of question types at roughly school-level difficulty.
https://github.com/google-deepmind/mathematics_dataset

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

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README 

        
# 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](https://openreview.net/pdf?id=H1gR5iR5FX)

(Saxton, Grefenstette, Hill, Kohli).



## Example questions



```

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

Answer: 4



Question: Calculate -841880142.544 + 411127.

Answer: -841469015.544



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)).

Answer: 54*a - 30



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

Answer: False



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.

Answer: 1/110

```



## Pre-generated data



[Pre-generated files](https://console.cloud.google.com/storage/browser/mathematics-dataset)



### 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:



```shell

$ pip install mathematics_dataset

```



### From GitHub



Alternately you can get the source by cloning the mathematics_dataset

repository:



```shell

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

$ pip install --upgrade mathematics_dataset/

```



## Generating examples



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

example:



```shell

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.



## Dataset Metadata

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

    https://github.com/deepmind/mathematics_dataset

  

  

    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