arithmetic vs mathematics

arithmetic

noun
  • The mathematics of numbers (integers, rational numbers, real numbers, or complex numbers) under the operations of addition, subtraction, multiplication, and division. 

adj
  • Of a progression, mean, etc, computed solely using addition. 

  • Of, relating to, or using arithmetic; arithmetical. 

mathematics

noun
  • A person's ability to count, calculate, and use different systems of mathematics at differing levels. 

  • An abstract representational system studying numbers, shapes, structures, quantitative change and relationships between them. 

How often have the words arithmetic and mathematics occurred in a corpus of books? (source: Google Ngram Viewer )