higher arithmetic

higher arithmetic (uncountable)

1. (mathematics, chiefly dated) Number theory; the branch of pure mathematics concerned primarily with integers and integer-valued functions.
   • 1999 [1952], H. Davenport, The Higher Arithmetic: An Introduction to Number Theory, Cambridge University Press, 7th Edition, page 7,

     The higher arithmetic, or the theory of numbers, is concerned with the properties of the natural numbers 1, 2, 3, . . . .

   • 2008, Harold M. Edwards, Higher Arithmetic: An Algorithmic Introduction to Number Theory, American Mathematical Society, .
2. (education, obsolete) A loosely defined range of topics in arithmetic, distinguished from elementary arithmetic by the more advanced nature of the methods and concepts.
   • 1895, Report, Mississippi State Department of Education, page 10,

     Arithmetic should overlap algebra, because the simpler parts of Algebra are easier than higher arithmetic; and some knowledge of algebra would conduce to a more intelligent appreciation of such topics as proportion, evolution, application of percentage, etc.

   • 1898, John Henry Walsh, Mathematics for Common Schools: Part III: Higher Arithmetic, D. C. Heath & Co., .
   • 1976, Charles S. Peirce, The New Elements of Mathematics, Volume 1: Arithmetic, Mouton Publishers, page 95,

     With division higher arithmetic naturally begins, and for the more advanced pupil it will be proper here to insert a short course on that subject.

• vulgar arithmetic

• number theory — see number theory