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, , H. Davenport, The Higher Arithmetic: An Introduction to Number Theory, 7th edition, Cambridge University Press, 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