higher arithmetic

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English[edit]

Noun[edit]

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, 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, [1].
  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[2], 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.

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