Download An Introduction to the Early Development of Mathematics by Michael K. J. Goodman PDF

By Michael K. J. Goodman

An easy-to-read presentation of the early historical past of arithmetic

Engaging and obtainable, An advent to the Early improvement of arithmetic provides an enthralling advent to the historical past of historic arithmetic in early civilizations for a nontechnical viewers. Written with useful functions in quite a few components, the publication makes use of the old context of arithmetic as a pedagogical device to aid readers operating via mathematical and historic topics.

The e-book is split into sections on major early civilizations together with Egypt, Babylonia, China, Greece, India, and the Islamic international. starting each one bankruptcy with a basic ancient evaluate of the civilized zone, the writer highlights the civilization’s mathematical concepts, quantity representations, accomplishments, demanding situations, and contributions to the mathematical international. completely class-tested, An advent to the Early improvement of arithmetic features:

  • Challenging routines that lead readers to a deeper figuring out of mathematics
  • Numerous suitable examples and challenge units with exact reasons of the strategies and suggestions on the finish of every chapter
  • Additional references on particular subject matters and key terms from historical past, archeology, faith, tradition, and mathematics
  • Examples of sensible functions with step by step reasons of the mathematical ideas and equations during the lens of early mathematical problems
  • A spouse web site that incorporates extra exercises

An creation to the Early improvement of arithmetic is an excellent textbook for undergraduate classes at the historical past of arithmetic and a complement for common and secondary schooling majors. The ebook is additionally a suitable reference for pro and alternate audiences attracted to the historical past of mathematics.

Michael ok. J. Goodman is Adjunct arithmetic teacher at Westchester group collage, the place he teaches classes within the heritage of arithmetic, modern arithmetic, and algebra. he's additionally the landlord and operator of the training Miracle, LLC, which supplies educational tutoring and attempt instruction for either collage and highschool students.

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Additional resources for An Introduction to the Early Development of Mathematics

Sample text

Chinese mathematicians worked with the high‐order digits first so they would quickly get a good estimate of the final answer. If we were to add 7846 + 5619 the way American schoolchildren are taught to, our first operation would be to add the 6 and the 9. This pinpoints the least significant digit but does not say anything about the magnitude of the sum. The Chinese approach, adding 7000 + 5000 first, tells them immediately approximately how big the sum will be. Counting boards were put to much more sophisticated uses than what we just saw: they were used to do multiplication problems and to find square roots.

It won’t always work. When it doesn’t 6 12 18 20 work, try something else, like , , or . The goal is to get a large enough pool of 12 18 20 factors that some combination of them matches the numerator. Multiplying by Exercise Verify that 8 cannot be expressed as the sum of unit fractions when you mul17 6 tiply it by , but can be expressed as the sum of unit fractions when you multiply 6 20 it by . 11 Any multiple of 30 is a sensible guess, because the denominators of the unit fractions in the equation multiply to 30.

7 19 . Start by listing the factors of 20 20 1 2 4 20 10 5 We need a combination of the factors of the denominator to add up to the numerator. Here, 4 5 10 19. 9 3 15 and 17 17 10 20 1 4 19 20 1 2 34 ANCIENT EGYPTIAN MATHEMATICS 17 is a prime number, so its only factors are 1 and 17. Obviously, no combination 6 of 1 and 17 adds up to 3 or 15. So, we multiply these fractions by 1 in the form of 6 6 to make equivalent fractions. Multiplying by often works. 6 3 6 17 6 18 102 15 6 90 17 6 102 The new denominator is 102, which has many factors.

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