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

By Michael K. J. Goodman

An easy-to-read presentation of the early background of arithmetic

Engaging and obtainable, An advent to the Early improvement of arithmetic provides a charming advent to the background of historical arithmetic in early civilizations for a nontechnical viewers. Written with functional purposes in various components, the booklet makes use of the old context of arithmetic as a pedagogical software to help readers operating via mathematical and ancient topics.

The e-book is split into sections on major early civilizations together with Egypt, Babylonia, China, Greece, India, and the Islamic global. starting every one bankruptcy with a normal old evaluate of the civilized quarter, the writer highlights the civilization’s mathematical thoughts, quantity representations, accomplishments, demanding situations, and contributions to the mathematical global. completely class-tested, An creation to the Early improvement of arithmetic features:

  • Challenging routines that lead readers to a deeper knowing of mathematics
  • Numerous correct examples and challenge units with precise causes of the techniques and recommendations on the finish of every chapter
  • Additional references on particular issues and key terms from heritage, archeology, faith, tradition, and mathematics
  • Examples of functional purposes with step by step factors of the mathematical techniques and equations during the lens of early mathematical problems
  • A better half site that comes with extra exercises

An creation to the Early improvement of arithmetic is a terrific textbook for undergraduate classes at the background of arithmetic and a complement for trouble-free and secondary schooling majors. The ebook can be a suitable reference for pro and exchange 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 background of arithmetic, modern arithmetic, and algebra. he's additionally the landlord and operator of the educational Miracle, LLC, which supplies educational tutoring and attempt training for either university and highschool students.

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Extra info for An Introduction to the Early Development of Mathematics

Sample text

13 EGYPTIAN NUMERICAL SYMBOLS Exercise Confirm that the results are the same whether we compute twelve 35s or thirty‐ five 12s by the first method, and whether we swap which number gets doubled and which gets cut in half in the second method. 1 Use the Egyptian doubling method to multiply 67 × 42. 2 Use the Egyptian doubling method to multiply 33 × 99. 3 Multiply 68 × 43 using the Egyptian method that ­combines ­doubling and dividing by 2. 4 Multiply 75 × 49 with the “duplication and mediation” method.

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. In multiplication, the same principle of computing high‐order digits first was followed. If we today were to multiply 7846 × 5619 (by hand), the very first calculation we would make is 9 × 6, and we might think, “54, write the 4, carry the 5…” and we’d have no idea what our approximate final result would be until we had carried out many more steps.

Perhaps, a stimulus to represent zero directly came from the empty spaces that occurred on counting boards. 9. 9 The addition problem 327 + 852. The first column represents 327. The second column represents 852. Chinese numbers were typically written vertically, with the largest digit on top. The first thing a Chinese scribe would do is add the hundreds. He would see he has 3 hundreds in the first column and 8 hundreds in the second column, which together make 11 hundreds. He would know to write this as 1 thousand and 1 hundred.

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