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How to Free Your Inner MathematicianNotes on Mathematics and Life$
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Susan D'Agostino

Print publication date: 2020

Print ISBN-13: 9780198843597

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198843597.001.0001

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Find balance, as in coding theory

Find balance, as in coding theory

(p.211) 34 Find balance, as in coding theory
How to Free Your Inner Mathematician

Susan D'Agostino

Oxford University Press

“Find balance, as in coding theory” explains how mathematicians construct codes to transmit messages as accurately and efficiently as possible. Since “noise” may corrupt messages during transmission, a good code repeats some of the information in a sent message so that errors due to noise in the received message may be detected and (ideally) corrected. However, too much repetition increases not only the code word length but the transmission time—an undesirable outcome. Mathematician Claude Shannon proved that “optimal” codes with just the right balance between repetition in transmission and error detection exist. Mathematics students and enthusiasts are encouraged to find a balance that is just right between repetition and forward momentum in mathematical and life pursuits. At the chapter’s end, readers may check their understanding by working on a problem concerning book International Standard Book Numbers (ISBNs). A solution is provided.

Keywords:   coding theory, optimal code, Claude Shannon, math, student, ISBN

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