By Keith Devlin
ISBN-10: 071673379X
ISBN-13: 9780716733799
"The nice e-book of nature," stated Galileo, "can be learn simply by way of those that understand the language during which it used to be written. And this language is mathematics."
In The Language of Mathematics, award-winning writer Keith Devlin finds the very important function arithmetic performs in our everlasting quest to appreciate who we're and the area we are living in. greater than simply the learn of numbers, arithmetic presents us with the eyes to acknowledge and describe the hidden styles of life--patterns that exist within the actual, organic, and social worlds with no, and the area of rules and strategies inside of.
Taking the reader on a wondrous trip during the invisible universe that surrounds us--a universe made noticeable by way of mathematics--Devlin indicates us what retains a jumbo jet within the air, explains how we will see and listen to a soccer video game on television, permits us to foretell the elements, the habit of the inventory industry, and the result of elections. Microwave ovens, cellphone cables, children's toys, pacemakers, cars, and computers--all function on mathematical ideas. faraway from a dry and esoteric topic, arithmetic is a wealthy and dwelling a part of our tradition.
A remarkable exploration of a frequently woefully misunderstood topic The Language of Mathematics celebrates the simplicity, the precision, the purity, and the attractiveness of arithmetic.
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Additional resources for The Language of Mathematics: Making the Invisible Visible
Example text
One of the topics Gauss examined in that book is the idea of finite arithmetic. You get a finite arithmetic whenever you use a counting system that periodically cycles back on itself and starts again. For instance, when you tell the time, you count the hours 1, 2, 3, and so on, but when you reach 12 you start over again, 1, 2, 3, and so on. Similarly, you count minutes from 1 to 60 and then start over again. This use of finite arithmetic to tell the time is why it is sometimes referred to as 'clock arithmetic'.
For example, you cannot divide 5 by 6. One way to see this is to observe that if you multiply any of the numbers from 1 to 11 by 6, the result will be an even number, and hence cannot be congruent to 5 modulo 12. However, in the case where the modulus n is a prime number, division is always possible. So, for a prime modulus, the corresponding modular arithmetic has all the familiar properties of ordinary arithmetic performed with the rational or the real numbers; in mathematician's language, it is a field.
So, if P is not prime, it must be evenly divisible by some prime different from (and hence bigger than) all of p1, . . , pn. In particular, there must be a prime bigger than all of p1, . . , pn, so again, the sequence can be continued. It is interesting to observe that, when you look at the number P = p1 × p2 × . . × pn + 1 used in Euclid's proof, you don't actually know whether P is itself prime or not. The proof uses two arguments, one that works when P is prime, one that works when it is not.
The Language of Mathematics: Making the Invisible Visible by Keith Devlin
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