Mathematics Made Difficult
- Mathematics Made Difficult
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Mathematics Made Difficult is a book[1] by Carl. E Linderholm that uses advanced mathematical methods to prove results normally shown by elementary means. Although the aim is largely satirical[2], it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers.
As an example, the proof that two is a prime number starts:
It is easily seen that the only numbers between 0 and 2, including 0 but excluding 2, are 0 and 1. Thus the remainder left by any number on division by 2 is either 0 or 1. Hence the quotient ring Z/2Z, where 2Z is the ideal in Z generated by 2, has only the elements [0] and [1], where these are the images of 0 and 1 under the canonical quotient map. Since [1] must be the unit of this ring, every element of this ring except [0] is a unit, and the ring is a field ...[3]
References
- ^ Linderholm, C.E. (1972). Mathematics made difficult. World Publishing. ISBN 0529045524.
- ^ Knuth, D.E. and Larrabee, T. and Roberts, P.M. (1989). Mathematical writing. Mathematical Assn of Amer. ISBN 088385063X. , page 6.
- ^ Linderholm, Page 76.
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