 | |
| Author | Carl E. Linderholm |
|---|---|
| Subject | Mathematics, Satire |
| Publisher | World Publishing |
Publication date | 1972 |
| Pages | 207 |
| ISBN | 978-0-529-04552-2 |
| OCLC | 279066 |
| 510 | |
Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical, [1] [2] it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers. Linderholm discusses these seemingly-obvious ideas using concepts like categories and monoids. [3]
As an example, the proof that 2 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 ... [4]
References
-
^ Knuth, D.E. and Larrabee, T. and Roberts, P.M. (1989).
Mathematical writing. Mathematical Assn of Amer.
ISBN
0-88385-063-X.
{{ cite book}}: CS1 maint: multiple names: authors list ( link), page 6. - ^ Howson, A. G. (March 1972). "Mathematical Fantasia". Nature. 236 (5341): 83–84. Bibcode: 1972Natur.236...83H. doi: 10.1038/236083b0. ISSN 1476-4687.
- ^ Quadling, D. A. (October 1972). "Mathematics Made Difficult. By Carl E. Linderholm. Pp. 207. £2·75. 1971. (Wolfe.)". The Mathematical Gazette. 56 (397): 255–256. doi: 10.2307/3617023. ISSN 0025-5572. JSTOR 3617023.
- ^ Linderholm, Page 76.
|
| |
| Author | Carl E. Linderholm |
|---|---|
| Subject | Mathematics, Satire |
| Publisher | World Publishing |
Publication date | 1972 |
| Pages | 207 |
| ISBN | 978-0-529-04552-2 |
| OCLC | 279066 |
| 510 | |
Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical, [1] [2] it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers. Linderholm discusses these seemingly-obvious ideas using concepts like categories and monoids. [3]
As an example, the proof that 2 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 ... [4]
References
-
^ Knuth, D.E. and Larrabee, T. and Roberts, P.M. (1989).
Mathematical writing. Mathematical Assn of Amer.
ISBN
0-88385-063-X.
{{ cite book}}: CS1 maint: multiple names: authors list ( link), page 6. - ^ Howson, A. G. (March 1972). "Mathematical Fantasia". Nature. 236 (5341): 83–84. Bibcode: 1972Natur.236...83H. doi: 10.1038/236083b0. ISSN 1476-4687.
- ^ Quadling, D. A. (October 1972). "Mathematics Made Difficult. By Carl E. Linderholm. Pp. 207. £2·75. 1971. (Wolfe.)". The Mathematical Gazette. 56 (397): 255–256. doi: 10.2307/3617023. ISSN 0025-5572. JSTOR 3617023.
- ^ Linderholm, Page 76.