Collins Dictionary of Mathematics By E. J. and J. M. Borwein Borowski
Publisher: Collins 2005 | 529 Pages | ISBN: 0007800800 | DJVU | 7 MB
Publisher: Collins 2005 | 529 Pages | ISBN: 0007800800 | DJVU | 7 MB
Some dictionaries of mathematics lack reach. This one has high aspirations, and it succeeds. It is written with the undergraduate mathematics student in mind, which is to say: for anyone with a serious interest in mathematics, formal student or not. Here's an example of an entry. Fully capitalized terms are entries themselves.
"Galois theory, n. the algebraic study of GROUPS of AUTOMORPHISMS of FIELDS in which one associates an EXTENSION FIELD with a given ALGEBRAIC EQUATION. The theory grew out of Galois' highly original study of the solubility of equations, devised in part to prove the impossibility of SOLUTION BY RADICALS of the general QUINTIC, Abel's proof of which was unknown to him. See also CARDANO'S FORMULA."
The entry for Cardano's formula takes up half a page. For more examples, entries concerned with terminology involving 'limit' fill two pages, including entries on limit, limit inferior or lower limit, limit of integration, limit ordinal, limit point (which refers directly without definition to the entry on cluster point), limit superior or upper limit. There are many examples of this kind of usefulness. The entry on exponential function takes up three-quarters of a page. Whenever I browse a mathematics dictionary in a bookstore, the first term I look for is CATEGORY. Then I check for FUNCTOR. This dictionary includes them both. In fact, the entry on category takes up a third of the page, and the entry on functor takes up about the same amount. There is also an entry on COMMUTATIVE DIAGRAM, of nearly the same length. This is no mere "dictionary", with terse, unhelpful definitions or descriptions. This is a reference dictionary of real value.
"Galois theory, n. the algebraic study of GROUPS of AUTOMORPHISMS of FIELDS in which one associates an EXTENSION FIELD with a given ALGEBRAIC EQUATION. The theory grew out of Galois' highly original study of the solubility of equations, devised in part to prove the impossibility of SOLUTION BY RADICALS of the general QUINTIC, Abel's proof of which was unknown to him. See also CARDANO'S FORMULA."
The entry for Cardano's formula takes up half a page. For more examples, entries concerned with terminology involving 'limit' fill two pages, including entries on limit, limit inferior or lower limit, limit of integration, limit ordinal, limit point (which refers directly without definition to the entry on cluster point), limit superior or upper limit. There are many examples of this kind of usefulness. The entry on exponential function takes up three-quarters of a page. Whenever I browse a mathematics dictionary in a bookstore, the first term I look for is CATEGORY. Then I check for FUNCTOR. This dictionary includes them both. In fact, the entry on category takes up a third of the page, and the entry on functor takes up about the same amount. There is also an entry on COMMUTATIVE DIAGRAM, of nearly the same length. This is no mere "dictionary", with terse, unhelpful definitions or descriptions. This is a reference dictionary of real value.
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