By Boyer J.

**Read Online or Download Histoire des mathematiques PDF**

**Best elementary books**

How do you draw a directly line? How do you identify if a circle is absolutely around? those could sound like easy or perhaps trivial mathematical difficulties, yet to an engineer the solutions can suggest the variation among luck and failure. How around Is Your Circle? invitations readers to discover some of the similar primary questions that operating engineers take care of each day--it's not easy, hands-on, and enjoyable.

This ebook, designed for complicated graduate scholars and post-graduate researchers, introduces Lie algebras and a few in their functions to the spectroscopy of molecules, atoms, nuclei and hadrons. The publication includes many examples that aid to explain the summary algebraic definitions. It offers a precis of many formulation of functional curiosity, resembling the eigenvalues of Casimir operators and the size of the representations of all classical Lie algebras.

This complete, best-selling textual content makes a speciality of the examine of many alternative geometries -- instead of a unmarried geometry -- and is punctiliously glossy in its process. each one bankruptcy is largely a brief path on one point of recent geometry, together with finite geometries, the geometry of variations, convexity, complex Euclidian geometry, inversion, projective geometry, geometric facets of topology, and non-Euclidean geometries.

- Intermediate Algebra (11th Edition)
- Algebra in 15 Minutes a Day
- Mathématiques, 1re S, E
- Dachshunds For Dummies, 2nd edition (For Dummies (Pets))

**Extra info for Histoire des mathematiques**

**Example text**

It is not difficult to see that equality occurs in all the inequalities (10) for (10) for B see Remark (4). ~ iff it occurs in all the corresponding inequalities ~ and~. n If d n = cnx , nLN, n > 0, then ~ and 2. are a-logarithmically concave (convex) together so we can immediately state the following generalisation. Corollary 8. If and ~ bare logarithmically convex (concave) sequences then for every x > 0, Y > 0 so i8 the sequence nt Theorem 9. (a) If (b) If a ~ > ~(x,y) N. and bare logarithmically concave so is 0, ß > 0, a + ß • , and ~ (13) ~*~.

E is logarithmically convex iff c n2 -< c n+l c n_ 1 which for positive sequences i8 equivalent to ( 10) 15 INTRODUCTION c < s -c s+1 r, s == 1, 2, ••• ( 11) in the case of logarithmic concavity inequalities (10) and (11) are reversed. The results of this section show that the logarithmic concavity property is conserved under the operation of convolution. Not all the results are needed in the sequel but are included for the sake of completeness. Theorem 7. If ~ and ~ are logarithmically convex (concave) so is c Proof (1) Convex Case.

If ~ and ware two positive n-tples then (1) with equality iff a 1 = ••• Inequality (1) will be referred to as a n GA, or as the GA-inequality, for short. Corollary 2. If ~ and ware two positive n-tples then H (a;w) < G (a;w) < A (a;w) n-- - with equality iff Proof. 1. 4#17. 2. Some Preliminary Results. Before proving Theorem 1 we will consider some results that help to simplify the later work. We first consider 1(9)1 that is GA in its simplest form, n Lemma 3. If a > 0 and b > 0 then Iäb < with equality iff Remark (1).