# Differential Geometry and Statistics by Michael K. Murray, John W. Rice (auth.) By Michael K. Murray, John W. Rice (auth.)

Best geometry books

Geometry of Complex Numbers (Dover Books on Mathematics)

Illuminating, commonly praised publication on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries. "This ebook might be in each library, and each professional in classical functionality thought might be acquainted with this fabric. the writer has played a unique provider by means of making this fabric so very easily obtainable in one publication.

Geometric Tomography (Encyclopedia of Mathematics and its Applications)

Geometric tomography offers with the retrieval of knowledge a couple of geometric item from info pertaining to its projections (shadows) on planes or cross-sections through planes. it's a geometric relative of automated tomography, which reconstructs a picture from X-rays of a human sufferer. the topic overlaps with convex geometry and employs many instruments from that zone, together with a few formulation from essential geometry.

First Steps in Differential Geometry: Riemannian, Contact, Symplectic (Undergraduate Texts in Mathematics)

Differential geometry arguably deals the smoothest transition from the traditional college arithmetic series of the 1st 4 semesters in calculus, linear algebra, and differential equations to the better degrees of abstraction and facts encountered on the higher department by means of arithmetic majors. this day it truly is attainable to explain differential geometry as "the examine of constructions at the tangent space," and this article develops this perspective.

Extra info for Differential Geometry and Statistics

Sample text

The second comment is that in Barndorff-Nielsen (1978) notions of convexity for subsets of Euclidean space, play an important role. All these notions can also be applied to a finite-dimensional affine space. Given any two points p and q in an affine space there is a THE GEOMETRY OF EXPONENTIAL FAMILIES 24 = vector v such that q P + v. The line segment joining p and q is then defined to be the set [p, q] = {p + tv 1 t E [0, I]} and a set is said to be convex if whenever it contains two points it contains the line segment joining them.

N 0,)'(0) are to be, which by definition are the values d¢l(v), ... ,d¢n(v). In this case one can calculate dl( v) using the chain rule which, from the definition of differential, assumes the form dl(v) 01 oj = O¢l (p)d¢I(V) + ... + o¢n (p)d¢n(v) The chain rule thus becomes an identity between functions of tangent vector, and if we leave out the argument of the functions, as is usual when expressing an identity between functions, we obtain the formula for the so-called total differential 01 1 + ...

These are the variations for which all the coordinate functions are held constant except one, which changes at a unit rate. Specifically, if ¢} , ... 2 THE BASIC APPARATUS 31 set P and pEP then we let Ii (h) be the element of P such that We call 'Yi the ith co-ordinate variation through p. (See Figure. 2). These are exactly the variations used to define the partial derivatives of f with respect to 