Interrelated concepts are connected by hyperlinks, pointing toward easier or more difficult problems so as to show paths of mathematical reasoning.
Basic definitions and theorems can also be found by hyperlinks from relevant places. Problems are open to alternative formulations, generalizations, simplifications, and verification of hypotheses by the reader; this is shown to be helpful in solving problems. The book presents how advanced mathematical software can aid all stages of mathematical reasoning while the mathematical content remains in foreground.
The authors show how software can contribute to deeper understanding and to enlarging the scope of teaching for students and teachers of mathematics. It opens with ordinary differential equations and ends with the topic of mathematical statistics. The analysis chapters address: Fourier analysis and partial differential equations, complex analysis, and numeric analysis. The book is written by a pioneer in the field of applied mathematics. Die Reihe unterscheidet sich von traditionellen Texten dadurch, dass sie interaktiv ist und mit Hilfe des Computer-Algebra-Systems Mathematica die Berechnungen darstellt.
Author : Marlos A. Viana Publisher: American Mathematical Soc. A decade after the publication of Contemporary Mathematics Vol. In statistics, this volume includes, among others, new results and applications in cubic regression models for mixture experiments, multidimensional Fourier regression experiments, polynomial characterizations of weakly invariant designs, toric and mixture models for the diagonal-effect in two-way contingency tables, topological methods for multivariate statistics, structural results for the Dirichlet distributions, inequalities for partial regression coefficients, graphical models for binary random variables, conditional independence and its relation to sub-determinants covariance matrices, connectivity of binary tables, kernel smoothing methods for partially ranked data, Fourier analysis over the dihedral groups, properties of square non-symmetric matrices, and Wishart distributions over symmetric cones.
In probability, this volume includes new results related to discrete-time semi Markov processes, weak convergence of convolution products in semigroups, Markov bases for directed random graph models, functional analysis in Hardy spaces, and the Hewitt-Savage zero-one law. Table of Contents: S. Andersson and T. Klein -- Kiefer-complete classes of designs for cubic mixture models; V. Barbu and N. Limnios -- Some algebraic methods in semi-Markov chains; R.
Bates, H. Maruri-Aguilar, E. Riccomagno, R. Schwabe, and H. Wynn -- Self-avoiding generating sequences for Fourier lattice designs; F. Bertrand -- Weakly invariant designs, rotatable designs and polynomial designs; C.
Bocci, E. Carlini, and F. Rapallo -- Geometry of diagonal-effect models for contingency tables; P. Bubenik, G. Carlsson, P. Kim, and Z. Luo -- Statistical topology via Morse theory persistence and nonparametric estimation; G. Budzban and G. Hognas -- Convolution products of probability measures on a compact semigroup with applications to random measures; S. Chakraborty and A. Chang, R. Gupta, and D. Richards -- Structural properties of the generalized Dirichlet distributions; S.
Chaudhuri and G. Tan -- On qualitative comparison of partial regression coefficients for Gaussian graphical Markov models; M. Cueto, J. Morton, and B. Sturmfels -- Geometry of the restricted Boltzmann machine; M. Perturbation theory Sturm-Liouville systems Special functions Linear systems and Floquet theory Integrals and their approximation Stationary phase approximations Uniform approximations for differential… Expand.
Save to Library Save. Create Alert Alert. Share This Paper. Background Citations. Methods Citations. Figures from this paper. Citation Type. Has PDF. Publication Type. More Filters. Studying the Differential Problem with Maple. View 1 excerpt, cites background. This article uses the mathematical software Maple for the auxiliary tool to study the differential problem of two types of trigonometric functions.
We can obtain the Fourier series expansions of any … Expand. Highly Influenced. View 8 excerpts, cites background. Evaluating Some Integrals with Maple. View 2 excerpts, cites background. Application of Maple on the Integral Problems. This paper takes the mathematical software Maple as the auxiliary tool to study four types of integral problems related to hyperbolic functions.
0コメント