Tag: Sums

Free Download Random Sums and Branching Stochastic Processes By Ibrahim Rahimov (auth.)
1995 | 195 Pages | ISBN: 038794446X | PDF | 5 MB
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.

Free Download A Short Book on Long Sums: Infinite Series for Calculus Students (Undergraduate Texts in Mathematics) by Fernando Q. Gouvêa
English | December 8, 2023 | ISBN: 3031375564 | 156 pages | MOBI | 19 Mb
This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series―and infinite series in general―are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor’s guide with solutions to all the problems is available.

Free Download Natelle Quek, "Danny Chung Sums It Up"
English | 2021 | ISBN: 1419748211, 141974822X | EPUB | pages: 240 | 4.5 mb
Maisie Chan’s Danny Chung Sums it Up is a touching and funny middle-grade story about a boy whose life is unraveled when his Chinese grandmother moves in-illustrated by Natelle Quek.

Free Download A Short Book on Long Sums: Infinite Series for Calculus Students by Fernando Q. Gouvêa
English | PDF EPUB (True) | 2023 | 153 Pages | ISBN : 3031375564 | 13 MB
This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series-and infinite series in general-are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural.