This monograph presents a groundbreaking scholarly treatment of the German mathematician Jost Bürgi’s original work on logarithms, Arithmetische und Geometrische Progreß Tabulen. It provides the first-ever English translation of Bürgi’s text and illuminates his role in the development of the conception of logarithms, for which John Napier is traditionally given priority. High-resolutio…
This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and…
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and …
Predicting the time needed to complete a project, task or daily activity can be difficult and people frequently underestimate how long an activity will take. This book sheds light on why and when this happens, what we should do to avoid it and how to give more realistic time predictions. It describes methods for predicting time usage in situations with high uncertainty, explains why two plus tw…
This biography sheds light on all facets of the life and the achievements of Ernst Zermelo (1871-1953). Zermelo is best-known for the statement of the axiom of choice and his axiomatization of set theory. However, he also worked in applied mathematics and mathematical physics. His dissertation, for example, promoted the calculus of variations, and he created the pivotal method in the theory of …
Featuring contributions from industry and academia, this volume includes chapters covering a diverse range of theoretical and empirical aspects of actuarial science and quantitative finance, including portfolio management, derivative valuation, risk theory and the economics of insurance. Developed from the First International Congress on Actuarial Science and Quantitative Finance, held at the U…
This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compac…
This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new metho…
Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and commo…
Designed for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect …