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Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: • Brings together the perspectives of researchers in areas of inverse problems and data assimilation. • Assesses the current state-of-the-art and identify needs and opportunities for future research. • Focuses on the computational methods used to analyze and simulate inverse problems. • Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Presents an introduction to Bayesian statistics, presents an emphasis on Bayesian methods (prior and posterior), Bayes estimation, prediction, MCMC,Bayesian regression, and Bayesian analysis of statistical modelsof dependence, and features a focus on copulas for risk management Introduction to Bayesian Estimation and Copula Models of Dependence emphasizes the applications of Bayesian analysis to copula modeling and equips readers with the tools needed to implement the procedures of Bayesian estimation in copula models of dependence. This book is structured in two parts: the first four chapters serve as a general introduction to Bayesian statistics with a clear emphasis on parametric estimation and the following four chapters stress statistical models of dependence with a focus of copulas. A review of the main concepts is discussed along with the basics of Bayesian statistics including prior information and experimental data, prior and posterior distributions, with an emphasis on Bayesian parametric estimation. The basic mathematical background of both Markov chains and Monte Carlo integration and simulation is also provided. The authors discuss statistical models of dependence with a focus on copulas and present a brief survey of pre-copula dependence models. The main definitions and notations of copula models are summarized followed by discussions of real-world cases that address particular risk management problems. In addition, this book includes: • Practical examples of copulas in use including within the Basel Accord II documents that regulate the world banking system as well as examples of Bayesian methods within current FDA recommendations • Step-by-step procedures of multivariate data analysis and copula modeling, allowing readers to gain insight for their own applied research and studies • Separate reference lists within each chapter and end-of-the-chapter exercises within Chapters 2 through 8 • A companion website containing appendices: data files and demo files in Microsoft® Office Excel®, basic code in R, and selected exercise solutions Introduction to Bayesian Estimation and Copula Models of Dependence is a reference and resource for statisticians who need to learn formal Bayesian analysis as well as professionals within analytical and risk management departments of banks and insurance companies who are involved in quantitative analysis and forecasting. This book can also be used as a textbook for upper-undergraduate and graduate-level courses in Bayesian statistics and analysis. ARKADY SHEMYAKIN, PhD, is Professor in the Department of Mathematics and Director of the Statistics Program at the University of St. Thomas. A member of the American Statistical Association and the International Society for Bayesian Analysis, Dr. Shemyakin's research interests include informationtheory, Bayesian methods of parametric estimation, and copula models in actuarial mathematics, finance, and engineering. ALEXANDER KNIAZEV, PhD, is Associate Professor and Head of the Department of Mathematics at Astrakhan State University in Russia. Dr. Kniazev's research interests include representation theory of Lie algebras and finite groups, mathematical statistics, econometrics, and financial mathematics.

Featuring key topics within finance, small business management, and entrepreneurship to develop and maintain prosperous business ventures With a comprehensive and organized approach to fundamental financial theories, tools, and management techniques, Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business equips readers with the necessary fundamental knowledge and advanced skills to succeed in small firm and business settings. With a unique combination of topics from finance, small business management, and entrepreneurship, the book prepares readers for the challenges of today’s economy. Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business begins with key concepts of small business management and entrepreneurship, including management tools and techniques needed to establish, run, and lead business ventures. The book then delves into how small businesses are operated, managed, and controlled. General finance skills and methods are integrated throughout, and the book also features: Numerous practical examples and scenarios that provide a real-world perspective on entrepreneurship and small business management A brief summary, list of key concepts, and ten discussion questions at the end of each chapter to prepare readers for the challenges of today's economy A practical guide to the complete life of a small business, from establishing a new venture to training and developing young entrepreneurs tasked with maintaining and developing a prosperous economy An in-depth discussion of the entire process of writing a successful business plan, including the rationale, significance, and requirements Techniques needed to solidify the free enterprise tradition, develop entrepreneurial strategies, and grow small businesses Entrepreneurial Finance: Fundamentals of Financial Planning and Management for Small Business is an ideal textbook for upper-undergraduate and first-year graduate courses in entrepreneurial finance within business, economics, management science, and public administration departments. The book is also useful for MBA-level courses as well as for business and management PhD majors as a resource in methodology. The book is also an idea reference for entrepreneurs, business managers, market analysts, and decision makers who require information about the theoretical and quantitative aspects of entrepreneurial finance.

We all face risks in a variety of ways, as individuals, businesses and societies. The discipline of risk assessment and risk management is growing rapidly and there is an enormous drive for the implementation of risk assessment methods and risk management in organizations. There are great expectations that these tools provide suitable frameworks for obtaining high levels of performance and balance different concerns such as safety and costs. The analysis and management of risk are not straightforward. There are many challenges. The risk discipline is young and there area a number of ideas, perspectives and conceptions of risk out there. For example many analysts and researchers consider it appropriate to base their risk management policies on the use of expected values, which basically means that potential losses are multiplied with their associated consequences. However, the rationale for such a policy is questionable. A number of such common conceptions of risk are examined in the book, related to the risk concept, risk assessments, uncertainty analyses, risk perception, the precautionary principle, risk management and decision making under uncertainty. The Author discusses these concepts, their strenghts and weaknesses, and concludes that they are often better judged as misconceptions of risk than conceptions of risk. Key Features: Discusses common conceptions of risk with supporting examples. Provides recommendations and guidance to risk analysis and risk management. Relevant for all types of applications, including engineering and business. Presents the Author’s overall conclusions on the issues addressed throughout the book. All those working with risk-related problems need to understand the fundamental ideas and concepts of risk. Professionals in the field of risk, as well as researchers and graduate sutdents will benefit from this book. Policy makers and business people will also find this book of interest.