Rinaldo B. Schinazi

This textbook provides an accessible approach to concepts and applications of stochastic processes ideal for a wide range of readers. This revised third edition features an intuitive reorganization with concrete topics introduced early on which are then used to demonstrate more abstract concepts in later chapters. The author has kept chapters short and independent from each other, with several of the longer chapters from previous editions now divided into smaller, more manageable parts. These changes build upon previous editions to allow readers even greater flexibility. The applications that are covered feature active areas of research within biological modeling, such as cancerous mutations, influenza evolution, drug resistance, and immune response. Important problems in fields such as engineering and mathematical physics are presented as well. These topics elegantly apply various classical stochastic models and are motivated throughout with many worked out examples. This third edition of Classical and Spatial Stochastic Processes is suitable as a textbook for a first course in stochastic processes at the upper-undergraduate or graduate level. Because of its accessible approach, it may also be used as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology.

This textbook, now in its third edition, offers a practical introduction to probability with statistical applications, covering material for both a first and second undergraduate probability course. The author focuses on essential concepts that every student should thoroughly understand. The content is organized into brief, easy-to-follow chapters, motivated by plenty of examples. The first part of the book focuses on classical discrete probability distributions, then goes on to study continuous distributions, confidence intervals, and statistical tests. The following section introduces more advanced concepts suitable for a second course in probability, such as random vectors and sums of random variables. The last part of the book is dedicated to mathematical statistics concepts such as estimation, sufficiency, Bayes' estimation, and multiple regression. This third edition includes a new chapter on combinatorics and a more distinct separation betweendiscrete and continuous distributions. Some of the longer chapters in the previous editions have been divided into shorter chapters to allow for more flexible teaching.Probability with Statistical Applications, Third Edition is intended for undergraduate students taking a first course in probability; later chapters are also suited for a second course in probability and mathematical statistics. Calculus is the only prerequisite; prior knowledge of probability is not required.

This textbook, now in its third edition, offers a practical introduction to probability with statistical applications, covering material for both a first and second undergraduate probability course. The author focuses on essential concepts that every student should thoroughly understand. The content is organized into brief, easy-to-follow chapters, motivated by plenty of examples. The first part of the book focuses on classical discrete probability distributions, then goes on to study continuous distributions, confidence intervals, and statistical tests. The following section introduces more advanced concepts suitable for a second course in probability, such as random vectors and sums of random variables. The last part of the book is dedicated to mathematical statistics concepts such as estimation, sufficiency, Bayes' estimation, and multiple regression. This third edition includes a new chapter on combinatorics and a more distinct separation betweendiscrete and continuous distributions. Some of the longer chapters in the previous editions have been divided into shorter chapters to allow for more flexible teaching.Probability with Statistical Applications, Third Edition is intended for undergraduate students taking a first course in probability; later chapters are also suited for a second course in probability and mathematical statistics. Calculus is the only prerequisite; prior knowledge of probability is not required.

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis.To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuityon metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis.To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuityon metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral. Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

The revised and expanded edition of this textbook presents the concepts and applications of random processes with the same illuminating simplicity as its first edition, but with the notable addition of substantial modern material on biological modeling. While still treating many important problems in fields such as engineering and mathematical physics, the book also focuses on the highly relevant topics of cancerous mutations, influenza evolution, drug resistance, and immune response. The models used elegantly apply various classical stochastic models presented earlier in the text, and exercises are included throughout to reinforce essential concepts.The second edition of Classical and Spatial Stochastic Processes is suitable as a textbook for courses in stochastic processes at the advanced-undergraduate and graduate levels, or as a self-study resource for researchers and practitioners in mathematics, engineering, physics, and mathematical biology.Reviews of the first edition:An appetizing textbook for a first course in stochastic processes. It guides the reader in a very clever manner from classical ideas to some of the most interesting modern results. … All essential facts are presented with clear proofs, illustrated by beautiful examples. … The book is well organized, has informative chapter summaries, and presents interesting exercises. The clear proofs are concentrated at the ends of the chapters making it easy to find the results. The style is a good balance of mathematical rigorosity and user-friendly explanation. —Biometric JournalThis small book is well-written and well-organized. ... Only simple results are treated ... but at the same time many ideas needed for more complicated cases are hidden and in fact very close. The second part is a really elementary introduction to the area of spatial processes. ... All sections are easily readable and it is rather tentative for the reviewerto learn them more deeply by organizing a course based on this book. The reader can be really surprised seeing how simple the lectures on these complicated topics can be. At the same time such important questions as phase transitions and their properties for some models and the estimates for certain critical values are discussed rigorously. ... This is indeed a first course on stochastic processes and also a masterful introduction to some modern chapters of the theory. —Zentralblatt Math

This book is intended as a text for a first course in stochastic processes at the upper undergraduate or graduate levels, assuming only that the reader has had a serious calculus course-advanced calculus would even be better-as well as a first course in probability (without measure theory). In guiding the student from the simplest classical models to some of the spatial models, currently the object of considerable research, the text is aimed at a broad audience of students in biology, engineering, mathematics, and physics. The first two chapters deal with discrete Markov chains-recurrence and tran­ sience, random walks, birth and death chains, ruin problem and branching pro­ cesses-and their stationary distributions. These classical topics are treated with a modem twist: in particular, the coupling technique is introduced in the first chap­ ter and is used throughout. The third chapter deals with continuous time Markov chains-Poisson process, queues, birth and death chains, stationary distributions. The second half of the book treats spatial processes. This is the main difference between this work and the many others on stochastic processes. Spatial stochas­ tic processes are (rightly) known as being difficult to analyze. The few existing books on the subject are technically challenging and intended for a mathemat­ ically sophisticated reader. We picked several interesting models-percolation, cellular automata, branching random walks, contact process on a tree-and con­ centrated on those properties that can be analyzed using elementary methods.

This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course—important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.