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This textbook introduces readers to the fundamental notions of modern probability theory. The only prerequisite is a working knowledge in real analysis. Highlighting the connections between martingales and Markov chains on one hand, and Brownian motion and harmonic functions on the other, this book provides an introduction to the rich interplay between probability and other areas of analysis.Arranged into three parts, the book begins with a rigorous treatment of measure theory, with applications to probability in mind. The second part of the book focuses on the basic concepts of probability theory such as random variables, independence, conditional expectation, and the different types of convergence of random variables. In the third part, in which all chapters can be read independently, the reader will encounter three important classes of stochastic processes: discrete-time martingales, countable state-space Markov chains, and Brownian motion. Each chapter ends with a selection of illu

This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. "Safe" - that is, paradox-free - informal set theory is introduced following on the heels of Russell's Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor's diagonalisation technique. Predicate logic "for the user" is introduced along with axioms and rules and extensive examples. Partial orders and the minimal condition are studied in detail with the latter shown to be equivalent to the induction principle. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of functions and sets. Techniques for solving recurrence relations i

This concise, easy-to-read pocket guide offers medical trainees, researchers, and clinicians at every level the perfect resource on Evidence Based Medicine (EBM). Based on the author's many years of experience teaching EBM to medical students and medical residents at Columbia University, this handy title addresses not only all the basic concepts and issues in EBM, but also takes an example-based approach and is replete with numerous illustrations. This brief book provides readers with all the tools needed to tell the good from the bad in healthcare research. It discusses every type of study design, from the assessment of diagnostic tests to clinical trials and meta-analysis. The work also introduces readers to novel methods, such as the Bayesian analysis of clinical trials. In addition, to help readers better retain the information, the guide includes thought-provoking review questions and answers in an appendix. In all, Pocket Evidence-Based Medicine: A Survival Guide for Clinicians a

Practicing evidence-based medicine is widely regarded both as best clinical practice, and as the cornerstone of meeting the ACGME competencies in Practice-Based Learning and Improvement. Training programs recognize the need to teach the skills of EBM and yet struggle with readily available content and guidance on putting together a curriculum. Time frames for delivering curricula in residency can be very tight, often restricted to scattered one hour conferences. This book provides a modular curriculum structure for instructors, with each topic area taking up one section, or one hour of instructional time.Developed over the past 14 years as an introductory course for interns in the internal medicine residency program at Duke, the curriculum will cover core content areas in evidence-based medicine and best teaching practices for them and skills such as literature searching and applying evidence to patients. Most importantly, it will center on actual patient questions and use current lite