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This is a textbook for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, and so on. Without such a "bridge" course, most upper division instructors feel the need to start their courses with the . rudiments of logic, set theory, equivalence relations, and other basic mathematiCal raw materials before getting on with the subject at hand. Students who are new to higher mathematics are often startled to discover that mathematics is a subject of ideas, and not just formulaic rituals, and that they are now expected to understand and create mathematical proofs. Mastery of an assortment of technical tricks may have carried tHe students through calculus, but it is no longer a guarantee of academic success. Students need experience in working with abstract ideas at a n
Reprint of the original, first published in 1868.
Reprint of the original, first published in 1868.
___ ***SHORTLISTED FOR THE ROYAL SOCIETY SCIENCE BOOK PRIZE 2022*** Did you know that we can lead longer and healthier lives by making simple changes right now? Professor Rose Anne Kenny has 35 years of experience at the forefront of ageing medicine. In Age Proof, she draws on her own pioneering research and the latest evidence to demystify why we age and shows us that 80% of our ageing biology is within our control: we can not only live longer lives but become happier and healthier deep into our later years. Effortlessly distilling scientific theory into practical advice that we can apply to our everyday lives, Professor Kenny examines the impact that food, genetics, friendships, purpose, sex, exercise and laughter have on how our cells age. This illuminating book will show you the steps you can take to stay younger for longer - and will prove that you really are just as young as you feel.
The concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a comprehensive overview of the fundamental approaches in the area of frailty models. The book extensively explores how univariate frailty models can represent unobserved heterogeneity. It also emphasizes correlated frailty models as extensions of univariate and shared frailty models. The author analyzes similarities and differences between frailty and copula models; discusses problems related to frailty models, such as tests for homogeneity; and describes parametric and semiparametric models using both frequentist and Bayesian approaches. He also shows how to apply the models to real data using the statistical packages of R, SAS, and Stata. The appendix provides the technical mathematical results used throughout. Written in nontechnical terms accessible to nonspecialists, this book explains the basic ideas in frailty modeling and statistical techniques, with a focus on real-world data application and interpretation of the results. By applying several models to the same data, it allows for the comparison of their advantages and limitations under varying model assumptions. The book also employs simulations to analyze the finite sample size performance of the models.