Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

This book constitutes the thoroughly refereed conference proceedings of the 14th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, RSFDGrC 2013, held in Halifax, Canada in October 2013 as one of the co-located conference of the 2013 Joint Rough Set Symposium, JRS 2013. The 69 papers (including 44 regular and 25 short papers) included in the JRS proceedings (LNCS 8170 and LNCS 8171) were carefully reviewed and selected from 106 submissions. The papers in this volume cover topics such as inconsistency, incompleteness, non-determinism; fuzzy and rough hybridization; granular computing and covering-based rough sets; soft clustering; image and medical data analysis.

This book constitutes the thoroughly refereed post-conference proceedings of the 6th IPM International Conference on Fundamentals of Software Engineering, FSEN 2015, held in Tehran, Iran, in April 2015. The 21 full papers presented in this volume were carefully reviewed and selected from 64 submissions. The topics of interest in FSEN span over all aspects of formal methods, especially those related to advancing the application of formal methods in software industry and promoting their integration with practical engineering techniques.

GANIT MATHEMATICS series consists of ten textbooks; two textbooks for Primer A and B, eight textbooks for classes 1-8. This series is strictly bases on the syllabus prescribed by the Council for the Indian School Certificate. The series has been developed to guide the young minds to observe and experience mathematics all around them. Each concept has been related to everyday life in order to develop a spirit of curiosity and discovery. Concepts are gradually built up with easy-to-follow steps and plenty of examples.

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

This book, which is based on Pólya's method of problem solving, aids students in their transition from calculus (or precalculus) to higher-level mathematics. The book begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends with suggested projects for independent study. Students will follow Pólya's four step approach: analyzing the problem, devising a plan to solve the problem, carrying out that plan, and then determining the implication of the result. In addition to the Pólya approach to proofs, this book places special emphasis on reading proofs carefully and writing them well. The authors have included a wide variety of problems, examples, illustrations and exercises, some with hints and solutions, designed specifically to improve the student's ability to read and write proofs. Historical connections are made throughout the text, and students are encouraged to use the rather extensive bibliography to begin making connections of their own. While standard texts in this area prepare students for future courses in algebra, this book also includes chapters on sequences, convergence, and metric spaces for those wanting to bridge the gap between the standard course in calculus and one in analysis.

This concisely written text in finite mathematics gives a sequential, distinctly applied presentation of topics, employing a pedagogical approach that is ideal for freshmen and sophomores in business, the social sciences, and the liberal arts. The work opens with a brief review of sets and numbers, followed by an introduction to data sets, counting arguments, and the Binomial Theorem, which sets the foundation for elementary probability theory and some basic statistics. Further chapters treat graph theory as it relates to modelling, matrices and vectors, and linear programming. Requiring only two years of high school algebra, this book's many examples and illuminating problem sets - with selected solutions - will appeal to a wide audience of students and teachers.