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Mathematics-II (Probability and Statistics) for the paper BSC-106 of the latest AICTE syllabus has been written for the second semester engineering students of Indian universities. Paper BSC-106 is for the CS&E stream. The book has been planned with utmost care in the exposition of concepts, choice of illustrative examples, and also in sequencing of topics. The language is simple, yet accurate. A large number of worked-out problems have been included to familiarize the students with the techniques to solving them, and to instil confidence. Authors’ long experience of teaching various grades of students has helped in laying proper emphasis on various techniques of solving difficult problems.
This comprehensive study of probability considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics.
Suitable for self study Use real examples and real data sets that will be familiar to the audience Introduction to the bootstrap is included – this is a modern method missing in many other books
Probability and Mathematical Statistics: An Introduction provides a well-balanced first introduction to probability theory and mathematical statistics. This book is organized into two sections encompassing nine chapters. The first part deals with the concept and elementary properties of probability space, and random variables and their probability distributions. This part also considers the principles of limit theorems, the distribution of random variables, and the so-called student’s distribution. The second part explores pertinent topics in mathematical statistics, including the concept of sampling, estimation, and hypotheses testing. This book is intended primarily for undergraduate statistics students.
Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students.
Mathematics-II (Calculus, Ordinary Differential Equations and Complex Variable) for the paper BSC-104 of the latest AICTE syllabus has been written for the second semester engineering students of Indian universities. Paper BSC-104 is common for all streams except CS&E students. The book has been planned with utmost care in the exposition of concepts, choice of illustrative examples, and also in sequencing of topics. The language is simple, yet accurate. A large number of worked-out problems have been included to familiarize the students with the techniques to solving them, and to instil confidence. Authors’ long experience of teaching various grades of students has helped in laying proper emphasis on various techniques of solving difficult problems.
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Probability and Statistics is a calculus-based treatment of probability concurrent with and integrated with statistics. * Incorporates more than 1,000 engaging problems with answers* Includes more than 300 solved examples* Uses varied problem solving methods
One of the hardest questions that mathematics teachers have to answer is "Why?" Schoolroom sums are crucial in learning the awesome power of mathematics, but they are often a world away from how the knowledge is applied and where it came from. Inside Mathematics: Probability & Statistics is there to fill that gap. What are the chances of that? Mathematics can solve that mystery for you using a set of ideas that grew out of an aristocratic gambler's bafflement at betting on complex dice games. In stepped the mathematical giants of Pierre de Fermat and Blaise Pascal, who worked together to create what is now called probability theory. Gamblers need not rejoice in this powerful theory; it shows that the casino always wins in the end. The ideas of probability have since found many better uses elsewhere. For example, they are at work in the mathematics that describes the quantum world and drives the push for artificial intelligence. The mathematics of chance is involved in understanding systems where a myriad data points combine. Statistics is the branch of mathematics that wrangles that data and tames it into meaningful knowledge. It then allows us to get ever better at modeling complex phenomena, from the formation of stars and the path of a hurricane to the rise and fall of the markets. Inside Mathematics: Probability & Statistics introduces the reader to these awesome mathematical powers by telling the stories of who figured them out. They include a cavalry officer hoping to reduce injuries from horse kicks, Charles Darwin's cousin who discovered that we make the best guesses when we work together, and computers that are built to program themselves. Written to engage and enthuse young people, Inside Mathematics shows readers how the ideas of long-dead geniuses have ended up in their homework assignments. Probability & Statistics: How Mathematics Can Predict the Future changes the question from "Why?" to "What's next?" Arranged chronologically to show how ideas in mathematics evolved.