This book is written for high school and college students learning about probability for the first time. It will appeal to the reader who has a healthy level of enthusiasm for understanding how and why the various results of probability come about. All of the standard introductory topics in probability are covered: combinatorics, the rules of probability, Bayes' theorem, expectation value, variance, probability density, common distributions, the law of large numbers, the central limit theorem, correlation, and regression. Calculus is not a prerequisite, although a few of the problems do involve calculus. These are marked clearly. The book features 150 worked-out problems in the form of examples in the text and solved problems at the end of each chapter. These problems, along with the discussions in the text, will be a valuable resource in any introductory probability course, either as the main text or as a helpful supplement.
Author: David Morin
Release Date: 2017-01-20
This book is written for high school and college students learning about special relativity for the first time. It will appeal to the reader who has a healthy level of enthusiasm for understanding how and why the various results of special relativity come about. All of the standard introductory topics in special relativity are covered: historical motivation, loss of simultaneity, time dilation, length contraction, velocity addition, Lorentz transformations, Minkowski diagrams, causality, Doppler effect, energy/momentum, collisions/decays, force, and 4-vectors. Additionally, the last chapter provides a brief introduction to the basic ideas of general relativity, including the equivalence principle, gravitational time dilation, and accelerating reference frames. The book features more than 100 worked-out problems in the form of examples in the text and solved problems at the end of each chapter. These problems, along with the discussions in the text, will be a valuable resource in any course on special relativity. The numerous examples also make this book ideal for self-study. Very little physics background is assumed (essentially none in the first half of the book). An intriguing aspect of special relativity is that it is challenging due to its inherent strangeness, as opposed to a heavy set of physics prerequisites. Likewise for the math prerequisite: calculus is used on a few occasions, but it is not essential to the overall flow of the book.
Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.
Author: David J. Morin
Publisher: Createspace Independent Publishing Platform
Release Date: 2014-08-14
This problem book is ideal for high-school and college students in search of practice problems with detailed solutions. All of the standard introductory topics in mechanics are covered: kinematics, Newton's laws, energy, momentum, angular momentum, oscillations, gravity, and fictitious forces. The introduction to each chapter provides an overview of the relevant concepts. Students can then warm up with a series of multiple-choice questions before diving into the free-response problems which constitute the bulk of the book. The first few problems in each chapter are derivations of key results/theorems that are useful when solving other problems. While the book is calculus-based, it can also easily be used in algebra-based courses. The problems that require calculus (only a sixth of the total number) are listed in an appendix, allowing students to steer clear of those if they wish. Additional details: (1) Features 150 multiple-choice questions and nearly 250 free-response problems, all with detailed solutions. (2) Includes 350 figures to help students visualize important concepts. (3) Builds on solutions by frequently including extensions/variations and additional remarks. (4) Begins with a chapter devoted to problem-solving strategies in physics. (5) A valuable supplement to the assigned textbook in any introductory mechanics course.
Author: Charles Miller Grinstead
Publisher: American Mathematical Soc.
Release Date: 2012-10
This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. The text is also recommended for use in discrete probability courses. The material is organized so that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization does not emphasize an overly rigorous or formal view of probability and therefore offers some strong pedagogical value. Hence, the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. Features: Key ideas are developed in a somewhat leisurely style, providing a variety of interesting applications to probability and showing some nonintuitive ideas. Over 600 exercises provide the opportunity for practicing skills and developing a sound understanding of ideas. Numerous historical comments deal with the development of discrete probability. The text includes many computer programs that illustrate the algorithms or the methods of computation for important problems. The book is a beautiful introduction to probability theory at the beginning level. The book contains a lot of examples and an easy development of theory without any sacrifice of rigor, keeping the abstraction to a minimal level. It is indeed a valuable addition to the study of probability theory. --Zentralblatt MATH
This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.
Author: David Morin
Publisher: Cambridge University Press
Release Date: 2008-01-10
This textbook covers all the standard introductory topics in classical mechanics, including Newton's laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity. It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.
Author: Y. A. Rozanov
Publisher: Courier Corporation
Release Date: 2013-05-27
This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, and more. Includes 150 problems, many with answers.
Author: David Stirzaker
Publisher: Cambridge University Press
Release Date: 2003-08-18
Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.
Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics. In this Very Short Introduction, John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Fine-tune your numerical mindset with a quantitative review that serves as a tool for perceiving probability in a new way. Whether you’re a high school student, college student, or a test-prep candidate, this book’s wealth of explanations and insights makes it a perfect learning companion. Enjoy the benefits of your own short course in probability: •Be able to think conceptually by understanding how key problems “fit” within the main topics of probability, permutations, combinations, and enumerations. *Master basic probability using a simple “flowchart” to identify the correct formulas. *Understand when to “add” probabilities and when to “multiply” probabilities. *Be able to distinguish between events that are independent versus not independent and events that are mutually exclusive versus not mutually exclusive. *Grasp key differences between permutations and combinations and look for key words such as “arrangements” or “selections” to indicate the correct problem type. *Solve tricky permutation problems that involve repeated letters or numbers. *Approach probability problems with a newfound confidence and competency. This book is focused on honing those thinking skills that are essential for mastering basic probability. Such thinking skills make it much more likely that a person will be able to understand the “how” and “why” of problem solving, approach the subject in a conceptual way, and grasp those key principles that act as themes to bind related problems. These skills combine the science of math with the art of numbers. “To get started in probability theory, all you need are a few basic principles. Here they are, clear and uncluttered, in a short, simple book that comes as a welcome breath of fresh air.” —Dr. Ian Stewart, author of 17 Equations That Changed the World and the Cabinet of Mathematical Curiosities
Author: Laura Pedersen
Publisher: Ballantine Reader's Circle
Release Date: 2003
Sixteen-year-old Hallie Palmer answers an ad for a "yard person" to make enough money to buy a car, a job that brings her into the eccentric orbit of the Stockton family, who teach her a lesson in acceptance and being yourself.
Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions.