The Probability Lifesaver: All the Tools You Need to Understand Chance (Princeton Lifesaver Study Guides) by Steven J. Miller (PDF)

Description

The essential lifesaver for students who want to master probabilityFor students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That’s where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability’s terrain and achieve positive results.The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement―both in the guide and on the book’s website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus.The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses.A helpful introduction to probability or a perfect supplement for a courseNumerous worked-out examplesLectures based on the chapters are available free onlineIntuition of problems emphasized first, then technical proofs givenAppendixes review proof techniquesRelaxed, conversational approach

User’s Reviews

Editorial Reviews: Review “I recommend the book to everyone who is studying and fascinated by statistics.”—Singalakha Menziwa, Mathemafrica”Steven J. Miller’s The Probability Lifesaver presents, as its subtitle claims, ‘all the tools you need to understand chance’ in a clear, straightforward manner. . . . For the students that have a good understanding of Calculus, the combination of the probability discussions along with the calculus behind these topics is very beneficial.” ― MAA Reviews”The breadth of the book’s coverage and its clear, informal tone in addressing highly formal problems remind one of a friendly professor offering unlimited office hours, and the book will be a highly accessible supplement for students working through another, more conventional text. . . . [This is] a volume that deserves to be widely known in educational circles and will likely find its way to the shelves of practicing statisticians who wish to probe below the surface of fundamental theorems that they have learned by rote.”—H. Van Dyke Parunak, Computing Reviews Review “This is a superb book by a gifted writer and mathematician. Miller’s amiable, intuitive writing style weaves stories about probability into the narrative in a unique fashion.”―Larry Leemis, College of William & Mary”The Probability Lifesaver creates a wonderful mathematical experience. It combines important theories with fun problems, giving a new and creative perspective on probability. This book helped me understand the big questions behind the mathematics of probability: why the complex theories I was learning are true, where they come from, and what are their applications. This approach is a welcome complement to other heavy theoretical books, and was detailed and expansive enough to serve as the main textbook for our class.”―Alexandre Gueganic, Williams College ‘19″This fun book gives readers the feeling that they are having a live conversation with the author. A wonderful resource for students and teachers alike, The Probability Lifesaver contains clear and detailed explanations, problems with solutions on every topic, and extremely helpful background material.”―Iddo Ben-Ari, University of Connecticut”In The Probability Lifesaver, Miller does more than simply present the theoretical framework of probability. He takes complex concepts and describes them in understandable language, provides realistic applications that highlight the far-extending reaches of probability, and engages the problem-solving intuitions that lie at the heart of mathematics. Lastly, and most importantly, I am reminded throughout this textbook of why I chose to study mathematics: because it’s fun!”―Michael Stone, Williams College ‘16″The Probability Lifesaver motivates introductory probability theory with concrete applications in an approachable and engaging manner. From computing the probability of various poker hands to defining sigma-algebras, it strikes a balance between applied computation and mathematical theory that makes it easy to follow while still being mathematically satisfying.”―David Burt, Williams College ‘17″A balanced mix of theoretical and practical problem-solving approaches in probability―suited for personal study as well as textbook reading in and out of the classroom. After college, while working, I took a probability class remotely and with this book, I was able to follow easily despite being without a TA or easy access to the professor. From research examples to interview questions, it has saved my life more than once.”―Dan Zhao, Williams College ‘ 14″The Probability Lifesaver helped me build a foundation of probability theory and an appreciation for its nuances through engaging examples and easy-to-follow explanations. This well-written and extensive book will serve as your guide to probability and reward you for the time you give it.”―Jaclyn Porfilio, Williams ’15″I see a tremendous value in this fun, engaging, and informal book. It has a conversational tone, which invites students to engage the material and concepts. It is as if Miller is there, lecturing on the topics, helping students to think things through for themselves.”―John Imbrie, University of Virginia”The Probability Lifesaver contains a lot of explanations and examples and provides step-by-step instructions to how definitions and ideas are formulated. I appreciated that it tries to provide multiple solutions to each problem. Interesting, informative, approachable, and comprehensive, this book was easy to read and would make a good supplement for a first probability course at the undergraduate level.”―Jingchen Hu, Vassar College”Filled with many interesting and contemporary examples, The Probability Lifesaver would have undoubtedly helped me while I was taking statistics. Miller offers careful, detailed explanations in simple terms that are easy to understand.”―James Coyle, former student at Rutgers University From the Back Cover “This is a superb book by a gifted writer and mathematician. Miller’s amiable, intuitive writing style weaves stories about probability into the narrative in a unique fashion.”–Larry Leemis, College of William & Mary”The Probability Lifesaver creates a wonderful mathematical experience. It combines important theories with fun problems, giving a new and creative perspective on probability. This book helped me understand the big questions behind the mathematics of probability: why the complex theories I was learning are true, where they come from, and what are their applications. This approach is a welcome complement to other heavy theoretical books, and was detailed and expansive enough to serve as the main textbook for our class.”–Alexandre Gueganic, Williams College ’19″This fun book gives readers the feeling that they are having a live conversation with the author. A wonderful resource for students and teachers alike, The Probability Lifesaver contains clear and detailed explanations, problems with solutions on every topic, and extremely helpful background material.”–Iddo Ben-Ari, University of Connecticut”In The Probability Lifesaver, Miller does more than simply present the theoretical framework of probability. He takes complex concepts and describes them in understandable language, provides realistic applications that highlight the far-extending reaches of probability, and engages the problem-solving intuitions that lie at the heart of mathematics. Lastly, and most importantly, I am reminded throughout this textbook of why I chose to study mathematics: because it’s fun!”–Michael Stone, Williams College ’16″The Probability Lifesaver motivates introductory probability theory with concrete applications in an approachable and engaging manner. From computing the probability of various poker hands to defining sigma-algebras, it strikes a balance between applied computation and mathematical theory that makes it easy to follow while still being mathematically satisfying.”–David Burt, Williams College ’17″A balanced mix of theoretical and practical problem-solving approaches in probability–suited for personal study as well as textbook reading in and out of the classroom. After college, while working, I took a probability class remotely and with this book, I was able to follow easily despite being without a TA or easy access to the professor. From research examples to interview questions, it has saved my life more than once.”–Dan Zhao, Williams College ‘ 14″The Probability Lifesaver helped me build a foundation of probability theory and an appreciation for its nuances through engaging examples and easy-to-follow explanations. This well-written and extensive book will serve as your guide to probability and reward you for the time you give it.”–Jaclyn Porfilio, Williams ’15″I see a tremendous value in this fun, engaging, and informal book. It has a conversational tone, which invites students to engage the material and concepts. It is as if Miller is there, lecturing on the topics, helping students to think things through for themselves.”–John Imbrie, University of Virginia”The Probability Lifesaver contains a lot of explanations and examples and provides step-by-step instructions to how definitions and ideas are formulated. I appreciated that it tries to provide multiple solutions to each problem. Interesting, informative, approachable, and comprehensive, this book was easy to read and would make a good supplement for a first probability course at the undergraduate level.”–Jingchen Hu, Vassar College”Filled with many interesting and contemporary examples, The Probability Lifesaver would have undoubtedly helped me while I was taking statistics. Miller offers careful, detailed explanations in simple terms that are easy to understand.”–James Coyle, former student at Rutgers University About the Author Steven J. Miller is associate professor of mathematics at Williams College. He is the coauthor of An Invitation to Modern Number Theory (Princeton) and The Mathematics of Encryption: An Elementary Introduction and the editor of Benford’s Law: Theory and Applications (Princeton). Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a fantastic *supplement* to 3rd or 4th year undergraduate course in probability and a useful reference for a graduate courses that use probability. I think that needs to be emphasized very clearly. The author states that it’s intended to supplement a course in probability not replace it. Further, some of the later chapters are fairly self-contained and it is not necessary to read every single chapter to get a lot out of this book. However, I do think reading this book in its entirety will give you a pretty solid foundation in probability theory.The book covers basically everything you would expect in a standard probability course (basic set theory, combinatorics, counting, probability laws and axioms, independence/dependence, conditional and joint probability, Bayes’ theorem, PDFs/CDFs, convolutions, moments, continuous and discrete distribution, limit theorems) and some things that are not in every book (hypothesis testing, difference equations, Markov processes, least squares). In terms of math level, this book is not afraid to delve into these details with a lot of calculus and infinite series/summations. If you have not taken these courses that covered these topics yet then it is possible to still follow through this book but it may not be the right level for you.While the book is very thick, a lot of that is due to the conversational style of writing which makes it a pleasure to read. Many problems are proofs are walked through in great detail with a lot of explanation of what approach to use and even temporarily going down the wrong (but what might initially appear to be correct) path for didactic purposes. In many cases the author even guides the reader by trying to explain how one might even think about the problem and some good approaches to help to develop better strategies and intuitions. I truly appreciated reading this and felt like I learned a lot from this style. Also, check out the YouTube videos on the authors website. These are a very helpful supplement.What makes this book a little unusual is that there is a pretty heavy emphasis on proofs. A good deal of the text tries to teach the reader how to think about proofs, what and what not to try, and the appendices are full of information on proof strategies. If you are trying to learn this stuff very deeply or your teacher emphasizes proofs this could be extremely useful but sometimes this is just not what you need out of a probability textbook. I appreciate how much the author wants us to learn, and learn very well, but it all depends on why you bought this book. Thankfully, these sections can easily be skipped if they are not necessary.Looking at some of the reviews on here already it seems many readers were scared off by the introduction and heavy emphasis on combinatorics and counting early on. I can see how this might happen. The intro to the book and some of the first few chapters are quite frankly absurd for someone who is trying to learn probability. The author is very encouraging and has a lot of confidence in his readers but starting off the first chapter with a ton of summations could be extremely intimidating if this is your first textbook in probability. If you find the intro challenging I would recommend skipping it as well as all chapters on counting for the time being. These are difficult topics even when you have a pretty good grasp on the probability basics.Adding to the above, the author tries quite early on to ground some of probability in real analysis and sigma algebra. The author specifies that these sections can be skipped but if you have never thought about how probability spaces need to be defined, I can see how this might be very intimidating as well. In the end, if you are skipping around a lot it can make the book feel like it is meandering a bit too much. I don’t think this is a huge problem as the book is still very comprehensive but it makes me sad to see so many people in the reviews who got scared off.Finally, the Mathematica code is a nice addition but extremely poorly written from a coding perspective. Yes, a lot of this doesn’t matter when you are just writing one-off functions but when you are five levels deep in nested for-loops you should consider an alternative strategy. Also, consider that Mathematica is a fantastic language but not particularly popular. Rewriting the code in Python or R might be a good exercise for the reader.In summary, this book is a lot of fun to read, engaging, and comprehensive. However, the chapter organization and side-tracks to other topics may lead to the book being intimidating for some. I recommend just skipping these sections and getting out of the book what you need. It’s a great book and I highly recommend it.

⭐I purchased this by mistake, thinking I was getting The Probability Tutoring Book, by Carol Ash.Professor Miller’s lectures on youtube are amazing; he is one of those infectious geniuses who seems to be able to make you smart just by proximity.However, I ended up returning the book after closely reading the first chapter; it (figuratively) made me dizzy. Perhaps if I had more natural talent I would be able to juggle teacups while riding a unicycle on a tightrope at the same time I am booking an airline flight and frying an egg for breakfast. That’s what reading the book felt like.The opposite of this kind of book would be something like a “Just the facts” Joe Friday kind of book. I am following the EdX MIT probability course, and the teacher recommends the out of print book by Drake (with a pdf on the MIT OCW) site for the course.I think this book is great if your brain has enough RAM.I never did get the probability tutoring book; I will use the MIT/EdX structure and see how it goes.

⭐it is just as its description

⭐This book is intended to support MATHEMATICAL Probability courses. It presupposes Differential and Integral calculus. He does some brilliantwork with infinite series but I could not sustain my interest beyond chapter 1. I am afraid it is beyond my level of sophistication. That should notbe considered a criticism of the book or the author. I was unprepared for that level of prerequisites.

⭐This book is a long read, however, well worth it. It takes the probability principles which are part of all our lives and explains the basics of how formulae are derived. The book is a great read for people fascinated with the Science of Probability and who want a better understanding of how it affects our lives.

⭐This guide was a great supplement to my undergraduate mathematical probability and statistics class. It is very engaging, and explains the concepts well without being boring. It covers a lot of different topics.

⭐Using the examples in this book to apply to real world problelms

⭐Nice presentation of a broad range of topics

⭐Este libro es lo que habría deseado tener en mi licenciatura en Estadística. La secuencia de los temas se articula de forma progresiva, pedagógica y con rigor suficiente (σ-álgebras, procesos estocásticos, Teorema del Límite Central, función Gamma, Mínimos Cuadrados…), partiendo de lo primario de la Probabilidad, pasando por los Procesos Estocásticos, hasta llegar a la Inferencia Estadística y los Modelos Lineales. Lo que más me agrada es el enfoque pedagógico de contenido digerible y con pretensión de ser una base para los estudios más avanzados (de posgrado) en estos temas. 10/10.

⭐

⭐Good

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