Princeton Lifesaver Study Guides – serie

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution.The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory. The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus. * Serves as a companion to any single-variable calculus textbook * Informal, entertaining, and not intimidating * Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures * More than 475 examples (ranging from easy to hard) provide step-by-step reasoning * Theorems and methods justified and connections made to actual practice * Difficult topics such as improper integrals and infinite series covered in detail * Tried and tested by students taking freshman calculus

The essential lifesaver for students who want to master probability For 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 course* Numerous worked-out examples* Lectures based on the chapters are available free online* Intuition of problems emphasized first, then technical proofs given* Appendixes review proof techniques* Relaxed, conversational approach

The essential lifesaver for students who want to master probability For 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 course* Numerous worked-out examples* Lectures based on the chapters are available free online* Intuition of problems emphasized first, then technical proofs given* Appendixes review proof techniques* Relaxed, conversational approach

Real analysis is difficult. For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math. Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided "fill in the blanks" exercises to solidify understanding. Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs.* The essential "lifesaver" companion for any course in real analysis* Clear, humorous, and easy-to-read style* Teaches students not just what the proofs are, but how to do them--in more than 40 worked-out examples* Every new definition is accompanied by examples and important clarifications* Features more than 20 "fill in the blanks" exercises to help internalize proof techniques* Tried and tested in the classroom