Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200 increasingly complex problems. The puzzles delve into Gödel’s undecidability theorem and other examples of the deepest paradoxes of logic and set theory. Detailed solutions follow each puzzle.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    

    Volume 1 looks at the discipline's origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

    Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more!The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems.This book can serve as a complete Algebra I course, and also includes many concepts covered in Algebra II. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of algebra will find this book an instrumental part of their mathematics libraries.656About the author: Richard Rusczyk is a co-author of Art of Problem Solving, Volumes 1 and 2, the author of Art of Problem Solving's Introduction to Geometry. He was a national MATHCOUNTS participant, a USA Math Olympiad winner, and is currently director of the USA Mathematical Talent Search.

    Calculus is not a prerequisite, although examples and exercises using very basic calculus are included (labeled Calculus Required.) The most technology-friendly text on the market, Introductory Linear Algebra is also the most flexible. By omitting certain sections, instructors can cover the essentials of linear algebra (including eigenvalues and eigenvectors), to show how the computer is used, and to introduce applications of linear algebra in a one-semester course.

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

    But then the English-major-turned-award-winning-science-writer had a change of heart and decided to revisit the equations and formulas that had haunted her for years. The Calculus Diaries is the fun and fascinating account of her year spent confronting her math phobia head on. With wit and verve, Ouellette shows how she learned to apply calculus to everything from gas mileage to dieting, from the rides at Disneyland to shooting craps in Vegas-proving that even the mathematically challenged can learn the fundamentals of the universal language.

    Each concept is quick and easy to remember, described by means of an easy-to-understand picture and a maximum 200-word explanation. Concepts span all of the key areas of mathematics, including Fundamentals of Mathematics, Sets and Numbers, Geometry, Equations, Limits, Functions and Calculus, Vectors and Algebra, Complex Numbers, Combinatorics, Number Theory, Metrics and Measures and Topology. Incredibly quick - clear artworks and simple explanations that can be easily remembered. Based on scientific research that the brain best absorbs information visually. Compact and portable format - the ideal, handy reference.

    This book picks you up at the very beginning and guides you through the foundations of algebra using lots of examples and no-nonsense explanations. Each chapter contains well-chosen exercises as well as all the solutions. No prior knowledge is required. Topics include: Exponents, Brackets, Linear Equations and Quadratic Equations. For a more detailed table of contents, use the "Look Inside" feature. From the author of "Great Formulas Explained" and "Physics! In Quantities and Examples".

    Based on years of personal research and client feedback, best-selling author, naturopath and health coach Kylie Ansett answers the question;What is the secret to looking and feeling younger? You will learn: • How to have whiter teeth without using chemicals • How to firm and tone your face for free • How to wake early feeling refreshed and energized every day • How to have the energy of a 25 year old without taking a single supplement • Detox methods that will take years off your face and decades off your body • And much, much more! Do you ever hear yourself making the excuse: “I’m too old for that!”? Do you look in the mirror some days and not recognize who is looking back? (Other days you feel just as old as you look!) Every day more grey hairs. And wrinkles. You don’t have as much energy. You’re not as bendy as you used to be. Skin that used to be firm is, well, less firm. Is there a way? Can you recapture the energy, the vitality and the health of your younger days? Can you start looking younger instead of older every day? Is there a way to turn back time? Look at what others have said about 10 Years Younger: Way more than just about looking good. Straightforward and practical advice for anyone who wants to be more conscious about their health, looks and life choices. - Harmony Davis Interesting, heartfelt, practical and humorous. A great reminder of how easy, cheap and effective looking younger can be. An excellent resource to keep us healthy and younger looking. - Deborah Sutton There is something in here for every woman; all the tips are simple, inexpensive and easy to implement. Read this and your body will thank you. - Julie Extremely entertaining, informative and engaging. I felt like I’d just given myself an enjoyable self-pampering session. It is a workout, a spring clean & rejuvenation for the body and mind. - Melia Vlatko-Rulo Both practical and compelling - gives the most amazing ideas for how to look and feel 10 years younger. What I like the best is the 'try it on' approach. Try them all and see what fits - what a brilliant idea! - Jane E Infante A genuine and honest approach to looking younger; and good health is at the heart of it. - Coral For those who can't or don't want to try 'artificial' ways of staying young, this is a really good book. Many techniques are simple and quick, with proven effects on your body and mind. Well written and concise, with good summaries at the end of each chapter. - J This is an upbeat and original book, about aging well. I liked the format this material was presented in, providing passages followed by an action plan. If you don't envision/equate growing older as a steady, downward slide to multiple meds, limited mobility and sagging jowls, give this one a try! - Geraldine Helen Harman Every ingenious tip was made with either ingredients I could easily find in my cupboard, or no ingredients at all, so I could begin straight away. - Taya M A holistic viewpoint, rather than quick fixes, creams and lotions. Age is as much about attitude and the way we see life.

    Fully stocked with solved problemsN950 of themNit shows you how to solve problems that may not have been fully explained in class. Plus you ge"