For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes.Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

    Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. KEY TOPICS: Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gr�bner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra MARKET: For all readers interested in abstract algebra.

    A lecture class taught by Wittgenstein, however, hardly resembled a lecture. He sat on a chair in the middle of the room, with some of the class sitting in chairs, some on the floor. He never used notes. He paused frequently, sometimes for several minutes, while he puzzled out a problem. He often asked his listeners questions and reacted to their replies. Many meetings were largely conversation. These lectures were attended by, among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan Turing, G. H. von Wright, R. G. Bosanquet, Norman Malcolm, Rush Rhees, and Yorick Smythies. Notes taken by these last four are the basis for the thirty-one lectures in this book. The lectures covered such topics as the nature of mathematics, the distinctions between mathematical and everyday languages, the truth of mathematical propositions, consistency and contradiction in formal systems, the logicism of Frege and Russell, Platonism, identity, negation, and necessary truth. The mathematical examples used are nearly always elementary.

    Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces.The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back.Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

    But this book will help you to do something that humans have only recently understood how to do: to count to regions that no animal has ever reached. By the end of this book you'll be able to count to infinity... and beyond. On our way to infinity we'll discover how the ancient Babylonians used their bodies to count to 60 (which gave us 60 minutes in the hour), how the number zero was only discovered in the 7th century by Indian mathematicians contemplating the void, why in China going into the red meant your numbers had gone negative and why numbers might be our best language for communicating with alien life.But for millennia, contemplating infinity has sent even the greatest minds into a spin. Then at the end of the nineteenth century mathematicians discovered a way to think about infinity that revealed that it is a number that we can count. Not only that. They found that there are an infinite number of infinities, some bigger than others. Just using the finite neurons in your brain and the finite pages in this book, you'll have your mind blown discovering the secret of how to count to infinity.Do something amazing and learn a new skill thanks to the Little Ways to Live a Big Life books!

    Linear algebra is tightly integrated into the text.

    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

    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.

    The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

    This guide provides explanations of eigenvalues, eigenvectors, linear transformations, linear equations, vectors, and matrices.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    The real response to the question should be, "Yes, you will, because algebra gives you power" - the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on. Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra I For Dummies can provide the help you need.This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works.In Algebra I For Dummies, you'll discover the following topics and more:All about numbers - rational and irrational, variables, and positive and negative Figuring out fractions and decimals Explaining exponents and radicals Solving linear and quadratic equations Understanding formulas and solving story problems Having fun with graphs Top Ten lists on common algebraic errors, factoring tips, and divisibility rules. No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra I For Dummies can give you the tools you need to succeed.

    Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject.'W.W. Sawyer's deep understanding of how we learn and his lively, practical approach have made this an ideal introduction to mathematics for generations of readers. By starting at the level of simple arithmetic and algebra and then proceeding step by step through graphs, logarithms and trigonometry to calculus and the dizzying world of imaginary numbers, the book takes the mystery out of maths. Throughout, Sawyer reveals how theory is subordinate to the real-life applications of mathematics - the Pyramids were built on Euclidean principles three thousand years before Euclid formulated them - and celebrates the sheer intellectual stimulus of mathematics at its best.