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Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Seventh Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Seventh Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts.
Building on the success of its first five editions, the Sixth Edition of the market-leading text explores the important principles and real-world applications of plane, coordinate, and solid geometry. Strongly influenced by both NCTM and AMATYC standards, the text includes intuitive, inductive, and deductive experiences in its explorations. Goals of the authors for the students include a comprehensive development of the vocabulary of geometry, an intuitive and inductive approach to development of principles, and the strengthening of deductive skills that leads to both verification of geometric theories and the solution of geometry-based real world applications. Updates in this edition include the addition of 150 new problems, new applications, new Discover! activities and examples and additional material on select topics such as parabolas and a Three-Dimensional Coordinate System.
Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this book popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY, 13e, International Edition retains these features. The problems have been consistently praised for being at just the right level for precalculus students. The book also provides calculator examples, including specific keystrokes that show how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares readers for further courses in mathematics.
A lavishly illustrated book that explores the language of curves that spans the human body, science, engineering, and artCurves are seductive. These smooth, organic lines and surfaces-like those of the human body-appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world-from our bodies to Salvador Dali's paintings and the space-time fabric of the universe itself.The book focuses on seven curves-the fold, cusp, swallowtail, and butterfly, plus the hyperbolic, elliptical, and parabolic "umbilics"-and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician Rene Thom. In an accessible discussion illustrated with many photographs of the human nude, McRobie introduces these curves and then describes their role in nature, science, engineering, architecture, art, and other areas. The reader learns how these curves play out in everything from the stability of oil rigs and the study of distant galaxies to rainbows, the patterns of light on pool floors, and even the shape of human genitals. The book also discusses the role of these curves in the work of such artists as David Hockney, Henry Moore, and Anish Kapoor, with particular attention given to the delicate sculptures of Naum Gabo and the final paintings of Dali, who said that Thom's theory "bewitched all of my atoms."A unique introduction to the language of beautiful curves, this book may change the way you see the world.
More Geometry Snacks is a mathematical puzzle book filled with geometrical figures and questions designed to challenge, confuse and ultimately enlighten enthusiasts of all ages. It is the companion volume to the highly successful Geometry Snacks. Each puzzle is carefully designed to draw out interesting phenomena and relationships between the areas and dimensions of various shapes. Furthermore, unlike most puzzle books, the authors offer multiple approaches to solutions so that once a puzzle is solved, there are further surprises, insights and challenges to be had. As a teaching tool, More Geometry Snacks enables teachers to promote deep thinking and debate over how to solve geometry puzzles. Each figure is simple, but often deceptively tricky to solve - allowing for great classroom discussions about ways in which to approach them. By offering numerous solution approaches, the book also acts as a tool to help encourage creativity and develop a variety of strategies to chip away at problems that often seem to have no obvious way in. More Geometry Snacks offers another batch of puzzles.
Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Eight Edition, incorporates the dynamic link between concepts and applications to bring mathematics to life. By integrating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the eighth edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts.
This unique text provides students with a single-volume treatment
of the basics of calculus and analytic geometry. It reflects the
teaching methods and philosophy of Otto Schreier, an influential
mathematician and professor. The order of its presentation promotes
an intuitive approach to calculus, and it offers a strong emphasis
on algebra with minimal prerequisites.
Larson's ALGEBRA AND TRIGONOMETRY, 9E, International Edition is ideal for a two-term course and is known for delivering sound, consistently structured explanations and carefully written exercises of the mathematical concepts. With the Ninth Edition, the author continues to revolutionize the way students learn material by incorporating more real-world applications, on-going review and innovative technology. How Do You See It? exercises give you practice applying the concepts, and new Summarize features, Checkpoint problems and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.
Highlighted by numerous examples, this book explores methods of the
projective geometry of the plane. It derives the projective
properties of the conic and discusses representation by the general
equation of the 2nd degree, concluding with a study of the
relationship between Euclidean and projective geometry. 1960
This concise text introduces students to the elements of analytical geometry, covering basic ideas and methods. Topics include transformation of axes, the line at infinity, conics and pencils of conics, homographic correspondence, line-coordinates, and generalized homogeneous coordinates. An appendix discusses solutions to many of the examples. 1957 edition.
An examination of approaches to easy-to-understand but
difficult-to-solve mathematical problems, this classic text begins
with a discussion of Dirichlet's principle and the boundary value
problem of potential theory, then proceeds to examinations of
conformal mapping on parallel-slit domains and Plateau's problem.
Also explores minimal surfaces with free boundaries and unstable
minimal surfaces. 1950 edition.
Excellent text approaches characters via rings (or algebras). In addition to techniques for applying characters to "pure" group theory, much of the book focuses on properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Problems follow each chapter. Prerequisite a first-year graduate algebra course. "A pleasure to read."-American Mathematical Society. 1976 edition.
Born of the desire to understand the workings of motions of the heavenly bodies, trigonometry gave the ancient Greeks the ability to predict their futures. Most of what we see of the subject in school comes from these heavenly origins; 15th century astronomer Regiomontanus called it "the foot of the ladder to the stars". In this Very Short Introduction Glen Van Brummelen shows how trigonometry connects mathematics to science, and has today become an indispensable tool in predicting cyclic patterns like animal populations and ocean tides. Its historical journey through major cultures such as medieval India and the Islamic World has taken it through disciplines such as geography and even religious practice. Trigonometry has also been a major player in the most startling mathematical developments of the modern world. Its interactions with the concept of infinity led to Taylor and Fourier series, some of the most practical tools of modern science. The birth of complex numbers led to a shocking union of exponential and trigonometric functions, creating the most beautiful formulas and powerful modelling tools in science. Finally, as Van Brummelen shows, trigonometry allows us to explore the strange new worlds of non-Euclidean geometries, opening up bizarre possibilities for the shape of space itself. And indeed, one of those new geometries - spherical - takes us full circle back to ancient Greek astronomers and European navigators, who first used it to chart their ways across the heavens and the earth. 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.
Este texto lider en el mercado sigue ofreciendo a los estudiantes y profesores, explicaciones estructuradas de los conceptos matematicos. Disenado para un curso de un semestre, prepara a los estudiantes a estudiar calculo. La nueva octava edicion conserva las caracteristicas que han hecho de este texto una solucion completa para los estudiantes y los instructores: aplicaciones interesantes, diseno de vanguardia y tecnologia innovadora combinada con una gran cantidad de ejercicios cuidadosamente escritos.
Barron's E-Z Geometry contains everything students need to succeed in geometry. This edition covers the "how" and "why" of geometry, with examples, exercises, and solutions throughout, plus hundreds of drawings, graphs, and tables. The E-Z Series presents new, updated, and improved versions of Barron's longtime popular Easy Way books. Updated cover designs, interior layouts, and more graphic material than ever make these books ideal as self-teaching manuals. Teachers have discovered that E-Z titles also make excellent supplements to classroom textbooks. Skill levels range between senior high school and college-101 standards. All titles in the series present detailed reviews of the target subject plus short quizzes and longer tests to help students assess their learning progress.
Euclid’s Window takes us on a brilliantly entertaining journey through 3,000 years of genius and geometry, introducing the people who revolutionized the way we see the world around us.
Ever since Pythagorus hatched a ‘little scheme’ to invent a set of rules describing the entire universe, scientists and mathematicians have tried to seek order in the cosmos: Euclid, who in 300BC defined the nature of space; Descartes, a fourteenth-century gambler and idler who invented the graph; Gauss, the fifteen-year-old genius who discovered that space is curved; Einstein, who added time to the equation; and Witten, who ushered in today’s weird new world of extra, twisted dimensions. They all show how geometry is the key to understanding the universe. Once you have viewed life through Euclid’s Window, it will never be the same again.
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" "... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty." From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Gunter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdoes. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. Several hundred theorems and corollaries are formulated and proved completely; numerous others remain unproved, to be used by students as exercises. 1929 edition.
Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at universities around the world, and this book is based on a series of his lectures.
Roman geometric patterns radiate symmetry and order. Drawing the patterns is not just a question of mechanically copying the work of someone else square by square, but of understanding the underlying structure. The patterns are built up from simple elements which seem to 'grow' and develop in an almost organic or living way. This book is arranged as a series of drawing exercises. There is no better way of appreciating the skill and imagination of those artists than by drawing their designs yourself. To 'feel' how a cross 'grows' into a swastika pattern which then 'grows' into a complex interlocking design is something which can only be experienced at first hand. This second edition incorporates the same "drawing led" approach to learning about the subject and as such is invaluable in using the designs for contemporary mosaic, or pattern, design. New photographs and updated text strengthen this approach further. Ideal for schools, shops in or near Roman remains, and historical and art/design sections of shops.
This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.
This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory - to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements (shas).
There are many interactions between noncommutative algebra and representation theory on the one hand and classical algebraic geometry on the other, with important applications in both directions. The aim of this book is to provide a comprehensive introduction to some of the most significant topics in this area, including noncommutative projective algebraic geometry, deformation theory, symplectic reflection algebras, and noncommutative resolutions of singularities. The book is based on lecture courses in noncommutative algebraic geometry given by the authors at a Summer Graduate School at the Mathematical Sciences Research Institute, California in 2012 and, as such, is suitable for advanced graduate students and those undertaking early post-doctorate research. In keeping with the lectures on which the book is based, a large number of exercises are provided, for which partial solutions are included.
This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincare's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.
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