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Author : Richard Rusczyk
Publisher : Aops Incorporated
Page : 557 pages
File Size : 47,5 Mb
Release : 2007-07-01
Category : Juvenile Nonfiction
ISBN : 1934124087
Author : Baby Professor
Publisher : Baby Professor
Page : 64 pages
File Size : 41,7 Mb
Release : 2017-02-15
Category : Juvenile Nonfiction
ISBN : 1541904141
Did you know that the study of geometry will greatly help with your child's problem solving, logic and deductive reasoning skills? It has many benefits that will push your child's likelihood for academic excellence. Teach your child about the subject while he/she is still young. Start with this book today!
Author : Michael P. Hitchman
Publisher : Jones & Bartlett Learning
Page : 255 pages
File Size : 46,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780763754570
The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters.
Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 54,6 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
Author : C. R. Wylie
Publisher : Courier Corporation
Page : 578 pages
File Size : 41,5 Mb
Release : 2011-09-12
Category : Mathematics
ISBN : 9780486141701
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.
Author : Harold Scott Macdonald Coxeter
Publisher : Unknown
Page : 0 pages
File Size : 46,8 Mb
Release : 2022
Category : Geometry
ISBN : 7519285901
Author : Diane Maclagan,Bernd Sturmfels
Publisher : American Mathematical Society
Page : 363 pages
File Size : 54,5 Mb
Release : 2021-12-13
Category : Mathematics
ISBN : 9781470468569
Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature. This wonderful book will appeal to students and researchers of all stripes: it begins at an undergraduate level and ends with deep connections to toric varieties, compactifications, and degenerations. In between, the authors provide the first complete proofs in book form of many fundamental results in the subject. The pages are sprinkled with illuminating examples, applications, and exercises, and the writing is lucid and meticulous throughout. It is that rare kind of book which will be used equally as an introductory text by students and as a reference for experts. —Matt Baker, Georgia Institute of Technology Tropical geometry is an exciting new field, which requires tools from various parts of mathematics and has connections with many areas. A short definition is given by Maclagan and Sturmfels: “Tropical geometry is a marriage between algebraic and polyhedral geometry”. This wonderful book is a pleasant and rewarding journey through different landscapes, inviting the readers from a day at a beach to the hills of modern algebraic geometry. The authors present building blocks, examples and exercises as well as recent results in tropical geometry, with ingredients from algebra, combinatorics, symbolic computation, polyhedral geometry and algebraic geometry. The volume will appeal both to beginning graduate students willing to enter the field and to researchers, including experts. —Alicia Dickenstein, University of Buenos Aires, Argentina
Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 49,6 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435189
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
Author : Richard Rusczyk
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 2009
Category : Algebra
ISBN : 1934124141
Author : Frank Schaffer Publications
Publisher : Unknown
Page : 80 pages
File Size : 52,7 Mb
Release : 2002-11-01
Category : Geometry
ISBN : 076470155X
With easy-to-use activities, students in grades 6-8 can learn the basics of geometry with exercises that relate to everyday events and things. Reproducibles included.
Author : Henry Parker Manning
Publisher : Courier Corporation
Page : 110 pages
File Size : 41,5 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 9780486442624
This fine and versatile introduction to non-Euclidean geometry is appropriate for both high-school and college classes. It begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. Major topics include hyperbolic geometry, single elliptic geometry, and analytic non-Euclidean geometry. 1901 edition.
Author : Saul Stahl,Catherine Stenson
Publisher : John Wiley & Sons
Page : 536 pages
File Size : 46,7 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118546147
An easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition “. . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained.” —CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition: • Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being • Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods • Bridges seemingly disparate topics by creating thoughtful and logical connections • Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic.
Author : A. C. Burdette
Publisher : Academic Press
Page : 448 pages
File Size : 54,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265223
An Introduction to Analytic Geometry and Calculus covers the basic concepts of analytic geometry and the elementary operations of calculus. This book is composed of 14 chapters and begins with an overview of the fundamental relations of the coordinate system. The next chapters deal with the fundamentals of straight line, nonlinear equations and graphs, functions and limits, and derivatives. These topics are followed by a discussion of some applications of previously covered mathematical subjects. This text also considers the fundamentals of the integrals, trigonometric functions, exponential and logarithm functions, and methods of integration. The final chapters look into the concepts of parametric equations, polar coordinates, and infinite series. This book will prove useful to mathematicians and undergraduate and graduate mathematics students.
Author : Nathan Altshiller-Court
Publisher : Dover Publications
Page : 336 pages
File Size : 53,6 Mb
Release : 2013-12-30
Category : Electronic
ISBN : 0486788474
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Author : Mark V. Lawson
Publisher : CRC Press
Page : 383 pages
File Size : 46,7 Mb
Release : 2016-11-25
Category : Mathematics
ISBN : 9781482246506
Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra