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Guide To Geometric Algebra In Practice

Author : Leo Dorst
ISBN : 0857298119
Genre : Computers
File Size : 57.33 MB
Format : PDF, ePub, Mobi
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This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
Category: Computers

Foundations Of Geometric Algebra Computing

Author : Dietmar Hildenbrand
ISBN : 9783642317941
Genre : Computers
File Size : 30.23 MB
Format : PDF, Mobi
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The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
Category: Computers

Geometric Algebra Applications Vol I

Author : Eduardo Bayro-Corrochano
ISBN : 9783319748306
Genre : Computers
File Size : 24.65 MB
Format : PDF, ePub, Docs
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The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.
Category: Computers

Discrete Geometry For Computer Imagery

Author : Elena Barcucci
ISBN : 9783319099552
Genre : Computers
File Size : 72.31 MB
Format : PDF, Mobi
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This book constitutes the thoroughly refereed proceedings of the 18th International Conference on Discrete Geometry for Computer Imagery, DGCI 2014, held in Siena, Italy, September 2014. The 34 revised full papers presented were carefully selected from 60 submissions. The papers are organized in topical sections on Models for Discrete Geometry, Discrete and Combinatorial Topology, Geometric Transforms, Discrete Shape Representation, Recognition and Analysis, Discrete Tomography, Morphological Analysis, Discrete Modelling and Visualization, Discrete and Combinatorial Tools for Image Segmentation and Analysis.
Category: Computers

Real Spinorial Groups

Author : Sebastià Xambó-Descamps
ISBN : 9783030004040
Genre : Mathematics
File Size : 23.59 MB
Format : PDF, Kindle
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This book explores the Lipschitz spinorial groups (versor, pinor, spinor and rotor groups) of a real non-degenerate orthogonal geometry (or orthogonal geometry, for short) and how they relate to the group of isometries of that geometry. After a concise mathematical introduction, it offers an axiomatic presentation of the geometric algebra of an orthogonal geometry. Once it has established the language of geometric algebra (linear grading of the algebra; geometric, exterior and interior products; involutions), it defines the spinorial groups, demonstrates their relation to the isometry groups, and illustrates their suppleness (geometric covariance) with a variety of examples. Lastly, the book provides pointers to major applications, an extensive bibliography and an alphabetic index. Combining the characteristics of a self-contained research monograph and a state-of-the-art survey, this book is a valuable foundation reference resource on applications for both undergraduate and graduate students.
Category: Mathematics

Idiot S Guides Basic Math And Pre Algebra

Author : Carolyn Wheater
ISBN : 9781615645299
Genre : Mathematics
File Size : 56.84 MB
Format : PDF, Kindle
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When not used on a daily basis, basic math concepts are difficult to recall and use. When people plan to return to school, they must take entrance and placement exams with a significant math portion. Idiot's Guides: Basic Math and Pre-Algebra helps readers get back up to speed and relearn the primary concepts of mathematics, geometry, and pre-algebra so that they can pass entrance exams, such as the GED, ASVAB, and Praxis, as well as remedial math courses. Ideal for both students and parents, Idiot's Guides: Basic Math and Pre-Algebra will include a workbook component with practice problems to help reinforce the math concepts. In this book, readers get: - An introduction to positive and negative numbers and place values - A solid review of the four basic math operations: addition, subtraction, multiplication, and division - Step-by-step guidance on how to understand and solve word problems - An explanation of the concepts of factors and multiples - Help in working with fractions, decimals, and percents - The basics of geometry - Weights, measures, and other practical applications of mathematics - How to create and interpret mathematical graphs - A grounding in statistics and probability - An introduction to algebraic concepts and problems, including expressions and equations
Category: Mathematics

Clinician S Guide To Psychological Assessment And Testing

Author : John M. Spores, PhD, JD
ISBN : 9780826199874
Genre : Psychology
File Size : 62.43 MB
Format : PDF, ePub
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"Overall, this is an excellent guide to the use and administration of psychological tests. It provides straightforward directions and instructions on how to utilize testing in such a way as to better inform clinical practice. I could see this book as a mainstay on any counselorís bookshelf, especially those who are seeking a way to utilize standardized testing in their practice."--The Professional Counselor Journal ìFinally, a detailed and crystal clear guide to psychological assessment that effectively integrates 'best practices' with the realities of negotiating the mental health care system and insurance providers. I plan to draw on this practical guide in my private practice and to incorporate it as a required text in my advanced counseling assessment classes at both the masterís and doctoral level. This book is a treasure for any mental health professional involved in psychological assessment.î Joseph G. Ponterotto, PhD Professor of Counseling Psychology, Fordham University Standardized psychological testing is often essential for reliably determining the presence of a wide range of psychiatric and personality disorders, along with effectively addressing related issues that may require a psychological referral. This nuts-and-bolts guide to conducting efficient and accurate psychological testing in clinical settings provides mental health professionals with experienced guidance in the entire process, and includes a complete set of forms and templates for all aspects of assessment and testing, from the initial referral and diagnostic interview to the final report. Based on the authorís experience with over two thousand psychological and neuropsychological testing cases, this highly practical book presents a standardized process of assessment, testing, interpretation, report-writing, and presenting feedback to patients, family members, and other professionals. Actual case examples of patients from a wide age range illustrate the assessment and testing process in action. The text provides printed and electronic versions of referral and related forms, initial psychological assessment report templates that include critical areas of coverage for obtaining insurance approval, and interpretation tables for an exceptional inventory of key standardized psychological tests. Integral to the book is a review of psychological tests in seven key categories that most effectively address differential diagnostic dilemmas and related referral questions that clinicians are likely to encounter in practice. It also provides effective strategies for selecting the appropriate tests based on the particular diagnostic questions, guidance for successfully obtaining insurance approval for a targeted yet feasible number of testing hours, and an efficient system for simultaneous test interpretation and report writing. Key Features: Includes an overview of the assessment process, from the initial referral to completion of the final report Features effective reviews of commonly used tests, including neuropsychological, intelligence, personality, and behavioral inventories Includes print and digital templates and forms for all phases of assessment and testing Aids clinicians in both private practice and other health care settings to work within managed care and be effectively reimbursed for services Includes information on conducting forensic competency to stand trial assessments, including the authorís new measure of assessing a defendantís understanding of the legal system
Category: Psychology

Basic Algebra And Geometry Made A Bit Easier Lesson Plans

Author : Larry Zafran
ISBN : 9781451558203
Genre : Algebra
File Size : 80.7 MB
Format : PDF, Kindle
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This is the fifth book in the Math Made a Bit Easier series by independent math tutor Larry Zafran. It contains 50 abridged lesson plans covering basic algebra and geometry, for a target audience of tutors, parents, and homeschoolers. Each lesson plan includes all of the components of a typical classroom lesson such as aim, motivation, warm-up exercises, demonstrative examples, questions for thought and discussion, and connections to earlier and later material. This book is intended to be used in strict conjunction with the fourth book of the series (Basic Algebra and Geometry Made a Bit Easier: Concepts Explained in Plain English). The book assumes that the instructor actually knows the material him/herself, but could benefit from having a general guideline to follow. The author makes a point of identifying the concepts which most students tend to find easy or difficult, including suggestions on how to help with the latter. The book includes an introduction describing how the book can be put to best use, as well as a section on how to effectively work with students who are struggling with the material. The author explains that for the vast majority of students, the root of the problem can be traced back to never having fully mastered basic math concepts and skills. The book's lessons make frequent reference to reviewing earlier books in the series as needed so that the student masters all of the prerequisite material.
Category: Algebra

Pass The Compass Complete Study Guide And Practice Test Questions For The Compass Exam

Author : Complete Test Preparation Inc.
Genre : Study Aids
File Size : 90.83 MB
Format : PDF, ePub, Mobi
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COMPASS® study guide, prepared by our dedicated team of exam experts, including practice test questions. Everything you need to pass the COMPASS®! Pass the COMPASS®! will help you: Increase your score with multiple choice strategies from exam experts Practice with 2 complete practice question sets (over 500 questions) Make an COMPASS® study plan and study schedule Learn what you MUST do in the exam room Avoid common mistakes on a test Answer multiple choice questions strategically 2 Sets of practice test questions including: Reading Comprehension Basic Math - Including Fractions, Decimals, Percent, Word problems Algebra - Including One and Two Variable Equations, Polynomial Operations, Quadratics College Level Math - Including Cartesian and Coordinate Planes, Trigonometry, Sequences, Logarithms How to write an essay Hundreds of pages of review and tutorials on all COMPASS® topics. Complete Test Preparation Inc. is not affiliate with the makers of the COMPASS® exam. COMPASS is a registered trademark of ACT Inc., who are not involved in the production of, and do not endorse this publication. Maybe you have read this kind of thing before, and maybe feel you don't need it, and you are not sure if you are going to buy this eBook. Remember though, it only a few percentage points divide the PASS from the FAIL students. Even if our test tips increase your score by a few percentage points, isn't that worth it? Why not do everything you can to get the best score on the COMPASS®?
Category: Study Aids