Math Squared

Everybody knows and understands Pythagoras' theorem, but Maths Squared introduces you to the world of Einstein's relativity theory, Euclidean geometry, and the butterfly effect.

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

This book is intended for graduate students and research mathematicians interested in associative rings and algebras.

The first step-by-step guide to conducting successful Chi-squaredtests Chi-squared testing is one of the most commonly applied statisticaltechniques. It provides reliable answers for researchers in a widerange of fields, including engineering, manufacturing, finance,agriculture, and medicine. A Guide to Chi-Squared Testing brings readers up to date on recentinnovations and important material previously published only in theformer Soviet Union. Its clear, concise treatment and practicaladvice make this an ideal reference for all researchers andconsultants. Authors Priscilla E. Greenwood and Mikhail S. Nikulin demonstratethe application of these general purpose tests in a wide variety ofspecific settings. They also * Detail the various decisions to be made when applying Chi-squaredtests to real data, and the proper application of these tests instandard hypothesis-testing situations * Describe how Chi-squared type tests allow statisticians toconstruct a test statistic whose distribution is asymptoticallyChi-squared, and to compute power against various alternatives * Devote half of the book to examples of Chi-squared tests that canbe easily adapted to situations not covered in the book * Provide a self-contained, accessible treatment of themathematical requisites * Include an extensive bibliography and suggestions for furtherreading

Master the math behind CAD, game engines, GIS, and more! This hands-on book teaches you the geometry used to create simulations, 3D prints, and other models of the physical world. In Geometry for Programmers you will learn how to: Speak the language of applied geometry Compose geometric transformations economically Craft custom splines for efficient curves and surface generation Pick and implement the right geometric transformations Confidently use important algorithms that operate on triangle meshes, distance functions, and voxels Geometry for Programmers guides you through the math behind graphics and modeling tools. It’s full of practical examples and clear explanations that make sense even if you don’t have a background in advanced math. You’ll learn how basic geometry can help you avoid code layering and repetition, and even how to drive down cloud hosting costs with more efficient runtimes. Cheerful language, charts, illustrations, equations, and Python code help make geometry instantly relevant to your daily work as a developer. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Geometry is at the heart of game engines, robotics, computer-aided design, GIS, and image processing. This book draws back what is for some a mathematical curtain, giving them insight and control over this central tool. You’ll quickly see how a little geometry can help you design realistic simulations, translate the physical world into code, and even reduce your cloud services bill by improving the efficiency of graphics-intensive applications. About the Book Geometry for Programmers is both practical and entertaining. Fun illustrations and engaging examples show you how to apply geometry to real programming problems, like changing a scan into a CAD model or developing 3D printing contours from a parametric function. And don’t worry if you aren’t a math expert. There’s no heavy theory, and you’ll learn how to offload most equations to the SymPy computer algebra system. What’s Inside Speak the language of applied geometry Compose geometric transformations economically Craft custom splines for efficient curves and surface generation Confidently use geometry algorithms About the Reader Examples are in Python, and all you need is high school–level math. About the Author Oleksandr Kaleniuk is the creator of Words and Buttons Online, a collection of interactive tutorials on math and programming. Table of Contents 1 Getting started 2 Terminology and jargon 3 The geometry of linear equations 4 Projective geometric transformations 5 The geometry of calculus 6 Polynomial approximation and interpolation 7 Splines 8 Nonlinear transformations and surfaces 9 The geometry of vector algebra 10 Modeling shapes with signed distance functions and surrogates 11 Modeling surfaces with boundary representations and triangle meshes 12 Modeling bodies with images and voxels

If our goal is to broaden and deepen students’ awareness and understanding of mathematics, we advance the idea that engaging students with what we metaphorically call the personality of math. That is, we think that students who engage with the math’s (1) human champions, (2) with its history and philosophy, and (3) with the nature of its problems and inferential challenges, are more likely to have a positive attitude toward math that will encourage greater learning.