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This book presents functional analytic methods in a unified manner with applications to economics, social sciences, and engineering. Ideal for those without an extensive background in the area, it develops topology, convexity, Banach lattices, integration, correspondences, and the analytic approach to Markov processes. Many of the results were previously available only in esoteric monographs and will interest researchers and students who will find the material readily applicable to problems in control theory and economics.
ÒGeometry is a very beautiful subject whose qualities of elegance, order, and certainty have exerted a powerful attraction on the human mind for many centuries. . . Algebra's importance lies in the student's future. . . as essential preparation for the serious study of science, engineering, economics, or for more advanced types of mathematics. . . The primary importance of trigonometry is not in its applications to surveying and navigation, or in making computations about triangles, but rather in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents, and the orbits of the planets around the sun.Ó In this brief, clearly written book, the essentials of geometry, algebra, and trigonometry are pulled together into three complementary and convenient small packages, providing an excellent preview and review for anyone who wishes to prepare to master calculus with a minimum of misunderstanding and wasted time and effort. Students and other readers will find here all they need to pull them through.
This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.
The Hitchhiker's Guide to Calculus begins with a rapid view of lines and slope. Spivak then takes up non-linear functions and trigonometric functions. He places the magnifying glass on curves in the next chapter and effortlessly leads the reader to the idea of derivative. In the next chapter he tackles speed and velocity, followed by the derivative of sine. Maxima and minima are next. Rolle's theorem and the MVT form the core of Chapter 11, "Watching Experts at Play." The Hitchhiker's Guide to Calculus closes with a chapter on the integral, the fundamental theorem, and applications of the integral.
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
A Programmer's Introduction to Mathematics uses your familiarity with ideas from programming and software to teach mathematics. You'll learn about the central objects and theorems of mathematics, including graphs, calculus, linear algebra, eigenvalues, optimization, and more. You'll also be immersed in the often unspoken cultural attitudes of mathematics, learning both how to read and write proofs while understanding why mathematics is the way it is. Between each technical chapter is an essay describing a different aspect of mathematical culture, and discussions of the insights and meta-insights that constitute mathematical intuition. As you learn, we'll use new mathematical ideas to create wondrous programs, from cryptographic schemes to neural networks to hyperbolic tessellations. Each chapter also contains a set of exercises that have you actively explore mathematical topics on your own. In short, this book will teach you to engage with mathematics. A Programmer's Introduction to Mathematics is written by Jeremy Kun, who has been writing about math and programming for 10 years on his blog "Math Intersect Programming." As of 2020, he works in datacenter optimization at Google.The second edition includes revisions to most chapters, some reorganized content and rewritten proofs, and the addition of three appendices.
Millions have seen the movie and thousands have read the book but few have fully appreciated the mathematics developed by John Nash's beautiful mind. Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.
A free, world-class education for anyone, anywhere: this is the goal of the Khan Academy, a passion project that grew from an ex-engineer and hedge funder's online tutoring sessions with his niece, who was struggling with algebra, into a worldwide phenomenon. Today millions of students, parents, and teachers use the Khan Academy's free videos and software, which have expanded to encompass nearly every conceivable subject; and Academy techniques are being employed with exciting results in a growing number of classrooms around the globe. Like many innovators, Khan rethinks existing assumptions and imagines what education could be if freed from them. And his core idea-liberating teachers from lecturing and state-mandated calendars and opening up class time for truly human interaction-has become his life's passion. Schools seek his advice about connecting to students in a digital age, and people of all ages and backgrounds flock to the site to utilize this fresh approach to learning. In The One World Schoolhouse, Khan presents his radical vision for the future of education, as well as his own remarkable story, for the first time. In these pages, you will discover, among other things: How both students and teachers are being bound by a broken top-down model invented in Prussia two centuries ago Why technology will make classrooms more human and teachers more important How and why we can afford to pay educators the same as other professionals/DIV How we can bring creativity and true human interactivity back to learning/DIV Why we should be very optimistic about the future of learning. Parents and politicians routinely bemoan the state of our education system. Statistics suggest we've fallen behind the rest of the world in literacy, math, and sciences. With a shrewd reading of history, Khan explains how this crisis presented itself, and why a return to "mastery learning," abandoned in the twentieth century and ingeniously revived by tools like the Khan Academy, could offer the best opportunity to level the playing field, and to give all of our children a world-class education now. More than just a solution, The One World Schoolhouse serves as a call for free, universal, global education, and an explanation of how Khan's simple yet revolutionary thinking can help achieve this inspiring goal.