This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.

This graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.

X-Men meets Marissa Meyer’s Renegades when New York Times bestselling author of the Uglies series Scott Westerfeld teams up with award-winning authors Margo Lanagan and Deborah Biancotti for this explosive trilogy filled with “cinematic nonstop action,” (Booklist) about six teens with unique abilities. Don’t call them heroes. But these six California teens have powers that set them apart. Take Ethan, a.k.a. Scam. He’s got a voice inside him that’ll say whatever you want to hear, whether it’s true or not. Which is handy, except when it isn’t—like when the voice starts gabbing in the middle of a bank robbery. The only people who can help are the other Zeroes, who aren’t exactly best friends these days. Enter Nate, a.k.a. Bellwether, the group’s “glorious leader.” After Scam’s SOS, he pulls the scattered Zeroes back together. But when the rescue blows up in their faces, the Zeroes find themselves propelled into whirlwind encounters with ever more dangerous criminals. At the heart of the chaos they find Kelsie, who can take a crowd in the palm of her hand and tame it or let it loose as she pleases. Filled with high-stakes action and drama, Zeroes unites three powerhouse authors for the opening installment of a thrilling new series.

Pulitzer Prize-winning author and astronomer Carl Sagan imagines the greatest adventure of all—the discovery of an advanced civilization in the depths of space. In December of 1999, a multinational team journeys out to the stars, to the most awesome encounter in human history. Who—or what—is out there? In Cosmos, Carl Sagan explained the universe. In Contact, he predicts its future—and our own.

A winner of the Nobel Peace Prize and bestselling author of Banker to the Poor offers his vision of an emerging new economic system that can save humankind and the planet Muhammad Yunus, who created microcredit, invented social business, and earned a Nobel Peace Prize for his work in alleviating poverty, is one of today's most trenchant social critics. Now he declares it's time to admit that the capitalist engine is broken -- that in its current form it inevitably leads to rampant inequality, massive unemployment, and environmental destruction. We need a new economic system that unleashes altruism as a creative force just as powerful as self-interest. Is this a pipe dream? Not at all. In the last decade, thousands of people and organizations have already embraced Yunus's vision of a new form of capitalism, launching innovative social businesses designed to serve human needs rather than accumulate wealth. They are bringing solar energy to millions of homes in Bangladesh; turning thousands of unemployed young people into entrepreneurs through equity investments; financing female-owned businesses in cities across the United States; bringing mobility, shelter, and other services to the rural poor in France; and creating a global support network to help young entrepreneurs launch their start-ups. In A World of Three Zeros, Yunus describes the new civilization emerging from the economic experiments his work has helped to inspire. He explains how global companies like McCain, Renault, Essilor, and Danone got involved with this new economic model through their own social action groups, describes the ingenious new financial tools now funding social businesses, and sketches the legal and regulatory changes needed to jumpstart the next wave of socially driven innovations. And he invites young people, business and political leaders, and ordinary citizens to join the movement and help create the better world we all dream of.

2024-25 RRB Technician Grade-I Signal Engineering Mathematics 264 495 E. This book covers all basic elementary mathematics and also the solution of asked previous questions.

In 1940, the mathematician Edward Kasner published the book "Mathematics and the Imagination", in which he popularized the words googol and googolplex which his nephew suggested as names for big numbers. The number googol has been defined as 1 followed by a hundred zeros: googol = 10^100 = 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 The much larger number googolplex has been defined as 1 followed by a googol zeros. While this number can easily be written as googolplex = 10^googol = 10^(10^100) using the exponential notation, it has often been claimed that the number googolplex is so large that it can never be written out in full. However in this "Googolplex Written Out" series of books, I am doing just that. It consists out of 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 volumes, and each volume contains 1 000 000 zeros of the number googolplex. The first volume also contains the initial digit one with which googolplex starts. www.GoogolplexWrittenOut.com

The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to … translate verbal discussions into analytical data.learn problem-solving methods for attacking collections of analytical questions or data.build a personal arsenal of internalized problem-solving techniques and solutions.become “armed problem solvers”, ready to do battle with a variety of puzzles in different areas of life.Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a “Challenge Problem” is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is available.

A Concrete Approach to Abstract Algebra presents a solid and highly accessible introduction to abstract algebra by providing details on the building blocks of abstract algebra.It begins with a concrete and thorough examination of familiar objects such as integers, rational numbers, real numbers, complex numbers, complex conjugation, and polynomials. The author then builds upon these familiar objects and uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices. The final four chapters present the more theoretical material needed for graduate study.This text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics which arise in courses in algebra, geometry, trigonometry, precalculus, and calculus. Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices