Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.]]>

Lectures, many never before published, that offer insights into the early thinking of the mathematician and polymath George Boole.

George Boole (1815-1864), remembered by history as the developer of an eponymous form of algebraic logic, can be considered a pioneer of the information age not only because of the application of Boolean logic to the design of switching circuits but also because of his contributions to the mass distribution of knowledge. In the classroom and the lecture hall, Boole interpreted recent discoveries and debates in a wide range of fields for a general audience. This collection of lectures, many never before published, offers insights into the early thinking of an innovative mathematician and intellectual polymath.

Bertrand Russell claimed that "pure mathematics was discovered by Boole," but before Boole joined a university faculty as professor of mathematics in 1849, advocacy for science and education occupied much of his time. He was deeply committed to the Victorian ideals of social improvement and cooperation, arguing that "the continued exercise of reason" joined all disciplines in a common endeavor. In these talks, Boole discusses the genius of Isaac Newton; ancient mythologies and forms of worship; the possibility of other inhabited planets in the universe; the virtues of free and open access to knowledge; the benefits of leisure; the quality of education; the origin of scientific knowledge; and the fellowship of intellectual culture. The lectures are accompanied by a substantive introduction by Brendan Dooley, the editor of the volume, that supplies biographical and historical context.

]]>How do dating sites match compatible partners? What do cell phones and sea coasts have in common? And why do computer scientists keep ant colonies? Jeff Suzuki answers these questions and more in Patently Mathematical , which explores the mathematics behind some of the key inventions that have changed our world.

In recent years, patents based on mathematics have been issued by the thousands--from search engines and image recognition technology to educational software and LEGO designs. Suzuki delves into the details of cutting-edge devices, programs, and products to show how even the simplest mathematical principles can be turned into patentable ideas worth billions of dollars. Readers will discover

* whether secure credit cards are really secure

* how improved data compression made streaming video services like Netflix a hit

* the mathematics behind self-correcting golf balls

* why Google is such an effective and popular search engine

* how eHarmony and Match.com find the perfect partner for those seeking a mate

* and much more!

A gifted writer who combines quirky historical anecdotes with relatable, everyday examples, Suzuki makes math interesting for everyone who likes to ponder the world of numerical relationships.

Praise for Jeff Suzuki's Constitutional Calculus

"Presents an entertaining and insightful approach to the mathematics that underlies the American system of government. The book is neatly organized, breaking down the United States Constitution by article, section, and amendment. Within each piece, Suzuki reviews the mathematical principles that went into the underlying framework."-- Mathematical Reviews

"A breath of fresh air.... A reaffirmation that mathematics should be used more often to make general public policy."-- MAA Reviews

]]>Advances in training models with log-linear structures, with topics including variable selection, the geometry of neural nets, and applications.

Log-linear models play a key role in modern big data and machine learning applications. From simple binary classification models through partition functions, conditional random fields, and neural nets, log-linear structure is closely related to performance in certain applications and influences fitting techniques used to train models. This volume covers recent advances in training models with log-linear structures, covering the underlying geometry, optimization techniques, and multiple applications. The first chapter shows readers the inner workings of machine learning, providing insights into the geometry of log-linear and neural net models. The other chapters range from introductory material to optimization techniques to involved use cases. The book, which grew out of a NIPS workshop, is suitable for graduate students doing research in machine learning, in particular deep learning, variable selection, and applications to speech recognition. The contributors come from academia and industry, allowing readers to view the field from both perspectives.

Contributors

Aleksandr Aravkin, Avishy Carmi, Guillermo A. Cecchi, Anna Choromanska, Li Deng, Xinwei Deng, Jean Honorio, Tony Jebara, Huijing Jiang, Dimitri Kanevsky, Brian Kingsbury, Fabrice Lambert, Aur lie C. Lozano, Daniel Moskovich, Yuriy S. Polyakov, Bhuvana Ramabhadran, Irina Rish, Dimitris Samaras, Tara N. Sainath, Hagen Soltau, Serge F. Timashev, Ewout van den Berg

Covering the general process of data analysis to finding, collecting, organizing, and presenting data, this book offers a complete introduction to the fundamentals of data analysis.

Using real-world case studies as illustrations, it helps readers understand theories behind and develop techniques for conducting quantitative, qualitative, and mixed methods data analysis. With an easy-to-follow organization and clear, jargon-free language, it helps readers not only become proficient data analysts, but also develop the critical thinking skills necessary to assess analyses presented by others in both academic research and the popular media.

It includes advice on:

- Data analysis frameworks

- Validity and credibility of data

- Sampling techniques

- Data management

- The big data phenomenon

- Data visualisation

- Effective data communication

Whether you are new to data analysis or looking for a quick-reference guide to key principles of the process, this book will help you uncover nuances, complexities, patterns, and relationships among all types of data.

]]>Showing how everyday experiences can be used to encourage early mathematical thinking, this book will help you to confidently support young children's mathematical development through play.

Developing Confident Mathematicians in the Early Years clearly explains the stages of mathematical development from birth to five years. It considers how practitioners and parents can create a mathematically rich environment and then offers a wealth of practical activities and suggestions for adult-child interactions to enhance children's mathematical learning. Features include:

60 activities each covering a core area of mathematical experience - measurement, algebra, data handling, counting and calculation. clear explanations of the mathematics taking place in each activity and how this forms the foundation for mathematical learning in the future. practical suggestions for home learning and working in partnership with parents. links to the EYFS and National Curriculum.Offering a rich source of ideas using everyday resources, this practical text will inspire practitioners and parents to nurture young children's innate confidence and ability in mathematics.

]]>Robust Nonlinear Regression: with Applications using R develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language, under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by both practitioners and researchers.

The main areas that will be covered in the book include theories and application of Nonlinear Robust Regression. In both parts the classic and robust aspects of nonlinear regression will be discussed. Outlier effects is among the main focus in the book.

]]>With some basic geometry under your belt, you'll discover that there is an optimal point on a soccer field from which to shoot a goal. And you'll be more clever with the gears of a bike. If you like to play cards or go to the casino, knowing something about probability will give you an edge. You'll also have an enhanced understanding of the "whispering effect" inside the Capitol rotunda, why a car's headlights are so bright, and even why sewer covers are round.

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The fourth edition of Numerical Methods Using MATLAB ® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors' approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature.

The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics.

]]>The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the third-grade level through visualization, play, and investigation.

During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message--that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:

There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics.With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

]]>Canonical systems occupy a central position in the spectral theory of second order differential operators. They may be used to realize arbitrary spectral data, and the classical operators such as Schrödinger, Jacobi, Dirac, and Sturm-Liouville equations can be written in this form. 'Spectral Theory of Canonical Systems' offers a selfcontained and detailed introduction to this theory. Techniques to construct self-adjoint realizations in suitable Hilbert spaces, a modern treatment of de Branges spaces, and direct and inverse spectral problems are discussed.

Contents

Basic definitions

Symmetric and self-adjoint relations

Spectral representation

Transfer matrices and de Branges spaces

Inverse spectral theory

Some applications

The absolutely continuous spectrum

The book presents basic facts from this field.

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Introducing the first-ever Robert Munsch counting book, beautifully styled in an oversized board book format perfect for gifting. Just as Classic Munsch ABC helps toddlers master the alphabet, Classic Munsch 123 uses favorite characters and illustrations from the wonderful world of Robert Munsch and Michael Martchenko to provide a delightful introduction to numeracy.

Numbers one through twelve are represented as numerals and are spelled out for early reading recognition. At the end, in one of two brand-new illustrations by Michael Martchenko just for this book, a joyful parade introduces the concept of numbers in sequence while providing an opportunity to repeat and reinforce the early numeracy concepts from previous pages. Like its companion ABC, Classic Munsch 123 is a must-have addition to every child's first library.

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