Linear Algebra Done Right

Now available in Open Access, this best-selling textbook for a second course in linear algebra is aimed at undergraduate math majors and graduate students. The fourth edition gives an expanded treatment of the singular value decomposition and its consequences. It includes a new chapter on multilinear algebra, treating bilinear forms, quadratic forms, tensor products, and an approach to determin…

Branes and DAHA Representations

In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which com…

Notes on algebraic potentials

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Flexibility Principles in Boolean Semantics: The Interpretation of Coordinati…

An investigation of the logical flexibility principles needed for a formal semantic account of coordination, plurality, and scope in natural language.Since the early work of Montague, Boolean semantics and its subfield of generalized quantifier theory have become the model-theoretic foundation for the study of meaning in natural languages. This book uses this framework to develop a new semantic…

Communication Complexity: A New Approach to Circuit Depth

Communication Complexity describes a new intuitive model for studying circuit networks that captures the essence of circuit depth. Although the complexity of boolean functions has been studied for almost 4 decades, the main problems the inability to show a separation of any two classes, or to obtain nontrivial lower bounds remain unsolved. The communication complexity approach provides clues as…

What is the Genus?

Exploring several of the evolutionary branches of the mathematical notion of genus, this book traces the idea from its prehistory in problems of integration, through algebraic curves and their associated Riemann surfaces, into algebraic surfaces, and finally into higher dimensions. Its importance in analysis, algebraic geometry, number theory and topology is emphasized through many theorems. Al…

Algebraic semantics of imperative programs

Algebraic Semantics of Imperative Programs presents a self-contained and novel "executable" introduction to formal reasoning about imperative programs. The authors' primary goal is to improve programming ability by improving intuition about what programs mean and how they run. The semantics of imperative programs is specified in a formal, implemented notation, the language OBJ; this makes the s…

WALCOM: Algorithms and Computation 9th International Workshop, WALCOM 2015, …

This book constitutes the thoroughly refereed conference proceedings of the 9th International Workshop on Algorithms and Computation, WALCOM 2015, held in Dhaka, Bangladesh, in February 2015. The 26 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 85 submissions. The papers are organized in topical sections on approximation algorithms, data s…

Visualization and Processing of Higher Order Descriptors for Multi-Valued Data

Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors …

Variational Analysis and Aerospace Engineering Mathematical Challenges for t…

This book presents papers surrounding the extensive discussions that took place from the ‘Variational Analysis and Aerospace Engineering’ workshop held at the Ettore Majorana Foundation and Centre for Scientific Culture in 2015. Contributions to this volume focus on advanced mathematical methods in aerospace engineering and industrial engineering such as computational fluid dynamics metho…