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Linear Algebra II
This book is the second of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first three chapters of this second volume round out the coverage of traditional linear algebra topics: generalized eigenspaces, further applications of Jordan form, as well as bilinear, quadratic, and multilinear forms. The final two chapters are different, being more or le...
Linear Algebra I
This book is the first of two volumes on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. This first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, diagonalization, and inner product spaces, giving an overview of linear algebra with sufficient mathematical precision for advanced use of the subject. This book provides a nice and varied selection of exercises; examples are well-crafted and provide a clear understanding of the methods involved. New notions are well motivated and interdisciplinary connections are often provided, to give a more intuitive and complete vision of linear algebra. Computational aspects are fully covered, but the study of linear operators remains the focus of study in this book.
Harmonic Analysis
Harmonic Analysis is an important tool that plays a vital role in many areas of mathematics as well as applications. It studies functions by decomposing them into components that are special functions. A prime example is decomposing a periodic function into a linear combination of sines and cosines. The subject is vast, and this book covers only the selection of topics that was dealt with in the course given at the Courant Institute in 2000 and 2019. These include standard topics like Fourier series and Fourier transforms of functions, as well as issues of convergence of Abel, Feier, and Poisson sums. At a slightly more advanced level the book studies convolutions with singular integrals, fr...
The Effect of Diet and Nutrition on Postprandial Metabolism
The postprandial period is the metabolic phase that directly follows the ingestion of a meal. This period is critical to the handling of nutrients to feed the body throughout the whole day but it is also a time of challenge for the body’s metabolism, which has to be flexible and adaptable regarding the quantity and the quality of the nutrient intake. Changes in postprandial metabolism have been considered to be potential early markers in the pathophysiological course, finally leading to an increased risk of disease development. This book aimed to broaden and add to the research on the importance of postprandial metabolism in nutrition. The book includes literature reviews that cover the br...
Linear Algebra (Volumes I and II)
This is a two-volume set. Both volumes focus on on linear algebra for graduate students in mathematics, the sciences, and economics, who have: a prior undergraduate course in the subject; a basic understanding of matrix algebra; and some proficiency with mathematical proofs. Proofs are emphasized and the overall objective is to understand the structure of linear operators as the key to solving problems in which they arise. Both volumes have been used for several years in a one-year course sequence, Linear Algebra I and II, offered at New York University's Courant Institute. The first volume re-examines basic notions of linear algebra: vector spaces, linear operators, duality, determinants, d...
Linear Algebra
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The Dictionary of British Women Artists
The most comprehensive volume of its kind, Gray's Dictionary of British Women Artists offers extensively-researched biographies of some of the most significant female contributors to British art.This volume will make a valuable contribution to the study of art history. It will also provide readers with significant insight into a long-neglected aspect of history - the lives and achievements of women artists. Each entry provides key biographical information, as well as (where possible) commentaryon the artist's studies, lifestyle, travels and family. Entries also detail significant works, exhibitions and membership of societies. Gray's introduction provides a useful context to the biographies.
