Softcover ISBN:  9781470461607 
Product Code:  CLN/29/30 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Softcover ISBN:  9781470461607 
Product Code:  CLN/29/30 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 

Book DetailsCourant Lecture NotesVolume: 29; 2020; 569 ppMSC: Primary 97; 15; 40; 20;
This is a twovolume set. Both volumes focus 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 oneyear course sequence, Linear Algebra I and II, offered at New York University's Courant Institute.
The first volume reexamines 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 wellcrafted 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
The first three chapters of the 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 less selfcontained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important.
The second volume provides a nice and varied selection of exercises; examples are wellcrafted and provide a clear understanding of the methods involved .Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
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Reviews

These two volumes comprise an excellent introduction to linear algebra at the beginning graduate level. The writing is clear and friendly, examples are numerous, and connections are made between standard linear algebra topics and many other areas of mathematics.
Benjamin Linowitz, Oberlin College


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This is a twovolume set. Both volumes focus 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 oneyear course sequence, Linear Algebra I and II, offered at New York University's Courant Institute.
The first volume reexamines 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 wellcrafted 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
The first three chapters of the 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 less selfcontained accounts of special topics that explore more advanced aspects of modern algebra: tensor fields, manifolds, and vector calculus in Chapter 4 and matrix Lie groups in Chapter 5. The reader can choose to pursue either chapter. Both deal with vast topics in contemporary mathematics. They include historical commentary on how modern views evolved, as well as examples from geometry and the physical sciences in which these topics are important.
The second volume provides a nice and varied selection of exercises; examples are wellcrafted and provide a clear understanding of the methods involved .
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

These two volumes comprise an excellent introduction to linear algebra at the beginning graduate level. The writing is clear and friendly, examples are numerous, and connections are made between standard linear algebra topics and many other areas of mathematics.
Benjamin Linowitz, Oberlin College