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Linear Algebra (Volumes I and II): The Set
 
Frederick P. Greenleaf Courant Institute, New York University, New York, NY
Sophie Marques Stellenbosch University, Stellenbosch, South Africa
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Linear Algebra
Softcover ISBN:  978-1-4704-6160-7
Product Code:  CLN/29/30
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
Linear Algebra
Click above image for expanded view
Linear Algebra (Volumes I and II): The Set
Frederick P. Greenleaf Courant Institute, New York University, New York, NY
Sophie Marques Stellenbosch University, Stellenbosch, South Africa
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Softcover ISBN:  978-1-4704-6160-7
Product Code:  CLN/29/30
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
  • Book Details
     
     
    Courant Lecture Notes
    Volume: 292020; 569 pp
    MSC: Primary 97; 15; 40; 20;

    This is a two-volume 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 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, 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

    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 self-contained 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 well-crafted and provide a clear understanding of the methods involved .

    Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

    This set contains the following item(s):
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 292020; 569 pp
MSC: Primary 97; 15; 40; 20;

This is a two-volume 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 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, 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

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 self-contained 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 well-crafted and provide a clear understanding of the methods involved .

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

This set contains the following item(s):
  • 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.